ideal

Let #92;mathbb#123;Z#125; be the ring of integers and let 2#92;mathbb#123;Z#125; be its ideal of even integers. Then the quotient ring #92;mathbb#123;Z#125;#47;2#92;mathbb#123;Z#125; is a Boolean ring.

The product of two ideals #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125; is an ideal #92;mathfrak#123;ab#125; which is a subset of the intersection of #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125;. This should help to understand why maximal ideals are prime ideals. Likewise, the union of #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125; is a subset of #92;mathfrak#123;a#43;b#125;.

In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the prime ideals.

2004, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, 2nd edition, Cambridge University Press, page 47:

If an ideal I of a ring contains the multiplicative identity 1, then we have seen that I must be the entire ring.

2009, John J. Watkins, Topics in Commutative Ring Theory, Princeton University Press, page 45:

However, every R has a minimal prime ideal consisting of left zero-divisors and one of right zero-divisors.

2010, W. D. Burgess, A. Lashgari, A. Mojiri, “Elements of Minimal Prime Ideals in General Rings”, in Sergio R. López-Permouth, Dinh Van Huynh, editors, Advances in Ring Theory, Springer (Birkhäuser), page 69:

(algebra, ring theory) A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.

理想

subring closed under multiplication by containing ring

1992, Unnamed translator, T. S. Fofanova, General Theory of Lattices, in Ordered Sets and Lattices II, American Mathematical Society, page 119,
An ideal A of L is called complete if it contains all least upper bounds of its subsets that exist in L. Bishop and Schreiner [80] studied conditions under which joins of ideals in the lattices of all ideals and of all complete ideals coincide.

1.35 Find a distributive lattice L with no minimal and no maximal prime ideals.

2011, George Grätzer, Lattice Theory: Foundation, Springer (Birkhäuser), page 125:

Definition 15.11 (Width Ideal) An ideal Q of a poset P = (X,≤) is a width ideal if maximal(Q) is a width antichain.

2015, Vijay K. Garg, Introduction to Lattice Theory with Computer Science Applications, Wiley, page 186:

partially ordered set
partially ordered set

w:Boolean prime ideal theorem#Prime ideal theorems

(algebra, order theory, lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).

Formally, an ideal I of a given set X is a nonempty subset of the powerset #92;mathcal#123;P#125;(X) such that: (1)#92;#92;emptyset#92;inI, (2)#92;A#92;inI#92;andB#92;subseteqA#92;impliesB#92;inI and (3)#92;A,B#92;inI#92;impliesA#92;cupB#92;inI.

(set theory) A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.

If 𝖌 is a Lie algebra, 𝖍 is an ideal and the Lie algebras 𝖍 and 𝖌/𝖍 are solvable, then 𝖌 is solvable.

1975, Zhe-Xian Wan, translated by Che-Young Lee, Lie Algebras, Pergamon Press, page 13:

What really put primitive ideals in enveloping algebras of semisimple Lie algebras on the map was Duflo's fundamental theorem that any such ideal is the annihilator of a very special kind of simple module, namely a highest weight module.

2006, W. McGovern, “The work of Anthony Joseph in classical representation theory”, in Anthony Joseph, Joseph Bernstein, Vladimir Hinich, Anna Melnikov, editors, Studies in Lie Theory: Dedicated to A. Joseph on His Sixtieth Birthday, Springer (Birkhäuser), page 3:

Next let L be an arbitrary semisimple Lie algebra. Then L can be written uniquely as a direct sum L#95;1#92;oplus#92;dots#92;oplusL#95;t of simple ideals (Theorem 5.2).

2013, J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, page 73:

(algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.

The set of natural numbers with multiplication as the monoid operation (instead of addition) has multiplicative ideals, such as, for example, the set {1, 3, 9, 27, 81, ...}. If any member of it is multiplied by a number which is not a power of 3 then the result will not be a power of three.

(algebra) A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.


inflection

en-noun

inflection (countable and uncountable, plural inflections)

From older inflexion, borrowed from Middle French inflexion, itself borrowed from Latin inflexiōnem (“alteration”, literally “bending”). The English spelling with ⟨ct⟩ is due to influence from inflect or related words like correction.

der

(mathematics) A change in curvature from concave to convex or from convex to concave.


straight

en-adj

straight (comparative straighter, superlative straightest)

straighter (comparative)
straightest (superlative)

→ Japanese: ストレート

From Middle English streight, streght, streiȝt, the past participle of strecchen (“to stretch”), from Old English streċċan (past participle ġestreaht, ġestreht), from Proto-West Germanic *strakkjan (“to stretch”). Doublet of straught. Equivalent to stretch + -ed

der

(sciences, mathematics) Concerning the property allowing the parallel transport of vectors along a course that keeps tangent vectors remain as such throughout that course (a course which is straight, a straight curve, is a geodesic).


bra

From bracket, referring to the notation introduced in 1939 by Paul Dirac.

(linear algebra, quantum mechanics) One of the two vectors in the standard notation for describing quantum states in quantum mechanics, the row vector; the other (column) vector being its complex conjugate, the ket.


addition

en-noun

addition (countable and uncountable, plural additions)

Sense of “what is added” dates from 14th century, from Middle English addicioun, addition, from Old French adition, from Latin additiōnem, accusative singular of additiō, from addō (“add, put”).

arithmetic operation
arithmetic operation

(uncountable, arithmetic) The arithmetic operation of adding.

remainder left over if divisor does not divide dividend


building

building (countable and uncountable, plural buildings)

From Middle English byldynge, buyldyng, byldyng, buldynge, buldyng, boldyng, equivalent to build + -ing. Compare also related Middle English bold (“edifice, castle, mansion”), from Old English bold (“building, dwelling, house”).

cog

List of building types on Wikipedia.Wikipedia

List of house types on Wikipedia.Wikipedia


circle

Pitcairn-Norfolk: sirkil

From Middle English circle, cercle, from Old French cercle and Latin circulus, diminutive of Latin circus (“circle, circus”), from Ancient Greek κίρκος (kírkos, “circle, ring”), related to Old English hring (“ring”). Compare also Old English ċircul (“circle, zodiac”), which came from the same Latin source.

دَائِرَة

geometry: set of all points in a plane within a radius

The set of all points (x, y) such that (x − 1)² + y² = r² is a circle of radius r around the point (1, 0).

(geometry) A two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from a given point (center).

аикәагьежь

geometry: set of points that are equally distant from a center


attention

en-noun

attention (countable and uncountable, plural attentions)

From Middle English attencioun, borrowed from Latin attentio, attentionis, from attendere, past participle attentus (“to attend, give heed to”); see attend.

attention deficit hyperactivity disorder

The attention mechanism is an important part of these models and plays a very crucial role. Before Transformer models, the attention mechanism was proposed as a helper for improving conventional DL models such as RNNs.

