key

From Middle English keye, kaye, keiȝe, from Old English cǣġ (“key, solution, experiment”) (whence also Scots key and kay (“key”)), of uncertain origin. The only sure cognates are Saterland Frisian Koai (“key”), West Frisian kaai (“key”), and North Frisian kay (“key”). Possibly from Proto-Germanic *kēgaz, *kēguz (“stake, post, pole”), from Proto-Indo-European *ǵogʰ-, *ǵegʰ-, *ǵegʰn- (“branch, stake, bush”), which would make it cognate with Middle Low German kāk (“whipping post, pillory”), and perhaps to Middle Dutch keige (“javelin, spear”) and Middle Low German keie, keige (“spear”). For the semantic development, note that medieval keys were simply long poles (ending in a hook) with which a crossbar obstructing a door from the inside could be removed from the outside, by lifting it through a hole in the door. Liberman has noted, however, "The original meaning of *kaig-jo- was presumably '*pin with a twisted end.' Words with the root *kai- followed by a consonant meaning 'crooked, bent; twisted' are common only in the North Germanic languages."

шпи́лка

object used to maintain the orientation between two others

Key in the Encyclopædia Britannica (11th edition, 1911)

(cryptography) A piece of information (e.g., a password or passphrase) used to encode or decode a message or messages.

sleutel

cryptography: piece of information used to encode or decode


field

→ Japanese: フィールド (fīrudo)

From Middle English feeld, feld, from Old English feld, from Proto-West Germanic *felþu, from Proto-Germanic *felþuz (“field”), ultimately from Proto-Indo-European *pleh₂- (“field, plain”) or *pleth₂- (“flat”) (with schwebeablaut).
Cognate with Scots feld, feild (“field”), North Frisian fjild (“field”), West Frisian fjild (“field”), Dutch veld (“field”), German Feld (“field”), Swedish fält (“field”). Related also to Old English folde (“earth, land, territory”), Old English folm (“palm of the hand”). More at fold.

veld

land area free of woodland, cities, and towns; open country

fushë

sports: area reserved for playing a game

Euclidean domain ⊂ principal ideal domain ⊂ unique factorization domain

Noetherian domain ⊂ integral domain ⊂ commutative ring

The set of rational numbers, #92;mathbb#123;Q#125;, is the prototypical field.

Whereas a ring has three binary operators: (1) an additive operator, (2) a subtractive operator, and (3) a multiplicative operator, a field has four binary operators: the three ring binary operators and (4) a divisive operator. (N.B.: Only the additive and multiplicative operators are axiomatic. The subtractive operator may be derived by combining the additive and the unary negative operators; the divisive operator may be derived by combining the multiplicative and the unary inversive operators.)

Any of various figurative meanings, often dead metaphors.

Any of certain structures serving cognition.

(algebra) A non-zero commutative ring in which all non-zero elements are invertible; a simple commutative ring.

veld

mathematics (algebra): a commutative ring satisfying the field axioms


crown

→ Japanese: クラウン (kuraun)

→ Korean: 크라운 (keuraun)

→ Maori: karauna

From Middle English coroune, from Anglo-Norman corone, from Latin corōna (“crown, wreath”), from Ancient Greek κορώνη (korṓnē). Doublet of corona, korona, koruna, krona, króna, and krone. Displaced native Old English corenbēag (“crown”); and Middle English kinehelm, kynehelm, from Old English cynehelm (“crown”).
* (paper size): So called because originally watermarked with a crown.

doublet

(geometry) The area enclosed between two concentric perimeters.

rengas

geometry: area enclosed between two concentric perimeters


cute

en-adj

cute (comparative cuter, superlative cutest)

cuter (comparative)
cutest (superlative)

→ Arabic: كْيُوت (kyūt), كِيُوت (kiyūt)

→ Armenian: քյութ (kʻyutʻ)

→ Dutch: kjoet

→ Japanese: キュート (kyūto)

Aphetic form of acute, originally “keenly perceptive or discerning, shrewd” (1731). Meaning transferred to “pretty, fetching” by US students (slang) c. 1834. Meaning drifted further to describe the pleasing attraction to features usually possessed by the young.

having features mainly attributed to infants and small

There's a cute alternative proof of this using lambda calculus.

Cute solution to pin one Knight by unpinning the other and so force discovered guard for the Bishop: it took me hours to find that Bishop key.

We state a cute result that can be derived from our calcuations^([sic]). It is not applied anywhere later, but shows that graphs with heavy tails and large clustering coefficients have large cores.

2012, “Vertex neighborhoods, low conductance cuts, and good seeds for local community methods”, in Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining:

(especially mathematics) Evincing cleverness; surprising in its elegance or unconventionality (but of limited importance).


malleable

malleable (comparative more malleable, superlative most malleable)

more malleable (comparative)
most malleable (superlative)

From Middle French malléable, borrowed from Late Latin malleābilis, derived from Latin malleāre (“to hammer”), from malleus (“hammer”), from Proto-Indo-European *mal-ni- (“crushing”), an extended variant of *melh₂- (“crush, grind”).

(cryptography, of an algorithm) in which an adversary can alter a ciphertext such that it decrypts to a related plaintext


orbit

en-noun

orbit (countable and uncountable, plural orbits)

Inherited from Middle English orbite, orbita, from Latin orbita (“course, track, impression, mark”).

គន្លង

kɔɔkŭənlɔɔng

The curved path of one object around a point or another body.

(astronomy) An elliptical movement of an object about a celestial object or Lagrange point, especially a periodic elliptical revolution.

The Moon's orbit around the Earth takes nearly one month to complete.

One complete circuit round an orbited body.

(uncountable) The state of moving in an orbit.

(mathematics) A collection of points related by the evolution function of a dynamical system.

(geometry, group theory) The subset of elements of a set X to which a given element can be moved by members of a specified group of transformations that act on X.


right angle

(geometry) Half of the angle formed by a single straight line, equivalent to 90 degrees.


state

Etymology tree
Proto-Indo-European *steh₂-
Latin statuslbor.
Old French estatbor.
Middle English stat
English state
From Middle English stat (as a noun); adopted c. 1200 from both Old French estat and Latin status (“manner of standing, attitude, position, carriage, manner, dress, apparel; and other senses”), from stare (“to stand”). Doublet of estate and status. The sense of "polity" develops in the 14th century. Compare French être, Greek στέω (stéo), Italian stare, Portuguese estar, Romanian sta, and Spanish estar.

der

something is rotten in the state of Denmark

there is something rotten in the state of Denmark

(mathematics, stochastic processes) An element of the range of the random variables that define a random process.

Zustand

math: an element of the range of random variables


handle

desctree

→ Japanese: ハンドル (handoru)
→ Hokkien: 捍多路 (hăn-tó͘-luh)
→ Sakizaya: handulu

From Middle English handel, handle, from Old English handle (“a handle”), from handlian (“to handle, feel, deal with, discuss”). See verb below. Cognate with Danish handel (“a handle”).

Such a 2-handle cancels the 1-handle so the manifold is D⁴.

2003, Gordana Matić, Clint McCrory, Topology and geometry of manifolds, →ISBN, page 182:

(topology) A topological space homeomorphic to a ball but viewed as a product of two lower-dimensional balls.

(algebraic geometry) The smooth, irreducible subcurve of a comb which connects to each of the other components in exactly one point.


j

(mathematics) An alternative version of i, the positive square root of -1; used in the context of electronics.

(mathematics) The second unit vector, after i


t

head

t (lower case, upper case T, plural ts or t's)

The twentieth letter of the English alphabet, called tee and written in the Latin script.


t

The ordinal number twentieth, derived from this letter of the English alphabet, called tee and written in the Latin script.


t

Abbreviations.
t
# (stenoscript) Abbreviation of at
# (stenoscript) Abbreviation of to and homophone too.

ng

and homophone <i class="Latn mention" lang="en">too</i>.

(UK) Alternative letter-case form of T, tonne.


wedge

en-noun

wedge (countable and uncountable, plural wedges)

From Middle English wegge (“wedge”), from Old English weċġ (“wedge”), from Proto-West Germanic *wagi, from Proto-Germanic *wagjaz.

(geometry) A five-sided polyhedron with a rectangular base, two rectangular or trapezoidal sides meeting in an edge, and two triangular ends.

Any symbol shaped like a V in some given orientation.

(mathematics) The symbol ∧, denoting a meet (infimum) operation or logical conjunction.


wedge

en-verb

wedge (third-person singular simple present wedges, present participle wedging, simple past and past participle wedged)

wedges (present singular third-person)
wedging (participle present)
wedged (participle past)
wedged (past)

My Linux kernel wedged after I installed the latest update.

(computing, informal, intransitive) Of a computer program or system: to get stuck in an unresponsive state.


shock

en-noun

shock (countable and uncountable, plural shocks)

→ Bulgarian: шок (šok)

→ Chinese: 休克 (xiūkè)

→ Czech: šok

→ Italian: shock

→ Japanese: ショック (shokku)

→ Korean: 쇼크 (syokeu)

→ Macedonian: шок (šok)

→ Polish: szok

→ Russian: шок (šok)

→ Serbo-Croatian:

Cyrillic: шо̏к

Latin: šȍk

→ Slovak: šok

→ Spanish: shock

From Middle Dutch schokken (“to push, jolt, shake, jerk”) or Middle French choquer (“to collide with, clash”), from Old Dutch *skokkan (“to shake up and down, shog”), from Proto-Germanic *skukkaną (“to move, shake, tremble”). Of uncertain origin. Perhaps related to Proto-Germanic *skakaną (“to shake, stir”), from Proto-Indo-European *(s)kek-, *(s)keg- (“to shake, stir”); see shake.
Cognate with Middle Low German schocken (“collide with, deliver a blow to, move back and forth”), Old High German scoc (“a jolt, swing”), Middle High German schocken (“to swing”) (German schaukeln), Old Norse skykkr (“vibration, surging motion”), Icelandic skykkjun (“tremulously”), Middle English schiggen (“to shake”). Doublet of shog.

cog

shark (non-rhotic, father-bother merger)

partial differential equation
partial differential equation

(mathematics) A discontinuity arising in the solution of a partial differential equation.


cylinder

→ Japanese: シリンダー (shirindā)

→ Korean: 실린더 (sillindeo)

From Middle French chilindre, cylindre, from Latin cylindrus, from Ancient Greek κύλινδρος (kúlindros), from κυλίνδω (kulíndō) "I roll or wallow" (intransitive). Doublet of calander and calender.

When the two-dimensional curve is a circle, the cylinder is called a circular cylinder. When the axis is perpendicular to the plane of the curve, the cylinder is called a right cylinder. In non-mathematical usage, both right and circular are usually implied.

(geometry) A surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

(geometry) A solid figure bounded by a cylinder and two parallel planes intersecting the cylinder.


rate

en-noun

rate (countable and uncountable, plural rates)

From Middle English rate, from Old French rate, from Medieval Latin rata, from Latin prō ratā parte (“according to a fixed part”), from ratus (“fixed”), from rērī (“think, deem, judge, estimate", originally "reckon, calculate”).

der

We pay an hourly rate of between $10 – $15 per hour depending on qualifications and experience.

A wage calculated in relation to a unit of time.

норма

a set price or fee determined in relation to a particular scale or standard

разценка

a wage calculated in relation to a unit of time

daily rate; hourly rate; etc.

(horology) The gain or loss of a timepiece in a unit of time.


rate

en-verb

rate (third-person singular simple present rates, present participle rating, simple past and past participle rated)

rates (present singular third-person)
rating (participle present)
rated (participle past)
rated (past)

To ascertain the exact rate of the gain or loss of (a chronometer) as compared with true time.


continuous

From Latin continuus, from contineō (“hold together”). Displaced native Old English singal.

continuous erythropoietin receptor activator

mathematical analysis
mathematical analysis

(mathematical analysis, of a function) Such that, for every x in the domain, for each small open interval D about f(x), there's an interval containing x whose image is in D.