2021, Savas Yildirim, Meysam Asgari-Chenaghlu, Mastering Transformers […] , Packt Publishing Ltd, →ISBN, page 26:

(uncountable, machine learning) A kind of prioritisation technique in neural networks that assigns soft weights between tokens from two (or more) input sequences in order to compute the required output.


card

card (countable and uncountable, plural cards)

→ Bengali: কার্ড (karḍo)

→ Burmese: ကတ် (kat)

→ Chinese: 卡 (kǎ)

→ Gujarati: કાર્ડ (kārḍ)

→ Hausa: kati

→ Hindi: कार्ड (kārḍ)

→ Italian: card

→ Japanese: カード (kādo)

→ Korean: 카드 (kadeu)

→ Malay: kad

→ Pashto: کارډ (kārḍ)

Pitcairn-Norfolk: kaad

→ Sinhalese: කාඩ් (kāḍ)

→ Swahili: kadi

→ Tagalog: kard

→ Urdu: کارڈ (kārḍ)

From Middle English carde (“playing card”), from Old French carte, from Latin charta, from Ancient Greek χάρτης (khártēs, “paper, papyrus”). Doublet of chart.

der

Coordinate term: deck

(graph theory) A graph formed from a given graph by deleting one vertex.


theory

en-noun

theory (countable and uncountable, plural theories)

From Middle French théorie, from Late Latin theōria, from Ancient Greek θεωρία (theōría, “contemplation, divine perspective, speculation, a looking at, a seeking”), from θεωρέω (theōréō, “I look at, view, see, consider, examine”), from θεωρός (theōrós, “spectator”), from θέα (théa, “view, perspective, sight”) + ὁράω (horáō, “I see, look”) [i. e. θέαν ὁράω (théan horáō, “see, look at a view; survey + genitive”)].

der

Knot theory classifies the mappings of a circle into 3-space.

It's just a theory I have, and I wonder if women would agree. But don't men say a lot about themselves when a short-skirted woman slides out of a car or chair?

The theory is that by stripping costs to the bone, they are able to offer ludicrously low fares.

2003 June 21, Sean Coughlan, The Guardian:

(mathematics) A field of study attempting to exhaustively describe a particular class of constructs.


weight

en-noun

weight (countable and uncountable, plural weights)

Belizean Creole: wayt

→ Japanese: ウエイト (ueito)

→ Burmese: ဝိတ် (wit)

From Middle English weight, weiȝte, weght, wight, from Old English wiht, ġewiht (“weight”), from Proto-Germanic *wihtiz ("weight"; compare *weganą (“to move”)), from Proto-Indo-European *weǵʰ- (“to move; pull; draw; drive”). Equivalent to weigh + -th.
Cognate with Scots wecht, weicht (“weight”), Saterland Frisian Wächte (“scale”), Gewicht (“weight”), West Frisian gewicht (“weight”), Dutch gewicht (“weight”), German Low German Wicht, Gewicht (“weight”), German Wucht (“massiveness, force”), Gewicht (“weight”).

gloss

"weight"; compare <i class="Latn mention" lang="gem-pro">*weganą</i> (“to move”)

inh

(statistics) A variable which multiplies a value for ease of statistical manipulation.

(topology) The smallest cardinality of a base.

paino

topology: the smallest cardinality of a base

You’re no match for ’em. You ain’t up to their weight. It’s like little Black Strap standing up to Tom Spring,—the Black’s a pretty fighter but, Law bless you, his arm ain’t long enough to touch Tom,—and I tell you, you’re going it with fellers beyond your weight.

1848 November – 1850 December, William Makepeace Thackeray, The History of Pendennis. […], volume (please specify |volume=I or II), London: Bradbury and Evans, […], published 1849–1850, →OCLC:


weight

en-verb

weight (third-person singular simple present weights, present participle weighting, simple past and past participle weighted)

weights (present singular third-person)
weighting (participle present)
weighted (participle past)
weighted (past)

(transitive, mathematics) To assign weights to individual statistics.


simple

en-adj

simple (comparative simpler or more simple, superlative simplest or most simple)

simpler (comparative)
more simple (comparative)
simplest (superlative)
most simple (superlative)

Inherited from Middle English symple, simple, from Old French and French simple, from Latin simplex (“simple”, literally “onefold”) (as opposed to duplex (“double”, literally “twofold”)), from semel (“the same”) + plicō (“I fold”). See same and fold. Compare single, singular, simultaneous, etc.
Partially displaced native English onefold.

der

(heading, technical) Structurally uncomplicated.

(algebra, loosely, of an algebraic structure) Being non-trivial, and admitting no proper non-trivial quotients.

(group theory, of a group) Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).

(module theory, of a module) Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).

(ring theory, of a ring) Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.

equivalence relation
equivalence relation

(universal algebra, of an algebraic structure) Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation a≡b⟺a=b) and the universal relation (the equivalence relation such that a≡b for all a,b). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.

(category theory, of an object in a category with a terminal object) Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.

(algebra, of a Lie algebra) Being non-abelian and having no proper non-zero ideals. (Note that this is non-equivalent to the usual algebra sense; in particular, the abelian Lie algebra of dimension 1 over any given field is non-trivial and has no proper non-zero ideals, but is by convention not considered simple.)

(mathematics, real analysis, measure theory, of a real-valued function) Equal to a finite linear combination of indicator functions on measurable sets.


bag

→ Japanese: バッグ

→ Korean: 백 (baek)

→ Norwegian: bag

From Middle English bagge, from Old Norse baggi (“bag, pack, satchel, bundle”) (whence also Old French bague (“bundle, package, sack”)); related to Old Norse bǫggr (“harm, shame; load, burden”), of uncertain origin. Perhaps from Proto-Indo-European *bʰak- (compare Welsh baich (“load, bundle”), Ancient Greek βάσταγμα (bástagma, “load”)).

cog

A bag of three apples could be represented symbolically as {a,a,a}. Or, letting 'r' denote 'red apple' and 'g' denote 'green apple', then a bag of three red apples and two green apples could be denoted as {r,r,r,g,g}.

(mathematics) A collection of objects, disregarding order, but (unlike a set) in which elements may be repeated.


bag

en-verb

bag (third-person singular simple present bags, present participle bagging, simple past and past participle bagged)

bags (present singular third-person)
bagging (participle present)
bagged (participle past)
bagged (past)

(transitive) To furnish or load with a bag.

(transitive, medicine) To provide with artificial ventilation via a bag valve mask (BVM) resuscitator.

To expose exterior shape or physical behaviour resembling that of a bag

(nautical, intransitive) To drop away from the correct course.


boat

Belizean Creole: boat

→ Esperanto: boato

→ Dhivehi: ބޯޓު (bōṭu)

→ Fijian: boto

→ Hijazi Arabic: بوت (bōt)

→ Japanese: ボート (bōto)

→ Malay: bot

→ Pitcairn-Norfolk: boet (Norfuk)

→ Sinhalese: බෝට්ටුව (bōṭṭuwa)

→ Swahili: boti

→ Scots: boat, bote (compare native bait, bate)

→ Tahitian: poti

Tok Pisin: bot

From Middle English bot, boot, boet, boyt (“boat”), from Old English bāt (“boat”), from Proto-West Germanic *bait, from Proto-Germanic *baitaz, *baitą (“boat, small ship”), from Proto-Indo-European *bʰeyd- (“to break, split”). Cognate with Old Norse beit (“boat”), Middle Dutch beitel (“little boat”).
Old Norse bátr (whence Icelandic bátur, Norwegian båt, Danish båd), Dutch boot, German Boot, Occitan batèl and French bateau are all ultimately borrowings from the Old English word.

der

It creates 4 blocks, a boat, and a glider every 768 generations.

1994 May 7, David Bell, “HighLife - An Interesting Variant of Life (part 1/3)”, in comp.theory.cell-automata (Usenet):

The program is represented as a string of boats (1s) and blocks (0s).

2004 May 24, Paul Chapman, “A Prototype Programmable Universal Constructor for Conway's Life”, in comp.theory.cell-automata (Usenet):

For many stable patterns, by the way, there are other input glider lanes where the gliders are caught and turned into boats, which are then cleanly deleted by another glider coming in on the same lane.