Each continuous function from the real line to the rationals is constant, since the rationals are totally disconnected.

(mathematics, more generally, of a function between two topological spaces) Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).


gram

From French gramme, from Ancient Greek γράμμα (grámma, “a small weight, a scruple”). Doublet of gramma.

der

A unit of mass equal to one-thousandth of a kilogram. Symbol: g.


x-axis

independent variable
independent variable

(analytic geometry) The axis on a graph that is usually drawn left to right and usually shows the range of values of an independent variable.


array

en-noun

array (countable and uncountable, plural arrays)

From Middle English arrayen, from Anglo-Norman arraier (compare Old French arraier, areer (“to put in order”)), from Medieval Latin arrēdō (“to put in order, arrange, array”), from *rēdum (“preparation, order”), from Frankish *raid or *raidā (“preparation, order”) or Gothic 𐌲𐌰𐍂𐌰𐌹𐌸𐍃 (garaiþs, “ready, prepared”), from Proto-Germanic *raidaz, *raidiz (“ready”). Compare Old English rād (“condition, stipulation”), Old High German antreitī (“order, rank”). Doublet of ready.


rational number

en-noun

rational number (plural rational numbers)

From rational + number, ultimately from Latin rationalis + numerus. Compare analogous logarithm, from Ancient Greek.

(mathematics) A number that can be expressed as the ratio of two integers.


integer

[ˈɪn.tʰɪ.d͡ʒɚ]

[ˈɪn.ɾ̃ɪ.d͡ʒɚ]

Borrowed from Latin integer (“whole”), from Proto-Italic *əntagros (“untouched”). Doublet of entier and entire. Related to English tact, thack, and thwack.

God made the integers; all else is the work of man

1886, Leopold Kronecker, speech to the Berliner Naturforscher-Versammlung:

(arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.

when understood to include negative numbers and zero


domain

range

antonym(s) of “domain of definition of a function”

From Middle English demayne, demain (“rule”), from Old French demeine, demaine, demeigne, domaine (“power”), (French domaine), from Latin dominium (“property, right of ownership”), from dominus (“master, proprietor, owner”). See dame, and compare demain, danger, dungeon. Doublet of demesne, domino.

definisieversameling

(mathematics) the set on which a function is defined

(mathematics, set theory) The set of input (argument) values for which a function is defined.

(more generally, of a binary relation R between A and B) The set A; The subset of A consisting of elements a of A such that there exists an element b in B with (a,b) in R.

(mathematics) A ring with no zero divisors; that is, in which no product of nonzero elements is zero.

alue

(mathematics) ring with no zero divisors

(mathematics, topology, mathematical analysis) An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.


humongous

en-adj

humongous (comparative more humongous, superlative most humongous)

more humongous (comparative)
most humongous (superlative)

/ˌhjuːˈmʌŋɡəs/

/ˌhjuːˈmɒŋɡəs/

[çu̟ːˈmʊŋɡəs]

[ˌçu̟ːˈmɐŋɡəs]

Of expressive origin, likely inspired by “huge”, with the termination of “monstrous”.

Other students make wide detours to avoid the humiliation and fear of being chased and attacked by the humongous numbers of bees in front of Atkinson.

Solomon had pulled this humongous fish that was bigger than anything weʼd ever seen.

2015, Chigozie Obioma, The Fishermen, ONE, page 19:

“Thumbs!” ordered Mr Big. “Do your worst with the boy!” Frank looked on in terror as the man bent back his humongous Thumbs, ready to cause damage. The henchman pressed them hard into the boy’s ears. Frank felt like his brain was going to burst. “ARGH!” he screamed.

2017, David Walliams [pseudonym; David Edward Williams], Bad Dad, London: HarperCollins Children’s Books, →ISBN:


abundant number

en-noun

abundant number (plural abundant numbers)

The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30, and 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42, which is greater than 30, so 30 is an abundant number.

It has been shown that the largest odd number which cannot be written as the sum of two abundant numbers is 20161.

1970, Geometric Transformations III, Random House, page 128:

1992, Stanley Rabinowitz (editor), Index to Mathematical Problems, 1980-1984, MathPro Press, page 185,
(a) Let k be fixed. Do there exist sequences of k consecutive abundant numbers?

We shall not be concerned with abundant numbers in this book, nevertheless it may be helpful to use this historical example as an illustration. We note the property that any multiple of an abundant number is abundant.

1996, Richard R. Hall, Sets of Multiples, Cambridge University Press, page xi:

(number theory) A number that is less than the sum of its proper divisors (all divisors except the number itself).


hyperbola

hyperbola (plural hyperbolas or hyperbolae or hyperbolæ)

hyperbolas (plural)
hyperbolae (plural)
hyperbolæ (plural)

From New Latin hyperbola, from Ancient Greek ὑπερβολή (huperbolḗ). Doublet of hyperbole.

(geometry) A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone. The function y(x) = 1/x draws a hyperbola.


content

content (countable and uncountable, plural contents)

desctree

→ Russian: контент (kontent)
→ Armenian: կոնտենտ (kontent)

From Middle English content (plural contentes, contence), from Latin contentus, past participle of continēre (“to hold in, contain”), as Etymology 1, above. English apparently developed a substantive form of the adjective, which is not mirrored in Romance languages.

(mathematics) The n-dimensional space contained by an n-dimensional polytope (called volume in the case of a polyhedron and area in the case of a polygon); length, area or volume, generalized to an arbitrary number of dimensions.

inhoud

mathematics: space contained by a polytope

greatest common divisor
greatest common divisor

(algebra, ring theory, of a polynomial with coefficients in a GCD domain) The greatest common divisor of the coefficients; (of a polynomial with coefficients in an integral domain) the common factor of the coefficients which, when removed, leaves the adjusted coefficients with no common factor that is noninvertible.


similarity

en-noun

similarity (countable and uncountable, plural similarities)

From French similarité.
Morphologically similar + -ity

(geometry) A transformation (of a Euclidean space) that preserves angles and the ratios of distances

(mathematics, linear algebra) The property of two matrices being similar.


henry

Named after the American scientist Joseph Henry.

International System of Units
International System of Units

electrical inductance
electrical inductance

In the International System of Units, the derived unit of electrical inductance; the inductance induced in a circuit by a rate of change of current of one ampere per second and a resulting electromotive force of one volt. Symbol: H


singularity

singularity (countable and uncountable, plural singularities)

/ˌsɪŋɡjəˈlæɹətɪ/

From Middle English singularite, from Old French singularité, from Late Latin singulāritās (“singleness”), from Latin singulāris (“single”).
Morphologically singular + -ity

(mathematics) The value or range of values of a function for which a derivative does not exist.

奇異點 /奇异点

mathematics: value for which a derivative does not exist


tangle

From Middle English tanglen, probably of North Germanic origin, compare Swedish taggla (“to disorder”), Old Norse þǫngull, þang (“tangle; seaweed”), see Etymology 2 below.

(mathematics) A region of the projection of a knot such that the knot crosses its perimeter exactly four times.


conge

From French conge, from Latin congius. Only attested in English in the obsolete plural form congys.

(historical, obsolete) Alternative form of congy, congius, ancient Roman units of liquid measure and mass.


lifting

lifting (countable and uncountable, plural liftings)

(mathematics) A certain operation on a measure space; see lifting theory.


password

From pass + word; the sentry-passing sense predates the cryptographic sense and was its inspiration.

A strong password has a mixture of lowercase and uppercase letters, numbers, and punctuation marks.

(computing, cryptography) A string of characters used to log in to a computer or network, to access a level in a video game, and so on; archetypally a word but nowadays often an alphanumeric string or a phrase.

wagwoord

computing: string of characters known only to a user

passkey

coordinate in its sense contrasted with passwords

keyphrase

used either coordinately or hyponymously; equivalent except for containing spaces


suspension

suspension (countable and uncountable, plural suspensions)

Borrowed from Late Latin suspensiōnem (“arching, vaulting; suspension”), from suspendēre (“to hang up, to suspend”), from sub- (“under”) + pendere (“to hang, to suspend”), from Proto-Italic *pendō (“to hang, to put in a hanging position”), from Proto-Indo-European *(s)pénd-e-ti, from *(s)pend- (“to pull; to spin”)). Compare Anglo-Norman suspensiun, French suspension, Occitan suspensio.

der

To get an intuitive feeling for the characteristics of H'-spaces, it is instructive to consider an important class of such spaces, the suspensions. The suspension of an arbitrary topological space Y is defined to be the quotient space of Y#92;timesI where Y#92;times 0 is identified to one point and Y#92;times 1 is identified to another point. For example, the suspension of a circle is a cylinder with the two ends collapsed into one point each; in other words, a space homeomorphic to a sphere.

2012, H. Rasmussen, “Strategy-proofness of Continuous Aggregation Maps”, in Geoffrey M. Heal, editor, Topological Social Choice: With 45 Figures (Social Choice and Welfare; vol. 14, no. 2, 1997), Berlin: Springer-Verlag, →DOI, →ISBN, page 110:

(topology) A topological space derived from another by taking the product of the original space with an interval and collapsing each end of the product to a point.

suspensie

topology: A topological space derived from another by taking the product of the original space with an interval and collapsing each end of the product to a point

A model category is called pointed if the initial object and terminal object are the same. The homotopy category of any pointed model category acquires a suspension functor denoted by #92;Sigma. It turns out that #92;text#123;Ho#125;(M) is a pre-triangulated category in a natural way[…]. When the suspension is an equivalence, M is called a stable model category, and in this case #92;text#123;Ho#125;(M) becomes a triangulated category[…].

2010, Paul Arne Østvær, “Preliminaries”, in Homotopy Theory of C*-Algebras (Frontiers in Mathematics), Basel: Birkhäuser, Springer Basel, →DOI, →ISBN, page 17:

(topology) A function derived, in a standard way, from another, such that the instant function’s domain and codomain are suspensions of the original function’s.

suspensie

topology: A function derived, in a standard way, from another, such that the instant function’s domain and codomain are suspensions of the original function’s


floor

non-rhotic, without the horse–hoarse merger

non-rhotic, dough–door merger, African-American Vernacular

From Middle English flor, flore, from Old English flōr (“floor, pavement, ground, bottom”), from Proto-West Germanic *flōr, from Proto-Germanic *flōraz (“flat surface, floor, plain”), from Proto-Indo-European *pleh₂ros (“floor”), from Proto-Indo-European *pleh₂- (“flat”).
Cognate with Scots flair, Scots flure, fluir (“floor”), Saterland Frisian Floor (“floor”), West Frisian flier (“floor”), Dutch vloer (“floor”), German Low German Floor (“entry hall”), German Flur (“field, floor, entrance hall”), Swedish flor (“floor of a cow stall”), Irish urlár (“floor”), Scottish Gaelic làr (“floor, ground, earth”), Welsh llawr (“floor, ground”), Latin plānus (“level, flat”).

cog

The floor of 4.5 is 4.

(mathematics) The largest integer less than or equal to a given number.

dolní celá část

mathematics: the largest integer less than or equal to a given number


floor

en-verb

floor (third-person singular simple present floors, present participle flooring, simple past and past participle floored)

floors (present singular third-person)
flooring (participle present)
floored (participle past)
floored (past)

floored division


reason

en-noun

reason (countable and uncountable, plural reasons)

From Middle English resoun, reson, from Anglo-Norman raisun (Old French raison), from Latin ratiō, from ratus, past participle of reor (“reckon”), ultimately from Proto-Indo-European *h₂reh₁- (“to think”), reanalysed root of *h₂er- (“to put together”). Displaced native Middle English reden (found in compounds), from Old English rǣden (“condition, stipulation, calculation, direction”), from the same Proto-Indo-European source (compare West Frisian reden (“reason”), Dutch reden (“reason”)). Doublet of ration and ratio.

cog

[I]f two Quantities repreſented by the Numbers 20 and 4 be compared, by dividing the Antecedent 20 by the Conſequent 4, the Quotient is 5; but inverting the Terms, by dividing 4 by 20 the Quotient is #92;tfrac#123;4#125;#123;20#125;#61;#92;tfrac#123;1#125;#123;5#125;. By which Quotients are declared the Geometrical Reaſons of the propoſed Quantities, becauſe if the Quotient found be multiplied by the Conſequent, the Product is equal to the Antecedent; for in the former Compariſon 5#92;times4#61;20, in the latter #92;tfrac#123;1#125;#123;5#125;#92;times20#61;4; as Things again are referred to Equality.

1734, Isaac Barrow, “Lecture XVII. Of the Names and Diversities of the Twofold Kind of Reason or Proportion, viz. Arithmetical and Geometrical”, in John Kirkby, transl., The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University of Cambridge. […], London: […] Stephen Austen, […], →OCLC, pages 323–324:

(mathematics, obsolete) Ratio; proportion.


cryptography

en-noun

cryptography (usually uncountable, plural cryptographies)

[kɹ̥ɪpˈtʰɒɡɹəfiː]

We might abate...the strange cryptography of Gaffarell in his Starrie Booke of Heaven.

1658, Sir Thomas Browne (first use in English)

The discipline concerned with communication security (eg, confidentiality of messages, integrity of messages, sender authentication, non-repudiation of messages, and many other related issues), regardless of the used medium such as pencil and paper or computers.


aberrancy

aberrancy (countable and uncountable, plural aberrancies)

LL-Q1860 (eng)-Flame, not lame-aberrancy.wav

(geometry) The deviation of a curve from circular form.


pipe

→ Bengali: পাইপ (paip)

desc

→ Gulf Arabic: پيپ (pēp, bēb, “smoking pipe”), پايپ (pāyp, bāyb, “medium of transportation (sense 2.1)”)

→ Hindi: पाइप (pāip)

→ Japanese: パイプ (paipu)

→ Korean: 파이프 (paipeu)

→ Malay: paip

→ Maori: paipa

→ Russian: пайп (pajp)

→ Urak Lawoi': ปาเฮะ (pahëq)

From Middle English pīpe, pype (“hollow cylinder or tube used as a conduit or container; duct or vessel of the body; musical instrument; financial records maintained by the English Exchequer, pipe roll”), from Old English pīpe (“pipe (musical instrument); the channel of a small stream”), from Proto-West Germanic *pīpā. Reinforced by Vulgar Latin *pīpa, from Latin pipire, pipiare, pipare, from pīpiō (“to chirp, peep”), of imitative origin. Doublet of fife.
The “storage container” and “liquid measure” senses are derived from Middle English pīpe (“large storage receptacle, particularly for wine; cask, vat; measure of volume”), from pīpe (above) and Old French pipe (“liquid measure”). In specific contexts, calques similar units of measure such as Portuguese pipa.
The verb is from Middle English pīpen, pypyn (“to play a pipe; to make a shrill sound; to speak with a high-pitched tone”), from Old English pīpian (“to pipe”).

onomatopoeic

imitative

inh

Again, by 28 Hen. VIII, cap. 14, it is re-enacted that the tun of wine should contain 252 gallons, a butt of Malmsey 126 gallons, a pipe 126 gallons, a tercian or puncheon 84 gallons, a hogshead 63 gallons, a tierce 41 gallons, a barrel 31½ gallons, a rundlet 18½ gallons.

1882, James E[dwin] Thorold Rogers, “Weights and Measures”, in A History of Agriculture and Prices in England from the Year after the Oxford Parliament (1259) to the Commencement of the Continental War (1793) […], volumes IV (1401–1582), Oxford: At the Clarendon Press, →OCLC, page 205:

The contents of such a vessel, as a liquid measure, sometimes set at 126 wine gallons; half a tun.

thùng

contents of such a vessel as a liquid measure


generation

en-noun

generation (countable and uncountable, plural generations)

/ˌd͡ʒɛnəˈɹeɪʃən/

Inherited from Middle English generacioun, from Anglo-Norman generacioun, Middle French generacion, and their source, Latin generātiō, from generāre (“to beget, generate”). By surface analysis, generate + -ion.

inh+

the generation of a line or curve

(geometry) The formation or production of any geometrical magnitude, as a line, a surface, a solid, by the motion, in accordance with a mathematical law, of a point or a magnitude, by the motion of a point, of a surface by a line, a sphere by a semicircle, etc.

It runs for 17331 generations before stabilizing as 136 blinkers, 109 blocks, 65 beehives, 18 loaves, 18 boats, 7 ships, 4 tubs, 3 ponds, 2 toads, and 40 gliders.

1989 November 20, Dean Hickerson, “Life: glider gun origin”, in comp.theory.cell-automata (Usenet):

The glider is fast--it moves 2 cells every 3 generations. There is also a spinning thing (sixty degrees every 21 generations)

1999 June 15, hexatron, “A new hexagonal CA with a new glider”, in comp.theory.cell-automata (Usenet):

In B37/S23, it goes symmetrical after 10 ticks, and produces a familiar pair of B-heptominoes after 23 ticks (the next generation after this can be found in the rotor of a standard B3/S23 p46 oscillator):

2008 June 25, Dave Greene, “Life: B37/S23 - A Chaotic Universe.”, in comp.theory.cell-automata (Usenet):

(cellular automata) A single iteration of a cellular automaton rule on a pattern.


cycle

→ Japanese: サイクル (saikuru)

From Middle English cicle (“fixed length period of years”), from Late Latin cyclus, from Ancient Greek κύκλος (kúklos, “circle”), from Proto-Hellenic *kúklos, *kʷókʷlos, from Proto-Indo-European *kʷékʷlos (“circle, wheel”).
Doublet of chakra, chakram, charkha, chukker, cyclus, and wheel (see there for more).

pyörä

bicycle, tricycle, motorcycle etc. — see also bicycle

(graph theory) A closed walk or path, with or without repeated vertices allowed.

(topology, algebraic topology) A chain whose boundary is zero.


localization

en-noun

localization (countable and uncountable, plural localizations)

/ˌləʊkəlaɪˈzeɪʃən/

From localize + -ation; compare French localisation.

გაქართულება

specifically meaning localization to Georgian only

multiplicative inverse
multiplicative inverse

(algebra) A systematic method of adding multiplicative inverses to a ring.

lokalisasyon

3) Geometric interpretation of the localization.
 Let V be an irreducible algebraic variety. Then P = J(V) is a prime ideal of #92;mathbb#123;C#125;#91;X#95;1,...,X#95;n#93; and so #92;mathbb#123;C#125;#91;V#93;#61;#92;mathbb#123;C#125;#91;X#95;1,...,X#95;n#93;#47;J(V) is an integral domain.
 The localization #92;mathbb#123;C#125;#91;X#95;1,...,X#95;n#93;#95;P is a subring of #92;mathbb#123;C#125;(X#95;1,...,X#95;n) consisting of rational functions #92;#123;f#47;g#58;f,g#92;in#92;mathbb#123;C#125;#91;X#95;1,...,X#95;n#93;,g#92;notinP#92;#125; which are defined on a nonempty subset of V. If V = {x} is a point, then P is maximal and #92;mathbb#123;C#125;#91;X#95;1,...,X#95;n#93;#95;P#61;#92;#123;f#47;g#58;f,g#92;in#92;mathbb#123;C#125;#91;X#95;1,...,X#95;n#93;,g(x)#92;ne 0#92;#125; consists of rational functions which are defined at x.

2007, Ivan Fesenko, “Rings and modules”, in G13ALS Algebra 2, 2007/2008 @ maths.nottingham.ac.uk, page 27:

(algebra) A ring of fractions of a given ring, such that the complement of the set of allowed denominators is an ideal.


localize

en-verb

localize (third-person singular simple present localizes, present participle localizing, simple past and past participle localized)

localizes (present singular third-person)
localizing (participle present)
localized (participle past)
localized (past)

From local + -ize. Compare French localiser.

(algebra, transitive) To produce (from a ring and an ideal in that ring) the ring of fractions, where the set of allowed denominators is the compliment of the given ideal.


locally

en-adv

locally (comparative more locally, superlative most locally)

more locally (comparative)
most locally (superlative)

locally Euclidean

(mathematics, mathematical analysis) Within a sufficiently small sphere (or circle or interval) around a given point (sometimes, around any point).


penultimate

From Latin paenultimus (“penultimate”) + -ate (adjective-forming suffix), from paene (“almost”) + ultimus (“last”). Equivalent to pene- + ultimate. Compare French pénultième.

af

(mathematics, rare) Relating to or denoting an element of a related collection of curves that is arbitrarily close to a degenerate form.


penultimate

From a substantivation of the above adjective. Equivalent to Latin paenultimus + -ate (noun-forming suffix).

(uncommon) A penult, a next to last, particularly:

(mathematics, obsolete, rare) The penultimate element of a collection of curves.


polygonometry

en-noun

polygonometry (usually uncountable, plural polygonometries)


information

information (usually uncountable, plural informations)

/ˌɪn.fəˈmæɪ.ʃən/

From Middle English informacion, enformacion, borrowed from Anglo-Norman informacioun, enformation, Old French information, from Latin īnfōrmātiō (“formation, conception; education”), from the participle stem of īnformāre (“to inform”).

der

information and communications technology

(information theory) Any unambiguous abstract data, the smallest possible unit being the bit.


cardinal

en-noun

cardinal (countable and uncountable, plural cardinals)

From Middle French cardinal, from Latin cardinālis (“pertaining to a hinge, hence applied to that on which something turns or depends, important, principal, chief”), from cardin-, cardō (“hinge”) + -ālis, adjectival suffix.

der

This cardinal number is the smallest of the infinite cardinal numbers; it is the one to which Cantor has appropriated the Hebrew aleph with the suffix 0, to distinguish it from larger infinite cardinals. Thus the name of the smallest of infinite cardinals is ₀א.

1920, Bertrand Russell, Introduction to Mathematical Philosophy, page 83:

(mathematics) Short for cardinal number, a number indicating quantity, or the size of a set (e.g., 0, 1, 2, 3). (See Cardinal_number.)


size

en-noun

size (countable and uncountable, plural sizes)

→ Cantonese: size (saai1 si2)

→ Irish: saghas

→ Japanese: サイズ (saizu)

→ Korean: 사이즈 (saijeu)

→ Malay: saiz

→ Persian: سایز (sâyz)

→ Urdu: سائز (sāiz)

Attested since the 14th century, originally meant a “law or regulation that determines the amount to be paid”, from Middle English syse, sise (“regulation, control, limit”), from Old French cise, sise, aphetism of assise (“assize”), from the verb asseoir (“to sit down”), from Latin assidēre, composed of ad- (“to, towards, at”) + sedeō (“sit; settle down”), ultimately from Proto-Indo-European *sed-. Displaced native Old English miċelnes (literally “bigness”).

ncog

(graph theory) The number of edges in a graph.

koko

graph theory: a number of edges in a graph


group

→ Gulf Arabic: قروب (grūp)

→ Japanese: グループ (gurūpu)

→ Korean: 그룹 (geurup)

→ Tongan: kulupu

From French groupe (“cluster, group”), from Italian gruppo, groppo (“a knot, heap, group, bag (of money)”), from Vulgar Latin *cruppo, Renaissance Latin grupus, from Frankish *krupp, from Proto-Germanic *kruppaz (“lump, round mass, body, crop”), from Proto-Indo-European *grewb- (“to crumple, bend, crawl”). In the sense of group theory coined (in French, as groupe) by Évariste Galois.
Cognate with German Kropf (“crop, craw, bunch”); Old English cropp, croppa (“cluster, bunch, sprout, flower, berry, ear of corn, crop”) (whence English crop); Dutch krop (“craw”), Icelandic kroppr (“hump, bunch”). Doublet of crop and croup.

der

Throughout this section, we shall assume the existence of finitely presented groups with unsolvable word problem.