2005 February 23, Dave Greene, “exist glider gun able of reconstruction in Life?”, in comp.theory.cell-automata (Usenet):

(cellular automata) In Conway’s Game of Life, a particular still life consisting of a dead cell surrounded by five living cells.


body

en-noun

body (countable and uncountable, plural bodies)

Etymology tree
Proto-Indo-European *bʰewdʰ-
Proto-West Germanic *bodag
Old English bodiġ
Middle English bodi
English body
From Middle English bodi, bodiȝ, from Old English bodiġ (“body, trunk, chest, torso, height, stature”), from Proto-West Germanic *bodag (“body, trunk”), from Proto-Indo-European *bʰewdʰ- (“to be awake, observe”). Cognate with Old High German botah (whence Swabian Bottich (“body, torso”)).

der

body-focused repetitive behavior disorder

(geometry) A three-dimensional object, such as a cube or cone.


button

→ German: Button

→ Hindi: बटन (baṭan)

→ Gujarati: બટન (baṭan)

→ Korean: 버튼 (beoteun)

→ Maori: pātene

→ Marathi: बटण (baṭaṇ)

→ Urdu: بَٹَن (baṭan)

From Middle English boton, botoun, from Old French boton (Modern French bouton), from Old French bouter, boter (“to push; thrust”), ultimately from a Germanic language. Doublet of Biden and beat. More at butt.

(curling) The center (bullseye) of the house.

In attempting to touch down on the button of the runway, he misjudged his altitude and struck a pile of rocks short of the runway. The right wheel was torn off and the gear leg bent backwards.

1984, Synopses of Aircraft Accidents: Civil Aircraft in Canada, page 42:

The second and slightly higher aircraft on the approach showed no reaction to this barrage of pyrotechnics and continued blissfully down toward the button of the runway.

1999, Les Morrison, Of Luck and War, page 69:

(dated, Southern US) A clove (of garlic).


complex

en-adj

complex (comparative more complex, superlative most complex)

more complex (comparative)
most complex (superlative)

From French complexe, from Latin complexus, past participle of complector (“I entwine, encircle, compass, infold”), from com- (“together”) and plectere (“to weave, braid”). May be analyzed as com- + -plex. See complect. Doublet of complexus.

complex number

function of a complex variable

(mathematics, of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.

complex function

mathematical analysis
mathematical analysis

(mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.

complex polynomial

complex algebraic variety

(mathematics, algebra) Whose coefficients are complex numbers; defined over the field of complex numbers.

(geometry) A curve, polygonderi or other figure that crosses or intersects itself.


complex

en-noun

complex (plural complexes or (nonstandard) complices)

complexes (plural)
complices (nonstandard plural)

համալիր

assemblage of related things, collection

coordination complex

coordinated complex, metal complex, Werner complex

The interesting aspect here is that U₃ is irreducible, even though all irreps over the complexes are one-dimensional because ℤ₄ is abelian.

1996, Barry Simon, Representations of Finite and Compact Groups, page 50:


bridge

From Middle English brigge, from Old English brycġ (“bridge”), from Proto-Germanic *brugjō, *brugjǭ (“bridge”), from Proto-Indo-European *bʰerw-, *bʰrēw- (“wooden flooring, decking, bridge”).
Cognate with Scots brig, brigg, breeg (“bridge”), Saterland Frisian Brääch (“bridge”), West Frisian brêge (“bridge”), Dutch brug (“bridge”), German Brücke (“bridge”), Danish brygge (“wharf”), Icelandic brygga (“pier”), Gaulish briua (“bridge”).
The verb is from Middle English briggen, from Old English brycġian (“to bridge, make a causeway, pave”), derived from the noun. Cognate with Dutch bruggen (“to bridge”), Middle Low German bruggen (“to bridge”), Old High German bruccōn (“to bridge”) (whence Modern German brücken).
The musical connection sense is a semantic loan from German Steg, from Old High German steg.

ацҳа

construction or natural feature that spans a divide

if someone told you to jump off a bridge, would you do it

(graph theory) An edge which, if removed, changes a connected graph to one that is not connected.


branch

From Middle English branche, braunche, bronche, from Old French branche, branke, from Late Latin branca (“footprint”, later also “paw, claw”) (whence Middle High German pranke, German Pranke (“paw”)), of unknown origin.
Perhaps of Celtic origin, from a hypothetical Gaulish *vranca, from Proto-Indo-European *wrónk-eh₂. If so, then Indo-European cognates include Old Norse rá, vró (“angle, corner”), and possibly Lithuanian rankà (“hand”), Old Church Slavonic рѫка (rǫka, “hand”), Albanian rangë (“yardwork”).
The verb is from Middle English braunchen, from the noun.

unk

unknown

fall out of the ugly tree and hit every branch

the highest branch is not the safest roost

the branches of a hyperbola

(geometry) One of the portions of a curve that extends outwards to an indefinitely great distance.

haara

geometry: one of the portions of a curve that extends to infinity

(graph theory) A path of vertices of degree 2, ending at vertices whose degree is not 2.


curve

Attested since the 1690s, from Latin curvus (“bent, curved”), ultimately from Proto-Indo-European *(s)ker- (“to bend, curve, turn”) + *-wós. Doublet of curb, shrink, carcer, and cancer.

doublet

a curve line

a curve surface

(obsolete) Bent without angles; crooked; curved.


curve

(analytic geometry) A continuous map from a one-dimensional space to a multidimensional space.

(geometry) A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.

(algebraic geometry) An algebraic curve; a polynomial relation of the planar coordinates.


cell

From Middle English celle, selle, from Old English cell (attested in inflected forms), from Latin cella (“chamber, small room, compartment”), later reinforced by Old French cel, sele, Old French cele. ultimately from Proto-Italic *kelnā, from Proto-Indo-European *ḱelneh₂, from Proto-Indo-European *ḱel- (“to cover”). Doublet of cella and hall.

der

intrinsically photosensitive retinal ganglion cell

melanopsin-containing retinal ganglion cell

The upper right cell always starts with the color green.

Basically, I'm looking for a fast (the fastest?) way of updating grids, where each cell has to look at an arbitrary number of its neighbors.

1988 January 26, David Hiebeler, “Fast way to update grids”, in comp.theory.cell-automata (Usenet):

It is used for land-use change simulations, where the content of the cells surrounding a central cell defines how this cell is going to evolve (for example, a cell that is "agriculture" but has 3 urban neighbors will likely become urban, while if it is surrounded by forest or other agriculture cells, it will remain agriculture.)

2010 March 10, Jean H., “What is CA for?”, in comp.theory.cell-automata (Usenet):

I've seen this space colloqually referred to as MAP (presumably since it maps a 3x3 neighborhood into a future cell state)

2022 February 11, Mateon1, “Game of Life with real 8 neighbors”, in comp.theory.cell-automata (Usenet):

(cellular automata) The minimal unit of a cellular automaton that can change state and has an associated behavior.

कोशिका

(geometry) A three-dimensional facet of a polytope.

포

geometry: a three-dimensional facet of a polytope

(statistics) The unit in a statistical array (a spreadsheet, for example) where a row and a column intersect.

cella

statistics: the unit in a statistical array (a spreadsheet, for example) where a row and a column intersect


rewrite

(mathematics, computing) The replacement of subterms of a formula with other terms, according to certain rules, by way of transformation.


rewrite

en-verb

rewrite (third-person singular simple present rewrites, present participle rewriting, simple past rewrote, past participle rewritten)

rewrites (present singular third-person)
rewriting (participle present)
rewrote (past)
rewritten (participle past)

(mathematics, computing) To replace subterms of a formula with other terms, according to certain rules, by way of transformation.


ring

→ French: ring
→ Romanian: ring

→ Hungarian: ring

→ Italian: ring

→ Japanese: リング

→ Polish: ring

→ Serbo-Croatian: ring

→ Spanish: ring

→ Turkish: ring

From Middle English ryng, from Old English hring (“ring, circle”), from Proto-West Germanic *hring, from Proto-Germanic *hringaz (“ring”), from Proto-Indo-European *(s)krengʰ-, extended nasalized form of *(s)ker- (“to turn, bend”). Doublet of rank and rink, as well as indirectly range.
Cognates
* West Frisian ring
* Low German Ring
* Dutch ring
* German Ring
* Swedish ring
* Finnish rengas

(geometry) A planar geometrical figure included between two concentric circles.


ring

From a shortening of German Zahlring (“number(s) ring”) (coined by German mathematician David Hilbert in 1892). Apparently first used in English in 1930, E. T. Bell, “Rings whose elements are ideals,” Bulletin of the American Mathematical Society.

The set of integers, #92;mathbb#123;Z#125;, is the prototypical ring.

multiplicative operation
multiplicative operation

(algebra) An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.

The definition of ring without unity allows, for instance, the set 2#92;mathbb#123;Z#125; of even integers to be a ring.

(algebra) An algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element.


ring

(mathematical analysis, measure theory) A family of sets that is closed under finite unions and set-theoretic differences.

(mathematics, order theory) A family of sets closed under finite union and finite intersection.


run

rise

antonym(s) of “horizontal part of a step”

rise

antonym(s) of “horizontal distance of a set of stairs”

From Middle English runnen, rennen (“to run”), alteration (due to the past participle runne, runnen,
yronne) of Middle English rinnen (“to run”), from Old English rinnan, iernan (“to run”) and Old Norse rinna (“to run”), both from Proto-Germanic *rinnaną (“to run”) (compare also *rannijaną (“to make run”)), from Proto-Indo-European *h₃reyH- (“to boil, churn”).
Cognate with Scots rin (“to run”), West Frisian rinne (“to walk, march”), Dutch rennen (“to run, race”), Alemannic German ränne (“to run”), German rennen (“to run, race”), rinnen (“to flow”), Rhein, Danish rende (“to run”), Swedish ränna (“to run”), Swedish rinna (“to flow”), Icelandic renna (“to flow”). Non-Germanic cognates include Albanian rend (“to run, run after”). See random.

der

This morning's run of the SHIPS statistical model gave Hurricane Priscilla a 74% chance of gaining at least 30 knots of intensity in 24 hours, reconfirmed by the HMON and GFS dynamical models.

A literal or figurative path or course for movement relating to:

(mathematics, computing) The execution of a program or model

ajo

computing: execution of a program or model


set

From Middle English set, sete, sette (“that which is set, the act of setting, seat”), from Old English set (“setting, seat, a place where people remain, habitation, camp, entrenchment, a place where animals are kept, stall, fold”) and Old English seten (“a set, shoot, slip, branch; a nursery, plantation; that which is planted or set; a cultivated place; planting, cultivation; a setting, putting; a stopping; occupied land”), related to Old English settan (“to set”). Compare Middle Low German gesette (“a set, suite”), Old English gesetl (“assembly”). According to Skeat, in senses denoting a group of things or persons, representing an alteration of sept, from Old French sette (“a religious sect”), from Medieval Latin secta (“retinue”), from Latin secta (“a faction”). See sect. It is quite possible that the modern word is more of a merger between both, however.

cog

(set theory) A collection of zero or more objects, possibly infinite in size, and disregarding any order or repetition of the objects which may be contained within it.

(in plural, “sets”, mathematics, informal) Set theory.


shear

en-verb

shear (third-person singular simple present shears, present participle shearing, simple past sheared or shore, past participle shorn or sheared)

shears (present singular third-person)
shearing (participle present)
sheared (past)
shore (past)
shorn (participle past)
sheared (participle past)

From Middle English sheren, scheren, from Old English sċieran (“to shear; to shave”), from Proto-West Germanic *skeran, from Proto-Germanic *skeraną, from Proto-Indo-European *(s)ker- (“to cut”).
Cognate with West Frisian skarre, Low German scheren, Dutch scheren, German scheren, Danish skære, Norwegian Bokmål skjære, Norwegian Nynorsk skjera, Swedish skära, Finnish keritä; and (from Indo-European) with Ancient Greek κείρω (keírō, “I cut off”), Latin caro (“flesh”), Albanian shqerr (“to tear, cut”), harr (“to cut, to mow”), Lithuanian skìrti (“separate”), Welsh ysgar (“separate”). See also sharp.

inh

(mathematics) To transform by displacing every point in a direction parallel to some given line by a distance proportional to the point’s distance from the line.


shear

en-noun

shear (countable and uncountable, plural shears)

(mathematics) A transformation that displaces every point in a direction parallel to some given line by a distance proportional to the point's distance from the line.


arbitrary

en-adj

arbitrary (comparative more arbitrary, superlative most arbitrary)

more arbitrary (comparative)
most arbitrary (superlative)

/ˈɑɹ.bɪˌtɹɛ(ə).ɹi/

From Middle English arbitrarie, Latin arbitrārius (“arbitrary, uncertain”), from arbiter (“witness, on-looker, listener, judge, overseer”).

der

The equation is true for an arbitrary value of x.

(mathematics) Any, out of all that are possible.


gargantuan

en-adj

gargantuan (comparative more gargantuan, superlative most gargantuan)

more gargantuan (comparative)
most gargantuan (superlative)

/ɡɑːˈɡæn.t͡ʃu.ən/

/ɡɑɹˈɡæn.t͡ʃu.ən/

/ɡaːˈɡæn.t͡ʃʉ.ən/

François Rabelais
Gargantua and Pantagruel

From French Gargantua, a giant with a very large appetite in Rabelais's The Inestimable Life of Gargantua. Rabelais derived Gargantua from the Portuguese and Spanish garganta (“throat”).

Some distant observers of the Scottish football scene reckon that all - all! - Gerrard has to do is beat Celtic to become a legend. Even if that was true - and, demonstrably, it is not - then it would be a gargantuan task all on its own.

2018 May 4, Tom English, “Steven Gerrard: A 'seriously clever or recklessly stupid' Rangers appointment”, in BBC Sport:

Or the twinkling dining rooms: all frilly net curtains, pink walls, kaleidoscope-patterned carpets and tiny tables, crammed with teetering piles of hand-painted ceramic crockery (think plates covered in colorful swirls and cocktail mugs shaped like heaving bosoms or ladies’ faces) that showcase gargantuan portions of Italian fare.

2019 September 14, Elizabeth Paton, “A Fashion/Food Blowout in the Shadow of Brexit”, in New York Times:

Boxy and unrefined, the Hummer embodied an outlandishly masculine aesthetic that seemed to almost revel in its gargantuan fuel consumption.

2022 April 7, Oliver Milman, “I test-drove the all-electric Hummer. Can it win over America’s EV skeptics?”, in The Guardian, →ISSN:


ponderous

ponderous (comparative more ponderous, superlative most ponderous)

more ponderous (comparative)
most ponderous (superlative)

Ultimately from Latin ponderōsus (“weighty”).