1977, Roger C. Lyndon, Paul E. Schupp, Combinatorial Group Theory, Springer, page 192:

In this chapter we give some examples of Fuchsian groups. The most interesting and important ones are the so-called "arithmetic" Fuchsian groups, i.e., discrete subgroups of PSL(2,R) obtained by some "arithmetic" operations. One such construction we have already seen: if we choose all matrices of SL(2,R) with integer coefficients, then the corresponding elements of PSL(2,R) form the modular group PSL(2,Z).

1992, Svetlana Katok, Fuchsian Groups, University of Chicago Press, page 112:

2007, Zhong-Qi Ma, Group Theory for Physicists, World Scientific, page 277,
In Chap. 4 the fundamental concepts on Lie groups have been introduced through the SO(3) group and its covering group SU(2).

(group theory) A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.

(geometry, archaic) An effective divisor on a curve.


sequence

en-noun

sequence (countable and uncountable, plural sequences)

From Middle English sequence, borrowed from Old French sequence (“a sequence of cards, answering verses”), from Late Latin sequentia (“a following”), from Latin sequens (“following”), from sequi (“to follow”); see sequent.

der

(mathematics) An ordered list of objects, typically indexed with natural numbers.

مُتَتَالِيَة

in mathematics, an ordered list of objects


additive

en-adj

additive (comparative more additive, superlative most additive)

more additive (comparative)
most additive (superlative)

From Late Latin additivus, from the participial stem of Latin addere (“to add”).

(mathematics) Pertaining to addition; that can be, or has been, added.

Matrix multiplication is additive, in that M#92;vecv#43;M#92;vecw#61;M(#92;vecv#43;#92;vecw).

(mathematics, of a function, etc.) That is distributive over addition.

It is natural to look at a finite cyclic group as an additive group.

(group theory, of a group, semigroup, etc.) Whose operator is identified as addition.


kernel

→ Japanese: カーネル (kāneru)

From Middle English kernel, kirnel, kürnel, from Old English cyrnel, from Proto-West Germanic *kurnil, diminutive of Proto-Germanic *kurną (“seed, grain, corn”), equivalent to corn + -le. Cognate with Yiddish קערנדל (kerndl), Middle Dutch kernel, cornel, Middle High German kornel. Related also to Old Norse kjarni (“kernel”).

der

The Dirichlet kernel convolved with a function yields its Fourier series approximation.

(calculus) A function used to define an integral transform.

(mathematics) A set of pairs of a mapping's domain which are mapped to the same value.

Meronyms: root, zero

If a function is continuous then its kernel is a closed set.

linear transformation
linear transformation

(mathematics, linear algebra, group theory, functional analysis) For a given function (especially a linear transformation between vector spaces or homomorphism between groups), the set of elements in the domain which are mapped to zero; (formally) given f : X → Y, the set {x ∈ X : f(x) = 0}.

jádro

(mathematics, algebra) set of elements mapped to zero

(mathematics, category theory) For a category with zero morphisms: the equalizer of a given morphism and the zero morphism which is parallel to that given morphism.

(mathematics, fuzzy set theory) The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1).

ydin

(mathematics, fuzzy set theory) Set of members of a fuzzy set that are fully included


tournament

→ Japanese: トーナメント (tōnamento)

Old French tornoiement (Modern French tournoiement) from the verb tornoier.

(graph theory) A digraph obtained by assigning a direction to each edge in an undirected complete graph.


image

German: Image

Slovak: imidž

Russian: и́мидж (ímidž)

Armenian: իմիջ (imiǰ)

From Middle English ymage, borrowed from Old French image, from Latin imāgō (“a copy, likeness, image”), from Proto-Indo-European *h₂eym-; the same PIE root is the source of imitari (“to copy, imitate”); see imitate. Displaced native Old English biliþe (“an image, a representation, resemblance, likeness; pattern, example”). Doublet of imago.

cog

The number 6 is the image of 3 under f that is defined as f(x) = 2x.

The image of this step function is the set of integers.

(mathematics) The subset of a codomain comprising those elements that are images of something.


link

Azerbaijani: link

Belarusian: лінк (link)

Bulgarian: линк (link)

Catalan: link

Chinese:

Hong Kong Cantonese: link (ling1), 拎 (ling1)

Czech: link

Danish: link

Dutch: link

Estonian: link

Finnish: linkki

Georgian: ლინკი (linḳi)

German: link

Hebrew: לינק (línk)

Hindi: लिंक (liṅk)

Hungarian: link

Italian: link

Japanese: リンク (rinku)

Korean: 링크 (ringkeu)

Lower Sorbian: link

Macedonian: линк (link)

Persian: لینک (link)

Polish: link

Portuguese: link

Romanian: link

Serbo-Croatian: линк, link

Slovak: link

Spanish: link

Russian: линк (link)

Thai: ลิงก์ (líng)

Turkish: link

Ukrainian: лінк (link)

Yiddish: לינק (link)

From Middle English linke, lenke, from a merger of Old English hlenċe, hlenċa (“ring; chainlink”) and Old Norse *hlenkr, hlekkr (“ring; chain”); both from Proto-Germanic *hlankiz (“ring; bond; fettle; fetter”). Used in English since the 14th century. Related to lank.

tejlidhje

computing: short for hyperlink — see also hyperlink

a chain is only as strong as its weakest link

(mathematics) A space comprising one or more disjoint knots.

Verschlingung

mathematics: space comprising one or more disjoint knots


zeroth

The zeroth order polynomial approximation is constant.

(mathematics) In the initial position in a sequence whose elements are numbered starting at zero; the ordinal number corresponding to zero.


window

en-noun

window (countable and uncountable, plural windows)

From Middle English wyndowe, wyndown, from Old Norse vindauga (“window”, literally “wind-eye; wind-hole”), equivalent to wind + eye. Cognate with Scots windae and windock, Faroese vindeyga, Norwegian Bokmål vindu, Norwegian Nynorsk vindauge, Danish vindue, archaic Swedish vindöga, Elfdalian windog and older German Windauge. Displaced native Old English ēagþȳrel (literally “eye hole”) (the rare direct descendant is eyethurl (“window, pupil, etc.”)). The “windows” among early Germanic peoples were just unglazed holes (eyes) in the wall or roof that permitted wind to pass through .

ncog

not have a pot to piss in or a window to throw it out of

(signal processing) A function multiplied with a signal to reduce spectral leakage when performing a Fourier transform.


window

en-verb

window (third-person singular simple present windows, present participle windowing, simple past and past participle windowed)

windows (present singular third-person)
windowing (participle present)
windowed (participle past)
windowed (past)

(transitive, signal processing) To apply a window function to (a signal).


essential

en-adj

essential (comparative more essential, superlative most essential)

more essential (comparative)
most essential (superlative)

From Late Latin essentiālis, from Latin essentia (“being, essence”).

complementary region
complementary region

(geometry) Such that each complementary region is irreducible, the boundary of each complementary region is incompressible by disks and monogons in the complementary region, and no leaf is a sphere or a torus bounding a solid torus in the manifold.


extreme

Borrowed into late Middle English from Old French extreme, from Latin extrēmus, the superlative of exter.

(mathematics) Either of the two numbers at the ends of a proportion, as 1 and 6 in 1:2=3:6.

äärimmäinen jäsen

either of the two numbers at the ends of a proportion


(cryptography) Initialism of Message Digest 5, a cryptographic hash function.


spider

en-noun

spider (countable and uncountable, plural spiders)

[ˈspʌɪ̯ɾə(ɹ)]

From Middle English spiþre, spydyr, spider, spiþer, from Old English spīþra (“spider”), from Proto-West Germanic *spinþrijō, from Proto-Germanic *spinnaną (“to spin”). Mostly displaced attercop (“spider, unpleasant person”), now a dialectal term.

(mathematics) A spider graph or spider tree.


sense

sense (countable and uncountable, plural senses)

→ Afrikaans: sense

From Middle English sense, from Old French sens, sen, san (“sense, perception, direction”); partly from Latin sēnsus (“sensation, feeling, meaning”), from sentiō (“feel, perceive”); partly of Germanic origin (whence also Occitan sen, Italian senno), from Vulgar Latin *sennus (“sense, reason, way”), from Frankish *sinn ("reason, judgement, mental faculty, way, direction"; whence also Dutch zin, German Sinn, Swedish sinne, Norwegian sinn). Both Latin and Germanic from Proto-Indo-European *sent- (“to feel”).

gl

enough sense to pound sand into a rathole

where there's no sense there's no feeling

(mathematics) One of two opposite directions in which a vector (especially of motion) may point. See also polarity.

(mathematics) One of two opposite directions of rotation, clockwise versus anti-clockwise.


ordinal

Borrowed from Latin ōrdinālis, adjective formed from noun ōrdō (“order”), + adjective suffix -ālis.

"Three" is a cardinal number, while "third" is the corresponding ordinal number.

(mathematics, of a number) Indicating position in a sequence.

դասական

indicating position in a numerical sequence


order

en-noun

order (countable and uncountable, plural orders)

→ Swahili: oda

From Middle English ordre, from Old French ordre, ordne, ordene (“order, rank”), from Latin ōrdinem, accusative of ōrdō (“row, rank, regular arrangement”, literally “row of threads in a loom”), from Proto-Italic *ordō (“to arrange”), probably ultimately from Proto-Indo-European *h₂or-d-, from *h₂er-.
Related to Latin ōrdior (“begin”, literally “begin to weave”). In sense “request for purchase”, compare bespoke. Doublet of ordo.

cog

1911 [Cambridge University Press], William Burnside, Theory of Groups of Finite Order, 2nd Edition, Reprint, Dover (Dover Phoenix), 2004, page 222,
In this case, the conjugate set contains n(n − 1)/x(x − 1) distinct sub-groups of order m, and H is therefore self-conjugate in a group K of order x(x − l)m.

For various reasons it turns out to be better to enlarge this set of invariants to include suitable normalizers of subgroups of odd prime order.

2000, Michael Aschbacher, Finite Group Theory, 2nd edition, Cambridge University Press, page 260:

(set theory, of a set or algebraic structure) The number of elements contained within (the given object); formally, the cardinality (of the given object).

The object of this note is to observe that it is possible to calculate the order of an element A of G#61;#92;mathit#123;GL#125;(d,q) on average using O(d³#92;mathsf#123;log#125;#92;q) field operations, assuming that qⁱ-1 has been factorised for i#92;led.

1997, Frank Celler, C. R. Leedham-Green, “Calculating the Order of an Invertible Matrix”, in Larry Finkelstein, William M. Kantor, editors, Groups and Computation II, American Mathematical Society, page 55:

1999, A. Ehrenfeucht, T. Harju, G. Rozenberg, The Theory of 2-structures, World Scientific, page 15,
If Δ is a finite group, its cardinality is called the order of Δ. The order of an element a∈Δ is defined as the smallest nonnegative integer n such that aⁿ=1_Δ. The second case of the following result is known as Cauchy's theorem.
Theorem 1.10 Let Δ be a finite group.
(i) The order of an element a∈Δ divides the order |Δ| of the group.
(ii) If a prime number p divides |Δ|, then there exists an element a∈Δ of order p.