Ponderous thoughts take hold of the heart; musing maketh the fire to burn, and steady sight hath the greatest influence upon us.

c. 1660, Thomas Manton, “Sermon Upon John III”, in Works of Thomas Manton, 2002 edition, →ISBN, page 464:

The acute and ponderous mind of Dr. Johnson was not always right in its decisions.

1804, The Literary Magazine and American Register, volume 2, number 7, page 10:

They are the pleasantest of all companions, and perhaps the most affluent in correct opinions of men and things generally, although little addicted to ponderous consideration or deep research.

1850, Fraser's Magazine for Town and Country, volume 41, page 242:

(rare) Characterized by or associated with pondering.

pohdiskeleva

characterized by or associated with pondering


speed

en-noun

speed (countable and uncountable, plural speeds)

From Middle English spede (“prosperity, good luck, quickness, success”), from Old English spēd (“success”), from Proto-West Germanic *spōdi (“prosperity, success”), from Proto-West Germanic *spōan, from Proto-Germanic *spōaną (“to prosper, succeed, be happy”), from Proto-Indo-European *speh₁- (“to prosper, turn out well”). Cognate with Scots spede, speid (“success, quickness, speed”), Dutch spoed (“haste; speed”), German Low German Spood (“haste; speed; eagerness; success”), German Sput (“progress, acceleration, haste”). Related also to Old English spōwan (“to be successful, succeed”), Albanian shpejt (“to speed, to hurry”) and Russian спеши́ть (spešítʹ, “to hurry”), Latin spēs (“hope, expectation”), spērō (“hope”, verb), perhaps also to Ancient Greek σπεύδω (speúdō, “to urge on, hasten, press on”).

cog

Speed limits provide information to the drivers about the safe speed to travel in average conditions.

Train positions and speeds were established by a track magnet at each milepost, which produced a suitable mark on the punched recording tape whenever a train passed.

1960 December, “Talking of Trains: Recording Electric Operation”, in Trains Illustrated, London: Ian Allan Publishing, →ISSN, →OCLC, page 707:

(mathematics, physics) The rate of motion or action, specifically the magnitude of the velocity; the rate distance is traversed in a given time.


spat

en-verb

spat (third-person singular simple present spats, present participle spatting, simple past and past participle spatted)

spats (present singular third-person)
spatting (participle present)
spatted (participle past)
spatted (past)

Little Isabel leaped up and down, spatting her hands.

(US, dialect) To slap, as with the open hand; to clap together, as the hands.


split

split (third-person singular simple present splits, present participle splitting, simple past and past participle split)

splits (present singular third-person)
splitting (participle present)
split (participle past)
split (past)

Attested since about 1567, from Middle Dutch splitten (“to split”) and/or Middle Low German splitten (“to split”), both ultimately from Proto-West Germanic *splittjan, an intensive form of Proto-West Germanic *splītan (“to split”), from Proto-Germanic *splītaną (whence Danish splitte, Low German splieten, German spleißen), from Proto-Indo-European *(s)pley- (“to split, splice”).
Compare Middle English ysplett (“split”, past participle of splatten (“to split”)), Old English speld (“splinter”), Old High German spaltan (“to split”), Old Irish sliss (“splinter”), Lithuanian spaliai (“flax sheaves”), Czech půl (“half”), Old Church Slavonic рас-плитати (ras-plitati, “to cleave, split”).

cog

past participle of <i class="Latn mention" lang="enm">splatten</i> (“to split”)

plah

divide along a more or less straight line

(algebra, transitive and intransitive, acts on a polynomial) To factor into linear factors.

(generally, of an algebraic structure) To be expressable as a direct sum of sub-modules, -algebras, etc.

acts on a polynomial; generally; generally

short exact sequence
short exact sequence

(of an object which expresses the relationship between algebraic structures, particularly a short exact sequence) To contain an object which may be so expressed.

acts on a polynomial; particularly a short exact sequence; particularly a short exact sequence

In the first case X²-2, the minimum polynomial of #92;sqrt 2, splits completely over #92;Q(#92;sqrt 2); in the second case we see that X³-2, the minimum polynomial of 3#92;sqrt 2, does not split completely over #92;Q(3#92;sqrt 2).

2007, John M. Howie, Fields and Galois Theory, Springer, page 103:


split

(algebra, of a short exact sequence) Having the middle object (group, module, etc.) equal to the direct sum of the others.


spread

en-noun

spread (countable and uncountable, plural spreads)

From Middle English spreden, from Old English sprǣdan (“to spread, expand”), from Proto-Germanic *spraidijaną (“to spread”), from Proto-Indo-European *(s)per- (“to strew, sow, sprinkle”).
Cognate with Saterland Frisian spreede (“to spread”), West Frisian spriede (“to spread”), North Frisian spriedjen (“to spread”), Dutch spreiden (“to spread”), Low German spreden (“to spread”), German spreiten (“to spread, spread out”), Norwegian spre, spreie (“to spread, disseminate”), Swedish sprida (“to spread”), Latin spernō, spargō, Ancient Greek σπείρω (speírō), Persian سپردن (sepordan, “to deposit”), English spurn.

cog

The spread is usually measured using standard deviation and variance.

(statistics) A measure of how far the data tend to deviate from the average.

(geometry) An unlimited expanse of discontinuous points.


stiff

en-adj

stiff (comparative stiffer, superlative stiffest)

stiffer (comparative)
stiffest (superlative)

From Middle English stiff, stiffe, stif, from Old English stīf, from Proto-West Germanic *stīf, from Proto-Germanic *stīfaz, from Proto-Indo-European *steypós.
See also West Frisian stiif, Dutch stijf, Norwegian Bokmål stiv, German steif; also Latin stīpes, stīpō, from which English stevedore.
The expected Modern English form would be /staɪf/; /stɪf/ is probably originally from compounds such as stiffly, where the vowel was shortened before a consonant cluster.

(mathematics) Of an equation, for which certain numerical solving methods are numerically unstable, unless the step size is taken to be extremely small.


tore

non-rhotic, without the horse–hoarse merger

(geometry) The surface described by the circumference of a circle revolving about a straight line in its own plane.


upset

en-noun

upset (countable and uncountable, plural upsets)

From Middle English upset (“the act of setting up; establishment”), from Middle English upsetten, corresponding to up- + set. Cognate with Middle Low German upset (“setup; arrangement”).

cog

(mathematics) An upper set; a subset (X,≤) of a partially ordered set with the property that, if x is in U and x≤y, then y is in U.


shape

en-noun

shape (countable and uncountable, plural shapes)

From Middle English shap, schape, from Old English ġesceap (“shape, form, created being, creature, creation, dispensation, fate, condition, sex, gender, genitalia”), from Proto-West Germanic *ga- + *skap, from Proto-Germanic *ga- + *skapą (“shape, nature, condition”), possibly from Proto-Indo-European *(s)kep- (“to split, cut”).
The verb is from Middle English shapen, schapen, from Old English scieppan (“to shape, form, make, create, assign, arrange, destine, order, adjudge”), from Proto-West Germanic *skappjan, from Proto-Germanic *skapjaną (“to create”), from the noun.
The noun is cognate with Middle Dutch schap (“form”), Middle High German geschaf (“creature”), Icelandic skap (“state, condition, temper, mood”). The verb is cognate with Dutch scheppen, German schaffen, Swedish skapa (“create, make”), Norwegian Bokmål skape (“create”). Doublet of -ship.

cog

programming language
programming language

(programming) In the Hack programming language, a group of data fields each of which has a name and a data type.


round

From Middle English round, rounde, from Old Northern French roünt, rund, Old French ront, runt, reont ( > French rond), from both Late Latin retundus and the original Latin rotundus. The noun developed partly from the adjective and partly from the corresponding French noun rond. Doublet of rotund.

раздаване

card games: moment from the deal until the players are finished with the cards

A Cave[…],
Where light and darkness in perpetual round
Lodge and dislodge by turns.

1667, John Milton, “Book VI”, in Paradise Lost. […], London: […] [Samuel Simmons], and are to be sold by Peter Parker […]; [a]nd by Robert Boulter […]; [a]nd Matthias Walker, […], →OCLC; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873, →OCLC:


behemoth

/ˈbiː.əˌməθ/

From Middle English behemoth, bemoth, from Late Latin behemoth, from Hebrew בְּהֵמוֹת (behemót). Most likely, the Hebrew word is an intensive plural of בְּהֵמָה (behemá, “beast”), from Proto-Semitic (compare Ge'ez ብህመ (bəhmä, “to be dumb, to be speechless”), Arabic ب ه م (b h m)).
Some have instead suggested a borrowing from a hypothetical Egyptian pA-i-H-E1-mw (*pꜣ-jḥ-mw, “hippopotamus”, literally “the ox of the water”), from pꜣ (“definite article”) + jḥ (“ox, cattle”) + mw (“water”) in a direct genitive construction (for the pronunciation, compare the later Coptic descendants ⲡ- (p-) + ⲉϩⲉ (ehe) + ⲙⲟⲟⲩ (moou)); this, however, suffers from problems such as the lack of attestation of the supposed etymon, and there seems little reason to prefer it to the intensive plural explanation.

der

<i class="Latn mention" lang="egy">*pꜣ-jḥ-mw</i>

Coordinate term: leviathan

⸿ Beholde now Behemoth which I made with thee, hee eateth graſſe as an oxe.
 Loe now, his ſtrength is in his loynes, and his force is in the nauell of his belly.
 Hee moueth his taile like a Cedar: the ſinewes of his ſtones are wrapt together.
 His bones are as ſtrong pieces of braſſe: his bones are like barres of iron.

1611, The Holy Bible, […] (King James Version), London: […] Robert Barker, […], →OCLC, Job 40:15–18, column 1:

(biblical) A great and mighty beast which God shows to Job in Job 40:15–24.


comb

From Middle English comb, from Old English camb (“comb”), from Proto-West Germanic *kamb, from Proto-Germanic *kambaz (“comb”), from Proto-Indo-European *ǵómbʰos (“tooth”), a doublet of cam. The verb is derived from the noun and displaced the older verb kemb.
Cognates
Compare Saterland Frisian Koum, Swedish/Dutch kam, Norwegian kam, German Kamm); also Tocharian B keme, Lithuanian žam̃bas (“sharp edge”), Old Church Slavonic зѫбъ (zǫbŭ), Albanian dhëmb, Ancient Greek γομφίος (gomphíos, “backtooth, molar”), Sanskrit जम्भ (jambha)).

cog

(algebraic geometry) A connected and reduced curve with irreducible components consisting of a smooth subcurve (called the handle) and one or more additional irreducible components (called teeth) that each intersect the handle in a single point that is unequal to the unique point of intersection for any of the other teeth.


box

en-noun

box (plural boxes or (nonstandard, computing, humorous) boxen)

boxes (plural)
boxen (humorous nonstandard plural)

Tok Pisin: bokis

→ Afrikaans: boks

→ Bengali: বাক্স (bakśo)

→ Bulgarian: бокс (boks)

→ Crimean Tatar: boks

→ Danish: boks

→ Dutch: box m

→ Faroese: boks

→ French: box m

→ German: Box f

→ Hindustani:

Hindi: बकस m (bakas), बक्सा m (baksā)

Urdu: بکس m (baks, bakas)

→ Icelandic: box n

→ Indonesian: boks

→ Irish: bosca m

→ Italian: box m

→ Japanese: ボックス (bokkusu)

→ Korean: 박스 (bakseu)

→ Maori: pāka

→ Marwari: बकस (baks, bakas)

→ Nepali: बाकस (bākas)

→ Norman: bosc m

→ Norwegian: boks m

→ Pashto: بکس (baks)

→ Persian: باکس (bâks)

→ Polish: boks m

→ Portuguese: box m

→ Russian: бокс m (boks)

→ Scottish Gaelic: bogsa m, bocsa

→ Spanish: box m

→ Swedish: box c

→ Welsh: bocs

Etymology tree
Ancient Greek πῠ́ξος (pŭ́xos)
Ancient Greek -ις (-is)
Ancient Greek πυξίς (puxís)bor.
Late Latin buxisbor.
Proto-West Germanic *buhsā
Old English box
Middle English box
English box
From Middle English box (“container, box, cup”), from Old English box (“box, case”), from Proto-West Germanic *buhsā (“box”) from Late Latin buxis (“box”), Latin pyxis (“small box for medicines or toiletries”), of uncertain origin; compare Ancient Greek πύξος (púxos, “box or tablet made of boxwood; box; cylinder”) and Ancient Greek πυξίς (puxís, “box or tablet made of boxwood; box; cylinder”). Doublet of piseog, pyx, and pyxis.
Cognate with Middle Dutch bosse, busse (“jar; tin; round box”) (modern Dutch bos (“wood, forest”), bus (“container, box; bushing of a wheel”)), Old High German buhsa (Middle High German buhse, bühse, modern German Büchse (“box; can”)), Swedish bössa (“box”).
The humorous plural form boxen is from box + -en, by analogy with oxen.

rasia

compartment or receptacle for receiving items

ramme

rectangular border around an image, text, etc.

ruutu

small area on a document for a tick mark

tofu

empty box displayed by some computer systems in place of a character not supported by available fonts

(geometry, by extension) A rectangular object in any number of dimensions.


analysis

en-noun

analysis (countable and uncountable, plural analyses)

From Medieval Latin analysis, from Ancient Greek ἀνάλυσις (análusis), from ἀναλύω (analúō, “I unravel, investigate”), from ἀνα- (ana-, “thoroughly”) + λύω (lúō, “I loosen”).

language analysis for the determination of origin

List of terms used in mathematical analysis

2014, Lara Alcock, How to Think about Analysis, Oxford University Press:

(uncountable, mathematics) A broad field of study in modern mathematics (often mentioned alongside algebra) which developed out of the calculus, concerned with the behavior of functions, sequences, series, limits, metric spaces, measures and more.


act

en-verb

act (third-person singular simple present acts, present participle acting, simple past and past participle acted)

acts (present singular third-person)
acting (participle present)
acted (participle past)
acted (past)
act (infinitive)

From Middle English acte, from Old French acte, from Latin ācta (“register of events”), plural of āctum (“decree, law”), from agere (“to do, to act”), ultimately from Proto-Indo-European *h₂éǵeti. Compare German Akte (“file”). Partially displaced deed, from Old English dǣd (“act, deed”).