2010, A. R. Vasishta, A. K. Vasishta, Modern Algebra, Krishna Prakashan Media, 60th Edition, page 180,
Since in a finite group the order of an element must be a divisor of the order of the group, therefore o (a) cannot be 3 and so we must have o (a)=4=the order of the group G.

(group theory, of an element g of a group G) The smallest positive natural number n such that (denoting the group operation multiplicatively) gⁿ is the identity element of G, if such an n exists; if no such n exists the element is said to be of infinite order (or sometimes zero order).

(graph theory, of a graph) The number of vertices in the graph (i.e. the set-theoretic order of the set of vertices of the graph).

řád

graph theory: number of vertices in a graph

The monomial x²ʸ³ᶻ is of order 2#43;3#43;1#61;6.

(algebra, of a monomial) The sum of the exponents of the variables involved in the expression.

The quadratic polynomial ax²#43;bx#43;c, is said to be of order (or degree) 2 when a is nonzero.

(algebra, of a polynomial in one variable) The order of the leading monomial; (equivalently) the largest power of the variable involved in the given expression.


bath

Etymology tree
Proto-Indo-European *bʰeh₁-
Proto-Germanic *baþą
Proto-West Germanic *baþ
Old English bæþ
Middle English bath
English bath
From Middle English bath, baþ, from Old English bæþ (“bath”), from Proto-West Germanic *baþ, from Proto-Germanic *baþą (“bath”), from Proto-Indo-European *bʰeh₁- (“to warm”). Corresponding inherited verbs are beath and bathe.

etymon

barf (non-rhotic, trap–bath split, th-fronting)

Among the ancients, the public baths were of amazing extent and magnificence.

1842, Joseph Gwilt, Encyclopaedia of Architecture:

A building or area where bathing occurs.

The master bath has two sinks.

(real estate, informal) Clipping of bathroom.


bath

Ye shall have just balances, and a just ephah, and a just bath. The ephah and the bath shall be of one measure, that the bath may contain the tenth part of an homer, and the ephah the tenth part of an homer: the measure thereof shall be after the homer.

(historical units of measure) A former Hebrew unit of liquid volume (about 23 L or 6 gallons).


FOIL

Acronym of first outer inner last or similar.

(mnemonic) An acronym for the algorithm for multiplying two binomials.


multiplication

en-noun

multiplication (countable and uncountable, plural multiplications)

Borrowed from Middle French, from Old French multiplicacion, from Latin multiplicatio, multiplicationem; ~equivalent to multiplicate + -ion.

multiplication: (multiplier) × (multiplicand) = (factor) × (factor) =

(uncountable, arithmetic) The process of computing the sum of a number with itself a specified number of times, or any other analogous binary operation that combines other mathematical objects.

(countable, arithmetic) A calculation involving multiplication.

remainder left over if divisor does not divide dividend


subtraction

subtraction (countable and uncountable, plural subtractions)

Borrowed from Late Latin subtractio, subtractionis. Can be decomposed to subtract + -ion.

(arithmetic, uncountable) The process of subtracting a number from another.

The teacher has set us ten subtractions to do by tomorrow.

(arithmetic, countable) A calculation involving subtracting.


division

division (countable and uncountable, plural divisions)

PIE word
 *dwóh₁
From Middle English divisioun, from Old French division, from Latin dīvīsiō, dīvīsiōnem, noun of process form from perfect passive participle dīvīsus (“divided”), from dīvidō (“divide”). Doublet of divisio.

(arithmetic, uncountable) The process of dividing a number by another.

deel

arithmetic: process of dividing a number by another

I've got ten divisions to do for my homework.

(arithmetic) A calculation that involves this process.

deel

arithmetic: calculation involving this process


Borrowed from Middle French nul, from Latin nūllus.


en-adj

null (comparative more null, superlative most null)

more null (comparative)
most null (superlative)

(mathematics) Of or comprising a value of precisely zero.


cord

en-noun

cord (countable and uncountable, plural cords)

From Middle English corde, from Old French corde, from Latin chorda, from Ancient Greek χορδή (khordḗ, “string of gut, the string of a lyre”), from Proto-Indo-European *ǵʰerH- (“bowels, intestines”)). More at yarn and hernia.

der

Unerringly impelling this dead, impregnable, uninjurable wall, and this most buoyant thing within; there swims behind it all a mass of tremendous life, only to be adequately estimated as piled wood is—by the cord; and all obedient to one volition, as the smallest insect.

1851 November 14, Herman Melville, “The Battering-ram”, in Moby-Dick; or, The Whale, 1st American edition, New York, N.Y.: Harper & Brothers; London: Richard Bentley, →OCLC, page 376:

'If they buy three cords of birch logs,' said the witch, 'but they must be exact measure—and no bargaining about the price, and if they throw overboard the one cord of logs, piece by piece, when the first sea comes, and the other cord, piece by piece, when the second sea comes, and the third cord, piece by piece, when the third sea comes, then it's all over with us.'

1881, P. Chr. Asbjörnsen [i.e., Peter Christen Asbjørnsen], “Mackerel Trolling”, in H. L. Brækstad, transl., Round the Yule Log. Norwegian Folk and Fairy Tales, London: Sampson Low, Marston, Searle, & Rivington, →OCLC, page 187:

A unit of measurement for firewood, equal to 128 cubic feet (4 × 4 × 8 feet), composed of logs and/or split logs four feet long and none over eight inches diameter. It is usually seen as a stack four feet high by eight feet long.


binary operation

en-noun

binary operation (plural binary operations)

The "four rules" of addition, subtraction, multiplication and division are examples of binary operations.

(algebra) Any operation taking two operands.


syzygy

syzygy (countable and uncountable, plural syzygies)

From Late Latin sȳzygia (“conjunction”), from Ancient Greek συζυγία (suzugía, “union, yoke, pair”). This word was recognized as English in 1847 (in its astronomical meaning).

der

A finitely presented module is an A-module M given by a finite number of generators and relations. Therefore it is a module with a finite generator set having a finitely generated syzygy module.

2015, Henri Lombardi, Claude Quitté, Commutative Algebra: Constructive Methods: Finite Projective Modules, Springer, →ISBN, page 173:

(mathematics, linear algebra) A relation between generators of a module.


sequel

→ Catalan: seqüela (semantic loan)

→ Polish: sequel

→ Russian: си́квел (síkvel)

From Middle English sequele, sequelle, sequile, from Middle French sequele, sequelle and its etymon, Latin sequēla, from sequī (“to follow”). Doublet of sequela.

In the sequel we restrict ourselves to “nice” cases without going into details about the nicety conditions which have to be fulfilled (see, e.g., Freudenthal [1]).

1964, Hans Freudenthal, “Lie Groups in the Foundations of Geometry”, in Advances in Mathematics, volume 1, number 2, page 146:

(mathematics) The remainder of the text; what follows. Used exclusively in the set phrase "in the sequel".


alpha

en-noun

alpha (countable and uncountable, plural alphas)

From the Ancient Greek ἄλφα (álpha), the first letter of the Greek alphabet, from the Phoenician 𐤀 (ʾ, “aleph”). Doublet of alif and aleph.

(statistics) The significance level of a statistical test; the alpha level.


gamma

gamma (countable and uncountable, plural gammas)

Borrowed from Ancient Greek γάμμα (gámma). Doublet of gimel.

(mathematics) The Gamma function, symbolized by Γ.

gammafunktio

math: gamma function — see also gamma function

(mathematics) A constant approximately equal to 0.57721566, symbolized by γ (also known as the Euler–Mascheroni constant).


delta

From Ancient Greek δέλτα (délta), borrowed from a Phoenician word for "door", ultimately from Proto-Semitic *dalt-. Doublet of dalet.
* (river): from the triangular shape of the majuscule Greek letter delta Δ
* (USSF): from the delta wing, symbol of the USSF, a triangular wing, shaped like the majuscule Greek letter delta Δ

ΔV - "delta vee"(change in velocity, used in rocketry and orbital mechanics)

(mathematics, physics, engineering) The symbol Δ; A change in a quantity, likely from "d" for "difference".


delta

en-verb

delta (third-person singular simple present deltas, present participle deltaing, simple past and past participle deltaed)

deltas (present singular third-person)
deltaing (participle present)
deltaed (participle past)
deltaed (past)

Turingery worked on deltaed key to produce the deltaed contribution of the chi-wheels. Turing's discovery that delta-ing would reveal information otherwise hidden was essential to the developments that followed.

2007, B. J. Copeland, “Tunny and Colossus: Breaking the Lorenz Schlüsselzusatz traffic”, in Karl de Leeuw, Jan Bergstra, editors, The History of Information Security: A Comprehensive Handbook, Amsterdam: Elsevier, →ISBN, page 458:

(cryptography) To calculate the differences between the characters in an enciphered text and the characters a fixed number of positions previous.


epsilon

en-noun

epsilon (countable and uncountable, plural epsilons or epsila)

From Ancient Greek ἒ ψιλόν (è psilón, “simple Ε”).

uder

(mathematics) An arbitrarily small quantity.

An arbitrarily small quantity.
A small child.


zeta

From the Ancient Greek ζῆτα (zêta). Doublet of zed.

Zeta of 3 is irrational

Riemann zeta function
Riemann zeta function

(mathematics) A mathematical function formally known as the Riemann zeta function.

zeeta-funktio

Mathematics: Function formally known as the Riemann Zeta Function


natural

en-adj

natural (comparative more natural, superlative most natural)

more natural (comparative)
most natural (superlative)

/ˈnæt͡ʃ(ə)ɹəl/

From Middle English natural, borrowed from Old French natural, naturel, from Latin nātūrālis, from nātus, the perfect participle of nāscor (“be born”, verb). Displaced native Old English ġecynde. By surface analysis, nature + -al.

luonnollinen

that exists and evolved within the confines of an ecosystem

luonnollinen

having the character or sentiments properly belonging to one's position

Designating a standard trigonometric function of an angle, as opposed to the logarithmic function.

(algebra) Closed under submodules, direct sums, and injective hulls.


lune

What he worried about was any eventual convexity, a shrinking, it might be, of the planet itself to some palpable curvature of whatever he would be standing on, so that he would be left sticking out like a projected radius, unsheltered and reeling across the empty lunes of his tiny sphere.

(geometry) A concave figure formed by the intersection of the arcs of two circles on a plane, or on a sphere the intersection between two great semicircles.


universe

From Middle English universe, from Old French univers, from Latin universum (“all things, as a whole, the universe”), neuter of universus (“all together, whole, entire, collective, general, literally turned or combined into one”), from uni-, combining form of unus (“one”) + versus (“turned”), perfect passive participle of vertō (“to turn”). Analyzable as uni- + -verse through backformation of -verse.

der

God does not play dice with the universe

(mathematics) The set of all things considered.

Everything under consideration.
The set of all things considered.

In general content-related evidence demonstrates the degree to which the sample of items, tasks or questions on a test is representative of some defined universe or domain of content.

2005, Dato de Gruijter, Leo van der Kamp, Statistical Test Theory for Education and psychology, page 79:

(statistics, psychometrics) The set of all admissible observations.

Everything under consideration.
The set of all admissible observations.


theta

→ Malay: teta

Borrowed from Ancient Greek θῆτα (thêta).


mint

en-verb

mint (third-person singular simple present mints, present participle minting, simple past and past participle minted)

mints (present singular third-person)
minting (participle present)
minted (participle past)
minted (past)

From Middle English mynt, münet (“money, coin”), from Old English mynet (“coin”), from late Proto-West Germanic *munit, from Latin monēta (“place for making coins, coined money”), from the temple of Juno Moneta (named for Monēta mother of the Muses), where coins were made. Doublet of money and manat. The verb is from the noun; Old English mynetian (“to mint”) is a parallel formation.

der

Coordinate term: mine

Beeple’s collaged JPG was made, or “minted,” in February as a “nonfungible token,” or NFT.