This group acts on the circle, so it can't be left-orderable!

scalar multiplication
scalar multiplication

(intransitive, mathematics, construed with on or upon, of an algebraic structure) To possess an action onto (some other structure). Examples include the group action of a group on a set, the action of a ring on a module by scalar multiplication, and the action of a group or algebra on a vector space via a representation.


balance

en-noun

balance (countable and uncountable, plural balances)

bias

antonym(s) of “support for both viewpoints”

PIE word
 *dwóh₁
From Middle English balaunce, from Old French balance, from Late Latin *bilancia, from (accusative form of) Latin bilanx (“two-scaled”), from bi- + lanx (“plate, scale”).

The balance of the agreement remains in effect.

The invoice said he had only paid $50. The balance was $220.

Balance Luzon (Philippine usage)

(law, business, statistics) The remainder.


ball

ball (countable and uncountable, plural balls)

→ Cantonese: 波 (bo¹)

→ Japanese: ボール (bōru)

→ Makah: ba·la

→ Yoruba: bọ́ọ̀lù

From Middle English bal, ball, balle, from an unattested Old English *beall, *bealla (“round object, ball”) or Old Norse bǫllr (“a ball”), both from Proto-Germanic *balluz, *ballô (“ball”), from Proto-Indo-European *bʰol-n- (“ball, bubble”), from Proto-Indo-European *bʰel- (“to blow, inflate, swell”). Cognate with Old Saxon ball, Dutch bal, Old High German bal, ballo (German Ball (“ball”); Ballen (“bale”)). Related forms in Romance are borrowings from Germanic. See also balloon, bale.

ампыл

object, generally spherical, used for playing games

туп

ballistics: a solid nonexplosive missile

cold enough to freeze the balls off a brass monkey

(mathematics) Homologue or analogue of a disk in the Euclidean plane.

(mathematics) In 3-dimensional Euclidean space, the volume bounded by a sphere.

(mathematics) The set of points in a metric space of any number of dimensions lying within a given distance (the radius) of a given point.

գնդոլորտ

mathematics: set of points in a metric space lying within a given distance of a given point

(mathematics) The set of points in a topological space lying within some open set containing a given point.


base

en-noun

base (countable and uncountable, plural bases)

acid

antonym(s) of “chemical compound that will neutralize an alkali”

From Middle English base, bas, baas, from Old French base, from Latin basis, from Ancient Greek βάσις (básis). Doublet of basis and bass.

أَسَاس

something from which other things extend

(geometry) The lowest side of a triangle or other polygon, or the lowest face of a cone, pyramid or other polyhedron laid flat.

భూమి

త్రిభుజం వైశాల్యం = అర*భూమి*ఎత్తు

The logarithm to base 2 of 8 is 3.

(mathematics) A number raised to the power of an exponent.

base

math: number raised to the power of an exponent

(topology) The set of sets from which a topology is generated.

kanta

topology: set of sets from which a topology is derived

(topology) A topological space, looked at in relation to one of its covering spaces, fibrations, or bundles.

kanta

topology: topological space, looked at in relation to one of its covering spaces, fibrations, or bundles

(group theory) A sequence of elements not jointly stabilized by any nontrivial group element.


cover

cover (countable and uncountable, plural covers)

→ Hijazi Arabic: كَڤَر (kavar)

→ Portuguese: cover

Etymology tree
Proto-Indo-European *ḱe-?
Proto-Indo-European *ḱóm
Proto-Italic *kom
Old Latin com
Latin cum
Latin con-
Proto-Indo-European *h₁ep-?
Proto-Indo-European *h₁epi
Proto-Indo-European *h₂wer-
Proto-Indo-European *-yeti
Latin operiō
Latin cooperiō
Old French covrirbor.
Middle English coveren
English cover
From Middle English coveren, borrowed from Old French covrir, cueuvrir (modern French couvrir), from Late Latin coperire, from Latin cooperiō (“I cover completely”), from co- (intensive prefix) + operiō (“I close, cover”). Displaced native Middle English thecchen and bethecchen (“to cover”) (from Old English þeccan, beþeccan (“to cover”)), Middle English helen, (over)helen, (for)helen (“to cover, conceal”) (from Old English helan (“to conceal, cover, hide”)), Middle English wrien, (be)wreon (“to cover”) (from Old English (be)wrēon (“to cover”)), Middle English hodren, hothren (“to cover up”) (from Low German hudren (“to cover up”)).
According to the Oxford English Dictionary, the original sense of the verb and noun cover was “hide from view” as in its cognate covert. Except in the limited sense of “cover again”, the word recover is unrelated and is cognate with recuperate. Cognate with Spanish cubrir (“to cover”).

cumhdach

A cloth or similar material used to protect underlying items from dust, sunlight, insects etc. when not being used.

throw nickels around like manhole covers

The open intervals are a cover for the real numbers.

(combinatorics, topology) A collection (or family) of subsets of a given set, whose union contains every element of said original set.


collar

→ Hausa: kwala

→ Burmese: ကော်လာ (kaula)

→ Swahili: kola

From Middle English coler, borrowed from Old French coler (Modern French collier), from Late Latin collāre, from Latin collāris, from collum (“neck”). Cognate with Gothic 𐌷𐌰𐌻𐍃 (hals, “neck”), Old English heals (“neck”). Compare Spanish cuello (“neck”). More at halse.

(mathematics) A topological neighborhood around a submanifold that can be deformed to preserve a specified condition or structure.


control

en-verb

control (third-person singular simple present controls, present participle controlling, simple past and past participle controlled)

controls (present singular third-person)
controlling (participle present)
controlled (participle past)
controlled (past)

From Middle English controllen, from Old French contrerole, from Medieval Latin contrārotulum (“a counter-roll or register used to verify accounts”), from Latin contrā (“against, opposite”) + Medieval Latin rotulus, Latin rotula (“roll, a little wheel”), diminutive of rota (“a wheel”).

der

(transitive, statistics) (construed with for) To design (an experiment) so that the effects of one or more variables are reduced or eliminated.


connection

en-noun

connection (countable and uncountable, plural connections)

From Middle English conneccioun, connexioun, conneccyon, conneccion, from Latin connexionem (nominative connexio (“a conclusion, binding together”)), from connectō, an alternative spelling of cōnectō (“I bind together”), from compound of co- (“together”) and nectō (“I bind”).
In American English mid-18c., spelling shifted from connexion to connection (equivalent to connect + -ion), thus making connexion British dated and connection in international use.

disconnection

dysconnection, also archaic inconnection

(mathematics) A set of sets that contains the empty set, all one-element sets for any element that is included in any of the sets, and the union of any group of sets that are elements where the intersections of those sets is non-empty.


altitude

altitude (countable and uncountable, plural altitudes)

From Middle English, borrowed from Latin altitūdō (“height”), from altus (“high”).

The perpendicular height of a triangle is known as its altitude.

(geometry) The distance measured perpendicularly from a figure's vertex to the opposite side of the vertex.

yüksəklik

(commutative algebra, dated, of a ring) Krull dimension.


basis

basis (plural bases or (rare) baseis or (nonstandard) basises)

bases (plural)
baseis (plural rare)
basises (nonstandard plural)

From Latin basis, from Ancient Greek βάσις (básis), from Proto-Indo-European *gʷémtis, derived from Proto-Indo-European *gʷem- (whence also come). Doublet of base.

linearly independent
linearly independent

(linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.

բազիս

linearly independent, spanning set of vectors

The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.

(topology) A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.


spaceship

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

* space + ship
* (programming operator): From its resemblance to the shape of a flying saucer.

The spaceships look like a row of threshers harvesting a field of wheat; the thickness in the direction of motion is only about 10 cells.