2021 March 11, Scott Reyburn, “JPG File Sells for $69 Million, as ‘NFT Mania’ Gathers Pace”, in The New York Times, →ISSN:

(transitive, cryptocurrencies) To create a crypto token.


discrete

en-adj

discrete (comparative more discrete, superlative most discrete)

more discrete (comparative)
most discrete (superlative)

From Old French discret, from Latin discrētus, past participle of discernō (“divide”), from dis- + cernō (“sift”). Doublet of discreet.

a discrete sum

(mathematics) Consisting of or permitting only distinct values drawn from a finite, countable set.

(topology) Having each singleton subset open: said of a topological space or a topology.


quaternion

From Middle English quaternioun, from Late Latin quaterniō, from quaternī (“four each”) + -iō, from quater (“four times”). Doublet of kern. The mathematics sense was coined by Irish mathematician and astronomer William Rowan Hamilton in 1843.

coin

The right-hand side of the quaternion equation requires scalar multiplication and quaternion addition.

2004, David H. Eberly, 3D Game Engine Architecture: Engineering Real-Time Applications with Wild Magic:

(mathematics) A type of four-dimensional hypercomplex number consisting of a real part and three imaginary parts (real multiples of distinct, independent square roots of −1 denoted by i, j and k); commonly used in vector mathematics and as an alternative to matrix algebra in calculating the rotation of three-dimensional objects.


trigonometry

en-noun

trigonometry (countable and uncountable, plural trigonometries)

/ˌtɹɪɡəˈnɒmətɹi/

PIE word
 *tréyes
From 1610s, from New Latin trigōnometria, from Ancient Greek τρίγωνον (trígōnon, “triangle”) + μέτρον (métron, “measure”), equivalent to trigono- + -metry.

EtymOnLine

Douglas Harper (2001–2025) “trigonometry”, in Online Etymology Dictionary.

Trigonometry emerged in the Hellenistic world during the 3rd century BCE from applications of geometry to astronomy; the Greeks focused on the calculation of chords, while mathematicians in India created the earliest known tables of values for trigonometric functions such as sine.

Historically, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics and navigation.

Trigonometry was originally the science which treated only of the sides and angles of plane and spherical triangles; but it has been recently extended so as to include the analytic treatment of all theorems involving the consideration of angular magnitudes.

1892, Edward Albert Bowser, A Treatise on Plane and Spherical Trigonometry, D. C. Heath & Co., page 1:

In fact, the earliest practical uses of trigonometry were in the fields of astronomy and hence navigation.

2013, Paul Abbott, Hugh Neill, Trigonometry: A Complete Introduction, Hachette, unnumbered page:

The properties of these new trigonometries and identities flowing from the definitions are then developed.
The trigonometries derived from these generalizations will be jointly termed "The Fractional Trigonometry."

2016, Carl F. Lorenzo, Tom T. Hartley, The Fractional Trigonometry, Wiley, page 8:

right-angled triangle
right-angled triangle

trigonometric function
trigonometric function

(geometry, mathematical analysis) The branch of mathematics that deals with the relationships between the sides and angles of (in particular) right-angled triangles, as represented by the trigonometric functions, and with calculations based on said relationships.


quadratic

From French quadratique (1765), from Latin quadrātus + -ique (English -ic), form of quadrō (“I make square”), from quādrus (“square”), ultimately from Proto-Indo-European *kʷetwóres (“four”), whence also Latin quartus (“fourth”).

A linear or even a quadratic relation between the overall gain in efficiency η and the modularity Q would have been easily explained through S1 Fig, which shows a quadratic (inverse) relation between interedges fraction and modularity.

2015 November 17, “Fast Fragmentation of Networks Using Module-Based Attacks”, in PLOS ONE, →DOI:

(mathematics) Of a polynomial, equation or function, second-degree: involving the second power (square) of a variable but no higher powers, as ax²+bx+c.

քառակուսի

of a class of polynomial of the form y = ax² + bx + c


quadratic

If the binomial roots of a series of quadratics be squaredly squared, and those results be constant portions of the cube of the resolvend, and the dioristic limit; […]

1809, Charles Hutton, The Philosophical Transactions of the Royal Society of London from Their Commencement in 1665 to the Year 1800, volume 3, page 41:

(mathematics) A quadratic polynomial, function or equation.


homologous

en-adj

homologous (comparative more homologous, superlative most homologous)

more homologous (comparative)
most homologous (superlative)

/həˈmɒləɡəs/

From Late Latin homologus, from Ancient Greek ὁμόλογος (homólogos, “agreeing, of one mind”), from ὁμός (homós, “same”) + λόγος (lógos, “reason, reckoning”). Compare homo- (“same”) and -ous (adjectival suffix). From 1655, in the mathematical sense. See also homolog, homologue.

der

Coordinate term: homomorphic

Of equiangle triangles, the ſides that are about equall angles are proportionall, and the ſides that ſubtend the equall angles are homologous.

1655, Thomas Stanley, “[Thales.] Chapter VII. Of His Geometry.”, in The History of Philosophy. […], volume I, London: […] Humphrey Moseley, and Thomas Dring, […], →OCLC, 1st part ([Containing Those on whom the Attribute of Wise was Conferr’d]), page 18:

Showing a degree of correspondence or similarity.

(mathematics) In corresponding proportion.


linear

en-adj

linear (comparative more linear, superlative most linear)

more linear (comparative)
most linear (superlative)

From Latin līneāris, from līnea (“line”) + -āris (adjectival suffix), equivalent to line + -ar. Doublet of lineal.

lineêr

in mathematics, of first-degree polynomial

4x#43;5y#43;#92;frac#123;1#125;#123;2#125;z is a linear polynomial, but 4xy#43;#92;frac#123;1#125;#123;2#125;z and 4x#43;z² are not.

(mathematics) (of polynomials or polynomial equations)

(of a polynomial) Having degree one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n+b, where each x_i is a variable. See also Linear polynomials on Wikipedia.Wikipedia

The graph of the linear equation y#61;ax#43;b is a straight line with slope a and y-intercept b

(of a polynomial equation) Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia

The map f#58;#92;mathbb#123;R#125;³#92;to#92;mathbb#123;R#125;² taking (x,y,z)#92;mapsto(x#43;y#43;z,x-y#43;3z) is a linear map.

(of a function between vector spaces) An additive, homogeneous mapping; that is, a function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also linear map on Wikipedia.Wikipedia

Module homomorphism
w:Module homomorphism

(of a function over a module) A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia


linear

linear amplifier
linear amplifier#English

(radio slang) Ellipsis of linear amplifier.


cubic

From Middle French cubique, equivalent to cube + -ic.

On one recent day, officials said the fine dust concentration levels in Seoul rose above 130 micrograms per cubic meter.
Audio (US): (file)

2019, VOA Learning English (public domain)

cubic foot

(geometry) Used in the names of units of volume formed by multiplying a unit of length by itself twice.

(mathematics) Relating to polynomials of the form ax³+bx²+cx+d.


line

→ Scottish Gaelic: loidhne

From Middle English line, lyne, from Old English līne (“line, cable, rope, hawser, series, row, rule, direction”), from Proto-West Germanic *līnā, from Proto-Germanic *līnǭ (“line, rope, flaxen cord, thread”), from Proto-Germanic *līną (“flax, linen”), from Proto-Indo-European *līno- (“flax”).
Influenced in Middle English by Middle French ligne (“line”), from Latin linea. More at linen.
The oldest sense of the word is “rope, cord, thread”; from this the senses “path”, “continuous mark” were derived.

lyn

path through two or more points, threadlike mark

lyn

single horizontal row of text on a screen, printed paper, etc.

linja

measure of length, the main division of an inch or its local equivalent

A path through two or more points (compare ‘segment’); a continuous mark, including as made by a pen; any path, curved or straight.

(geometry) An infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness.

lyn

geometry: infinite one-dimensional figure

(geometry, informal) A line segment; a continuous finite segment of such a figure.

отсе́чка

geometry: continuous finite segment of such a figure

Any of an ill-defined set of units of length, varying according to the country, discipline, industry, and date of application, commonly with no indication of the intended magnitude:

(historical) A tsarist-era Russian unit of measure, approximately equal to one tenth of an English inch, used especially when measuring the calibre of firearms.

(baseball, slang, 1800s, with "the") The batter's box.


sphere

From Middle English spere, from Old French sphere, from Late Latin sphēra, earlier Latin sphaera (“ball, globe, celestial sphere”), from Ancient Greek σφαῖρα (sphaîra, “ball, globe”), of unknown origin. Not related to superficially similar Persian سپهر (sepehr, “sky”) .

uder

(mathematics) A surface in three dimensions consisting of all points equidistant from a center. .

(geometry) The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .

sferë

mathematics: regular three-dimensional object


polyhedron

en-noun

polyhedron (plural polyhedra or polyhedrons)

From New Latin polyedron, from Ancient Greek πολύεδρος (polúedros, “having many seats”), from πολυ- (polu-, “many”) + ἕδρα (hédra, “seat”); compare French polyèdre. By surface analysis, poly- + -hedron.

der

quasiregular polyhedronArchimedean solidCatalan solid

regular polyhedronKepler-Poinsot polyhedronPlatonic solidcube

semiregular polyhedronantiprismArchimedean solidCatalan soliddipyramidprismtrapezohedron

List of uniform polyhedra on Wikipedia.Wikipedia

Of the convex polyhedra with regular faces, the only ones that have tetrahedral, octahedral, or icosahedral symmetry are the Platonic and Archimedean solids.

1966, Norman W. Johnson, “Convex Polyhedra with Regular Faces”, in Canadian Journal of Mathematics, volume XVIII, number I, Toronto: University of Toronto Press, page 181:

(geometry) A solid figure with many flat faces and straight edges.


graph

Clipping of graphic formula. From 1878; verb from 1889.

Drawings and pictures are more than mere ornaments in scientific discourse. Blackboard sketches, geological maps, diagrams of molecular structure, astronomical photographs, MRI images, the many varieties of statistical charts and graphs: These pictorial devices are indispensable tools for presenting evidence, for explaining a theory, for telling a story.

2012 March, Brian Hayes, “Pixels or Perish”, in American Scientist, volume 100, number 2, archived from the original on 2013-02-19, page 106:

(applied mathematics, statistics) A data chart (graphical representation of data) intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative numbers) and a reference set, whose elements are indexed to those of the former set(s) and may or may not be numbers.

1969 [MIT Press], Thomas Walsh, Randell Magee (translators), I. M. Gelfand, E. G. Glagoleva, E. E. Shnol, Functions and Graphs, 2002, Dover, page 19,
Let us take any point of the first graph, for example, x=1/2,y=4/5, that is, the point M_1(1/2,4/5).

Graph of a function
w:Graph of a function

(mathematics) A set of points constituting a graphical representation of a real function; (formally) a set of tuples (x_1,x_2,…,x_m,y)∈ R ᵐ⁺¹, where y=f(x_1,x_2,…,x_m) for a given function f: R ᵐ→ R . See also Graph of a function on Wikipedia.Wikipedia

1973, Edward Minieka (translator), Claude Berge, Graphs and Hypergraphs, Elsevier (North-Holland), [1970, Claude Berge, Graphes et Hypergraphes], page vii,
Problems involving graphs first appeared in the mathematical folklore as puzzles (e.g. Königsberg bridge problem). Later, graphs appeared in electrical engineering (Kirchhof's Law), chemistry, psychology and economics before becoming a unified field of study.

Spectral graph theory has a long history. In the early days, matrix theory and linear algebra were used to analyze adjacency matrices of graphs. Algebraic methods are especially effective in treating graphs which are regular and symmetric.

1997, Fan R. K. Chung, Spectral Graph Theory, American Mathematical Society, page 1:

Graph (discrete mathematics)
w:Graph (discrete mathematics)

(graph theory) A set of vertices (or nodes) connected together by edges; (formally) an ordered pair of sets (V,E), where the elements of V are called vertices or nodes and E is a set of pairs (called edges) of elements of V. See also Graph (discrete mathematics) on Wikipedia.Wikipedia

2008, Unnamed translators (AMS), A. V. Alexeevski, S. M. Natanzon, Hurwitz Numbers for Regular Coverings of Surfaces by Seamed Surfaces and Cardy-Frobenius Algebras of Finite Groups, V. M. Buchstaber, I. M. Krichever (editors), Geometry, Topology, and Mathematical Physics: S.P. Novikov's Seminar, 2006-2007, American Mathematical Society, page 6,
First, let us define its 1-dimensional analog, that is, a topological graph. A graph Δ is a 1-dimensional stratified topological space with finitely many 0-strata (vertices) and finitely many 1-strata (edges). […] A graph such that any vertex belongs to at least two half-edges we call an s-graph. Clearly the boundary ∂Ω of a surface Ω with marked points is an s-graph.
A morphism of graphs φ:Δ'→Δ is a continuous epimorphic map of graphs compatible with the stratification; i.e., the restriction of φ to any open 1-stratum (interior of an edge) of Δ' is a local (therefore, global) homeomorphism with appropriate open 1-stratum of Δ.

(topology) A topological space which represents some graph (ordered pair of sets) and which is constructed by representing the vertices as points and the edges as copies of the real interval [0,1] (where, for any given edge, 0 and 1 are identified with the points representing the two vertices) and equipping the result with a particular topology called the graph topology.

(category theory, of a morphism f) A morphism Γ_f from the domain of f to the product of the domain and codomain of f, such that the first projection applied to Γ_f equals the identity of the domain, and the second projection applied to Γ_f is equal to f.


graph

en-verb

graph (third-person singular simple present graphs, present participle graphing, simple past and past participle graphed)

graphs (present singular third-person)
graphing (participle present)
graphed (participle past)
graphed (past)

(transitive, mathematics) To draw a graph of a function.


arity

en-noun

arity (countable and uncountable, plural arities)

From -ary (taken from unary/binary/ternary [function/operator]) + -ity. Compare adicity and adinity.

(logic, mathematics, computer science) The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian product.

(mathematics, computer science) The maximum number of child nodes that any node in a given tree (data structure) may have.


decameter

Borrowed from French décamètre. Equivalent to deca- + meter.


class

class (countable and uncountable, plural classes)

→ Assamese: ক্লাছ (klas)

desc

→ Bengali: ক্লাস (klaś), কেলাস (kelaś) — nonstandard

q

or from French <i class="Latn mention" lang="fr">classe</i>

→ Gulf Arabic: كلاس (klās) (or from French classe)

→ Hindustani:

Hindi: क्लास (klās)

Urdu: کلاس

→ Japanese: クラス (kurasu)

→ Korean: 클래스 (keullaeseu)

→ Nepali: क्लास (klās)

→ Scottish Gaelic: clas

→ Thai: คลาส (kláas)

→ Yoruba: kíláàsì

From Middle French classe, from Latin classis (“a class or division of the people, assembly of people, the whole body of citizens called to arms, the army, the fleet, later a class or division in general”), from Proto-Indo-European *kelh₁- (“to call, shout”). Doublet of clas and classis.

class action

class-action, class action lawsuit, class suit

(statistics) A grouping of data values in an interval, often used for computation of a frequency distribution.

luokka

statistics: grouping of data values in an interval

The class of all sets is not a set.

Every set is a class, but classes are not generally sets. A class that is not a set is called a proper class.

In the present section we shall discuss the various systems of set theory which admit, beside sets, also classes. Classes are like sets, except that they can be very comprehensive; an extreme example of a class is the class which contains all sets.[…]The main point which will, in our opinion, emerge from this analysis is that set theory with classes and set theory with sets only are not two separate theories; they are, essentially, different formulations of the same underlying theory.

1973, Abraham Fraenkel, Yehoshua Bar-Hillel, Azriel Lévy, Foundations of Set Theory, 2nd edition, Elsevier, page 119:

(set theory) A collection of sets definable by a shared property, especially one which is not itself a set (in which case the class is called proper).

դաս

set theory: collection of sets definable by a shared property


genus

en-noun

genus (plural genera or (all nonstandard) genuses or genusses or genii)

genera (plural)
genuses (nonstandard plural)
genusses (nonstandard plural)
genii (nonstandard plural)

→ Malayalam: ജീനസ് (jīnasŭ)

→ Swahili: jenasi

→ Thai: สกุล (sà-gun) (semantic loan)

Etymology tree
Proto-Indo-European *ǵenh₁-
Proto-Indo-European *-os
Proto-Indo-European *ǵénh₁os
Latin genusbor.
English genus
Borrowed from Latin genus (“birth, origin, a race, sort, kind”) from the root gen- in Latin gignō (“to beget, produce”). Doublet of gender, genre, and kin.

genus

rank in a taxonomic classification between family and species

(topology, graph theory, algebraic geometry) A natural number representing any of several related measures of the complexity of a given manifold or graph.


chaos

en-noun

chaos (usually uncountable, plural chaoses)

Borrowed from Ancient Greek χάος (kháos, “vast chasm, void”). Doublet of gas, which was borrowed through Dutch.
In Early Modern English, used in the sense of the original Greek word. In the meaning "primordial matter" from the 16th century. Figurative usage in the sense "confusion, disorder" from the 17th century. The technical sense in mathematics and science dates from the 1960s.

bor

(mathematics) A behaviour of iterative non-linear systems in which arbitrarily small variations in initial conditions become magnified over time.


chaos theory

(mathematics) The study of iterative non-linear systems in which arbitrarily small variations in initial conditions become magnified over time.


hectometre

(metrology) An SI unit of length equal to 10² metres. Symbol: hm


centimetre

Borrowed from French centimètre; equivalent to centi- + metre.

(metrology) An SI unit of length equal to 10⁻² metres. Symbol: cm


millimetre

An SI/MKS unit of measure, the length of ¹⁄₁₀₀₀ of a metre. Symbol: mm


decimetre

Borrowed from French décimètre. By surface analysis, deci- + metre.

If the aquarium is placed where it receives insufficient daylight, artificial lighting by means of ordinary incandescent lamps should be employed. For good plant growth 2 decalumens of luminous flux per square decimetre of water surface […]

1956, C. van Duijn, Diseases of Fishes, page 149:

(metrology) An SI unit of length equal to 10⁻¹ metres. Symbol: dm


NFL

First off, let us be clear that the No Free Lunch theorems that underwrite the displacement problem apply with perfect generality—NFL applies to any information that might supplement a blind search, and not just to fitness functions.

2002, William A. Dembski, No Free Lunch: Why Specified Complexity Cannot be Purchased Without Intelligence, Rowman & Littlefield, →ISBN, page 204:

(mathematics) Initialism of no free lunch: applied to various restricting theorems.


once

From Middle English ones, from Old English ānes, a remodelling (after ān (“one”)) of ǣnes, itself an extension of ǣne (“once”) with the genitive suffix -es. Compare Old Saxon ēnes (“once”), Old High German eines, einēst (“once”), modern German einst (“once”). More at one (including regarding the development of the pronunciation) and -s.

Once three is three.

(mathematics) Multiplied by one: indicating that a number is multiplied by one.


metre

Tok Pisin: mita

→ Burmese: မီတာ (mita)

→ Chinese: 米突 (mǐtū, mǐtú)

→ Japanese: メーター (mētā)

→ Korean: 미터 (miteo) (South Korea), 메터 (meteo) (North Korea, China)

→ Maori: mita

→ Swahili: mita

→ Yoruba: mítà

From French mètre, from Ancient Greek μέτρον (métron, “measure, rule, length, size, poetic metre”). Doublet of meter, metron, and mether.

der

The measures of length above the metre are ten times ... greater than the metre.

1797, The Monthly magazine and British register, number 3:

A dress length of 8 metres of the best quality costs 58 francs.

The 12-metre yachts ... can be sailed efficiently with four paid hands.

The basic unit of length in the International System of Units (SI: Système International d'Unités), equal to the distance travelled by light in a vacuum in 1/299 792 458 seconds. The metre is equal to 39+⁴⁷⁄₁₂₇ (approximately 39.37) imperial inches.


lambda

From Ancient Greek λάμβδα (lámbda). Doublet of lamed.

(physics, mathematics) Unit representation of wavelength.


centimeter

(American spelling) (Canadian spelling, alternative) Alternative form of centimetre


decimeter

Borrowed from French décimètre. Equivalent to deci- + meter.


millimeter

[ˈmɪləˌmiɾɚ]

From French millimètre, as if milli- + meter.


megameter

/mɛˈɡɐˌmɪtə/

/mɛˈɡɐˌmɪtəɹ/

[mɛˈɡɐˌmɪɾɚ]


kilo

The San Juan market is Mexico City's most famous deli of exotic meats, where an adventurous shopper can hunt down hard-to-find critters […]. But the priciest items in the market aren't the armadillo steaks or even the bluefin tuna. That would be the frozen chicatanas – giant winged ants – at around $500 a kilo.

2013 July 26, Nick Miroff, “Mexico gets a taste for eating insects […] ”, in The Guardian Weekly, volume 189, number 7, page 32:


dag

Abbreviations
* Initialism of directed acyclic graph.
* Clipping of dagwood.

partial ordering relation
partial ordering relation

(graph theory) A directed acyclic graph; an ordered pair (V,E) such that E is a subset of some partial ordering relation on V.


micrometre

An SI/MKS unit of measure, the length of one millionth of a metre. Symbol: µm, um, rm


decametre

Borrowed from French décamètre. Equivalent to deca- + metre.

(metrology) An SI unit of length equal to 10¹ metres. Symbol: dam


kilometre

/kɪˈlɔmɪtəɹ/

From French kilomètre, from Ancient Greek χίλιοι (khílioi, “thousand”) + μέτρον (métron, “measure”); equivalent to kilo- + metre.

When you fly over an undammed river like the Fraser I grew up with, the plume of silt spewed into the ocean is astonishing, a good three kilometres of brown refusing to mix with the green of the ocean.

2008, Brian Harvey, The End of the River:

The 34.2 kilometre (21.3 mile) pipeline, which will be built by Qinjin Natural Gas Co, is designed to have annual gas transmission capacity of 3.3 billion cubic metres and connect Ji county in Shanxi and Yichuan county in Shaanxi.

2021 July 5, Muyu Xu, Shivani Singh, “China approves a $55 mln gas pipeline in northern China”, in Louise Heavens, editor, Reuters, archived from the original on 2021-07-05, Energy:

(metrology) An SI unit of length equal to 10³ metres. Symbol: km


atom

→ Swahili: atomi

From Middle English attome, from Middle French athome, from Latin atomus (“smallest particle”), from Ancient Greek ἄτομος (átomos, “indivisible”), from ἀ- (a-, “not”) + τέμνω (témnō, “I cut”). Atoms are so named because historically the notion was that they were indivisible, given that chemically they are indeed so; the splitting of atoms awaited a later era of science and technology, and nonchemical means.

atoom

historical: theoretical particle of matter

atom

mathematics: member of a Boolean algebra

बूलियन बिजगणितीय प्रणालीतील एक घटक

In a Venn diagram, an atom is depicted as an area circumscribed by lines but not cut by any line.

partially ordered set
partially ordered set

(mathematics) A non-zero member of a partially ordered set that has only zero below it (assuming that the poset has a least element, its "zero").

(mathematics, set theory) An element of a set that is not itself a set; an urelement.


decibel

A common measure of sound intensity ratio that is one tenth of a bel on the logarithmic intensity scale. It is defined as dB = ⅒log₁₀(P₁ / P₂), where P₁ and P₂ are the relative powers of the sound.


area

It is about 4.5 million square kilometers in area and holds the world’s third largest collection of ice after Antarctica and Greenland.

2018, VOA Learning English > China's Melting Glacier Brings Visitors, Adds to Climate Concerns:

(mathematics) A measure of the extent of a surface; it is measured in square units.


mile

en-noun

mile (plural miles or (UK colloquial) mile)

miles (plural)
mile (UK colloquial plural)

From Middle English myle, mile, from Old English mīl, from Proto-West Germanic *mīliju, a borrowing of Latin mīlia, mīllia, plural of mīle, mīlle (“mile”) (literally ‘thousand’ but used as a short form of mīlle passūs (“a thousand paces”)).

a journey of a thousand miles begins with a single step

give someone an inch and someone will take a mile

give them an inch and they'll take a mile

Athelstan Arundel walked home all the way, foaming and raging. No omnibus, cab, or conveyance ever built could contain a young man in such a rage. His mother lived at Pembridge Square, which is four good measured miles from Lincoln's Inn.

1892, Walter Besant, The Ivory Gate: A Novel, page 16:

Ivor had acquired more than a mile of fishing rights with the house ; he was not at all a good fisherman, but one must do something ; one generally, however, banged a ball with a squash-racket against a wall.

1922, Michael Arlen, “3/19/2”, in “Piracy”: A Romantic Chronicle of These Days:

From the ground, Colombo’s port does not look like much.[…] But viewed from high up in one of the growing number of skyscrapers in Sri Lanka’s capital, it is clear that something extraordinary is happening: China is creating a shipping hub just 200 miles from India’s southern tip.

2013 June 8, “The new masters and commanders”, in The Economist, volume 407, number 8839, page 52:

Any of several customary units of length derived from the 1593 English statute mile of 8 furlongs, equivalent to 5,280 feet or 1,760 yards of various precise values.


milligram

(metrology) An SI unit of mass equal to 10⁻³ grams. Symbol: mg


density

density (countable and uncountable, plural densities)

Borrowed from Middle French densité or Latin densitas. Morphologically dense + -ity.

كَثَافَة

physics: amount of matter contained by a given volume

(mathematics, statistics) The probability that an outcome will fall into a given range, per unit of that range; the relative likelihood of possible values of a continuous random variable.

плъ́тност

number of particles or other quantity contained by a given volume


millilitre

From milli- + litre, from French millilitre.

A smaller mammal such as a dog has a sperm concentration of 300 000 000 per millilitre in an ejaculate of 8 ml in volume. Thus, each ejaculate will contain only 2 400 000 000 (24 × 10⁸).

2012, Tim Glover, Mating Males: An Evolutionary Perspective on Mammalian Reproduction, Cambridge: Cambridge University Press, →ISBN, page 79:

One serve of carbohydrates is approximately equal to a slice of bread, a piece of fruit, third of a cup of cooked rice, half a cup of grains, cereals, starchy vegetables or cooked pasta, 200 grams of plain yoghurt, or 300 millilitres of milk.

2012, Lesley Campbell, Alan L. Rubin, Type 2 Diabetes For Dummies, Australian Edition, page 117:

(British spelling) A unit of measure of capacity, being one thousandth of a litre. Symbol: ml


milliliter

A slurry of 10 grams of powder in 100 milliliters distilled water was carried on a cotton swab and the panels scrubbed until free from waterbreak when rinsed.

1960, American Electroplaters' Society, Proceedings of the Convention, page 92:

The following day, nonattached cells were harvested by centrifugation and resuspended in growth medium at a density of 1 × 10⁷ per milliliter.

2001 February 2, Richard J. Fisher et al., “Control of Fusion Pore Dynamics During Exocytosis by Munc18”, in Science, volume 291, number 5505, →DOI, pages 875–878:

In addition to having a relative with Type 1, people in that subgroup had insulin autoantibody levels equal to or greater than 80 milliunits per milliliter.

2007 November 20, Aliyah Baruchin, “Twins on a Medical Odyssey After a Diagnosis of Diabetes”, in The New York Times:

(American spelling) Alternative form of millilitre


em

Attested since 1808. In typography, the em is named after the em quadrat (later called em quad), from m quadrat, a metal type used in letterpress typesetting, which is as wide as the point size of the font.

etymid

name of the Latin script letter _M_, _m_

(typography) A unit of measurement equal to the height of the type in use.


em

head

em (third-person singular, gender-neutral, objective case, reflexive emself, possessive adjective eir, possessive pronoun eirs)

en-pron

emself (reflexive)
eir (adjective possessive)
eirs (possessive pronoun without-noun)

Coined by Christine M. Elverson by removing the "th" from them, perhaps influenced by the pre-existing em/'em, now often perceived as apheretic forms of them (though originally unrelated).

etymid

novel pronoun proposed by Christine M. Elverson, similar to apheresis of _them_

If the author uses such notation, it should be up to Em to indicate Eir intentions clearly, but there’s no harm checking first.

1986 April 1, Michael Spivak, The Joy of TeX: A Gourmet Guide to Typesetting with the AMS-TeX macro package, Providence: American Mathematical Society, →ISBN, →LCCN, LCC Z253.4.T47 S673 1986, page 68:

I may become quite intimate with someone, spend hours with em every night, and yet not have the slightest idea what eir voice sounds like, or what eir RL body looks, feels, and smells like.

1997, Steven Shaviro, Doom Patrols : A Theoretical Fiction About Postmodernism, London: Serpent's Tail, →ISBN, →LCCN, page 138:

E invites em to consider how ey represent emselves^([sic]), and in so doing, e focuses eir attention on the ethics that make human relations possible.

2000, Jane Love, “Ethics, Plugged and Unplugged: The Pegagogy of Disorderly Conduct”, in James A. Inman, Donna N. Sewell, editors, Taking flight with OWLs: Examining Electronic Writing Center Work, Taylor & Francis, →ISBN, LCC PE1414.T24 1999, page 193:

And ultimately: I think my readers are mature enough that knowing eir assigned gender is not going to give them an “excuse” to misgender em.

2011 March 15, RJ Edwards, “89: New Friend”, in Riot Nrrd, retrieved 2012-10-06:

“You idiot girl! Are you childsick?” She grabbed Asu’s wrist; Asu made no effort to twist away. “Sand and soil, tell me you’re not pregnant. Is it that—what’s eir name? Aeran? Have you lain with em? Tell me!”

2023, Aimee Ogden, “A Half-Remembered World”, The Magazine of Fantasy & Science Fiction, vol. 145, no. 1-2, whole no. 768 (July/August 2023), pages 146-202

(rare, nonstandard) A gender-neutral third-person singular object pronoun, the objective case of ey or e, equivalent to the singular them and coordinate with him and her.


em

speech filler, in the em-erm-um-uh class

She was abused by, em... David, I think. That was his name, he's a real em... what's the word, narcissist. You should really stay away from him.

(Scotland, Ireland) a form of hesitant speech, or an expression of uncertainty


em

name of Cyrillic letter homologous to Latin script _M_, _m_

Cyrillic script
Appendix:Cyrillic script#English

The name of the Cyrillic script letter М / м.


AI

en-noun

AI (countable and uncountable, plural AIs)

Audio (US)

“Wintermute is the recognition code for an AI. I've got the Turing Registry Numbers. Artificial Intelligence.”

1984, William Gibson, Neuromancer (Sprawl; book 1), New York, N.Y.: Ace Books, →ISBN, page 73:

The geth serve as a cautionary tale against the dangers of rogue AI, and in Citadel Space they are technically illegal. Advocacy groups argue, however, that an AI is a living, conscious entity deserving the same rights as organics. They argue that continued use of the term "artificial" is institutionalized racism on the part of organic life, the term "synthetic" is considered the politically correct alternative.

2008, BioWare, Mass Effect, Redwood City: Electronic Arts, →ISBN, →OCLC, PC, scene: Computers: Artificial Intelligence (AI) Codex entry:

The result, Gurry said, will be many new AI-based methods and products that can change lives across the world.
Audio (US): (file)

2019 February 3, “UN Study: China, US, Japan Lead World AI Development”, in Voice of America, archived from the original on 2019-02-07

A Vatican directive supplements such principles and states AI should be “explainable” to humans, i.e., we should be able to explain the reasons for a decision made by AI. The document also states that AI should avoid discrimination.

2022, Catriona Campbell, AI by Design: A Plan for Living with Artificial Intelligence (Chapman & Hall/CRC Artificial Intelligence and Robotics Series), Boca Raton, Fla.: CRC Press, →ISBN:

artificial intelligence
artificial intelligence#English

(artificial intelligence, countable and uncountable) Initialism of artificial intelligence.


artificial intelligence

artificial intelligence (countable and uncountable, plural artificial intelligences)

Coined by American computer scientist and cognitive scientist John McCarthy in 1955, and popularized at the Dartmouth Summer Research Project on Artificial Intelligence, 1956.

kunsmatige intelligensie

intelligence exhibited by an artificial entity

ሠው ሰራሽ ዕውቀት

śäw säraš ʿəwḳät

artificially intelligent → artificially intelligently

Research in the modern science of Artificial Intelligence started only in the 1950's, stimulated by the invention of modern computers. This inspired a flood of new ideas about how machines could do what only minds had done previously.

1988, Marvin Minsky, The Society of Mind:

Intelligence exhibited by an artificial (non-natural, man-made) entity.

(computer science) The branch of computer science dealing with the reproduction or mimicking of human-level intelligence, self-awareness, knowledge, conscience, thought in computer programs.

This computer possesses artificial intelligence.

A United Nations agency says the United States, China and Japan are leading the world in developing artificial intelligence, or AI, technology.
Audio (US): (file)

The essential quality of a machine which thinks in a manner similar to or on the same general level as a real human being.

The original Sniper: Ghost Warrior was a surprise hit when it was released in 2010. A surprise because it seemed an unequivocally awful game, with half broken graphics and artificial intelligence, a tediously linear story campaign, and an undernourished multiplayer mode.

2013 March 19, “Sniper: Ghost Warrior 2 review – scope for improvement”, in The Metro (UK):

(video games) A character or entity controlled by the game instead of a player; AI.

(countable, computing) A computer system or software package which is artificially intelligent.

While the humans scurried in confusion, the Artificial Intelligence (AI) created by MIT/Bell Labs linked itself into the network of high-speed, twentieth generation computers placed at its disposal by a Red Alert Priority, evaluated data thoughtfully for a minute and a half and then proceeded to get in touch with its opposite number in the Russian Republics.

1973, Gardner Dozois, Chains of the Sea, →ISBN, Chains of the Sea, page 83:

What Daedadus really is, is the world's first successful wholly autonomous AI. Whatever mysterious organization managed to create the first true artificial intelligence succeeded so well that their creation managed to convince them that they'd failed... and then escaped.

2000, Sheldon Pacotti (writer) & Warren Spector (director/producer), Deus Ex

Dylan Hunt: "This is Captain Dylan Hunt of the High Guard. Investigation has shown that an Artificial Intelligence was involved in the tragic death of your President. In such a case, Commonwealth law demands that the AI's personality be completely erased."

2001 January 15, Walter Jon Williams, All Great Neptune's Ocean (Andromeda), season 1, episode 10:

Also remember that Skynet's an artificial intelligence. Intelligence, for our purpose, means being able to use reason in order to achieve your goals.

2009, Josh Weisberg, “It Stands to Reason: Skynet and Self-preservation”, in Terminator and Philosophy: I'll Be Back, Therefore I Am, →ISBN:

(countable, chiefly science fiction) An intelligent, self-aware computer or computer program.

kunstmatige intelligentie

science fiction: intelligent, self-aware computer or computer program