1989 October 26, Richard Schroeppel, “Some recent Life results”, in comp.theory.cell-automata (Usenet):

We describe software that searches for spaceships in Conway's Game of Life and related two-dimensional cellular automata.

2002, Richard Nowakowski, More Games of No Chance, page 433:

Synthesis of spaceship flotillas is even more complicated than synthesis of oscillators, since spaceships are like oscillators that move[…]

2010, Andrew Adamatzky, Game of Life Cellular Automata, page 126:

(cellular automata) A finite pattern that reappears after a certain number of generations in the same orientation but in a different position.


effect

effect (countable and uncountable, plural effects)

Of the noun: from Middle English effect, from Old French effect (modern French effet), from Latin effectus (“an effect, tendency, purpose”), from efficiō (“accomplish, complete, effect”); see effect as a verb. Displaced Old English fremming, fremednes from fremman.
Of the verb: from Middle English effecten, partly from Medieval Latin effectuō, from Latin effectus, perfect passive participle of efficiō (“accomplish, complete, do, effect”), from ex (“out”) + faciō (“do, make”) (see fact and compare affect, infect) and partly from the noun effect.

der

effect size

therapeutic effect

(sciences, statistics) An influence or causal association between two variables.


distribution

en-noun

distribution (countable and uncountable, plural distributions)

From Old French, from Latin distributio, from distribuere 'to distribute', itself from dis- 'apart' + tribuere 'to' (from tribus).

probability distribution
probability distribution

(mathematics, statistics) A probability distribution; the set of relative likelihoods that a variable will have a value in a given interval.

تَوْزِيع

statistics: set of relative likelihoods — see also probability distribution

differential geometry
differential geometry

(mathematics, differential geometry) A subset of the tangent bundle of a manifold that satisfies certain properties; used to construct the notions of integrability and foliation of a manifold.


different

From Middle English different, from Old French different, from Latin differēns, present active participle of differō (“I differ”); see differ.
Broadly ousted the native Old English ungelic.


depth

depth (countable and uncountable, plural depths)

From Middle English depthe, from Old English *dīepþ (“depth”), from Proto-Germanic *diupiþō (“depth”), equivalent to deep + -th. Cognate with Scots deepth (“depth”), Saterland Frisian Djüpte (“depth”), West Frisian djipte (“depth”), Dutch diepte (“depth”), Low German Deepde (“depth”), Danish dybde (“depth”), Icelandic dýpt (“depth”), Gothic 𐌳𐌹𐌿𐍀𐌹𐌸𐌰 (diupiþa, “depth”).

(statistics) the lower of the two ranks of a value in an ordered set of values

(cryptography) A set of more than one ciphertext enciphered with the same key.

(algebra, ring theory) An invariant of rings and modules, encoding information about dimensionality; see Depth (ring theory).


end

beginning

antonym(s) of “final point of something”

→ Japanese: エンド

From Middle English ende, from Old English ende, from Proto-West Germanic *andī, from Proto-Germanic *andijaz, from Proto-Indo-European *h₂entíos, from *h₂ent- (“front, forehead”).
See also Dutch einde, German Ende, Norwegian ende, Swedish ände; also Old Irish ét (“end, point”), Latin antiae (“forelock”), Albanian anë (“side”), Ancient Greek ἀντίος (antíos, “opposite”), Sanskrit अन्त्य (antya, “last”). More at and and anti-.
The verb is from Middle English enden, endien, from Old English endian (“to end, to make an end of, complete, finish, abolish, destroy, come to an end, die”), from Proto-Germanic *andijōną (“to finish, end”), denominative from *andijaz.

der

snitches get stitches and end up in ditches

(mathematics) An ideal point of a graph or other complex. See End (graph theory)


flat

en-adj

flat (comparative flatter, superlative flattest)

flatter (comparative)
flattest (superlative)

bumpy

antonym(s) of “having no variations in altitude”

→ Portuguese: flat

From Middle English flat, a borrowing from Old Norse flatr (compare Norwegian and Swedish flat, Danish flad), from Proto-Germanic *flataz, from Proto-Indo-European *pleth₂- (“flat”); akin to Saterland Frisian flot (“smooth”), German Flöz (“a geological layer”), Ancient Greek πλατύς (platús), Latvian plats, Sanskrit प्रथस् (prathas, “extension”). Doublet of plat and pleyt.
The noun is from Middle English flat (“level piece of ground, flat edge of a weapon”), from the adjective.
The algebraic sense was coined by Serre in a 1956 paper, originally as French plat.

inh

(algebra, ring theory, of a ring homomorphism) Such that its target, regarded as a module over its source, is flat (as above).

(algebraic geometry, scheme theory, of a morphism of schemes) Such that the induced map on every stalk is flat (as a map of rings).


flat

(geometry) A subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.


apex

Borrowed from Latin apex (“point, tip, summit”).

The highest or the greatest part of something, especially forming a point.

(geometry) The highest point in a plane or solid figure, relative to a base line or plane.


butterfly

From Middle English buterflie, butturflye, boterflye, from Old English buterflēoge, equivalent to butter + fly. Cognate with Dutch botervlieg, German Butterfliege (“butterfly”). The name may have originally been applied to butterflies of a yellowish color, and/or reflected a belief that butterflies ate milk and butter (compare German Molkendieb (“butterfly”, literally “whey-thief”) and Low German Botterlicker (“butterfly”, literally “butter-licker”)), or that they excreted a butter-like substance (compare Dutch boterschijte (“butterfly”, literally “butter-shitter”)). Compare also German Schmetterling from Schmetten (“cream”), German Low German Bottervögel (“butterfly”, literally “butter-fowl”). More at butter, fly.
An alternate theory suggests that the first element may have originally been Old English butor- (“beater”), a mutation of bēatan (“to beat”), but this would not explain the cognates in other languages or the other names formed with milk products.
Superseded non-native Middle English papilion (“butterfly”) borrowed from Old French papillon (“butterfly”).

cog

Any of several plane curves that look like a butterfly; see Butterfly curve (transcendental) and Butterfly curve (algebraic).


power

en-noun

power (countable and uncountable, plural powers)

→ German: Power

→ Welsh: pŵer

/ˈpʌʊ̯.(ə)ɹ/

From Middle English power, poer, from Old French poeir, from Vulgar Latin potēre, from Latin posse, whence English potent. Compare French pouvoir. Displaced the native Old English anweald.

A product of equal factors (and generalizations of this notion): xⁿ, read as "x to the power of n" or the like, is called a power and denotes the product x×x×⋯×x, where x appears n times in the product; x is called the base and n the exponent.

(statistics) The probability that a statistical test will reject the null hypothesis when the alternative hypothesis is true.

voimakkuus

statistics: probability of correctly rejecting the null hypothesis


proportion

proportion (countable and uncountable, plural proportions)

/pɹəˈpɔɹʃən/

/pɹəˈpɔːʃən/

/pɹəˈpoəʃən/

From Middle English proporcion, from Old French proportion, from Latin prōportiō (“comparative relation, proportion, symmetry, analogy”), from pro (“for, before”) + portio (“share, part”); see portion.

der

(mathematics, countable) A statement of equality between two ratios.

пропорция

(mathematics) a statement of equality between two ratios

(mathematics, archaic) The "rule of three", in which three terms are given to find a fourth.


outcome

Three is a possible outcome of tossing a six-sided die.

(probability theory) The result of a random trial. An element of a sample space.


hedgehog

/ˈhɛd͡ʒ.hɒɡ/

/ˈhɛd͡ʒ.hɔɡ/

From Middle English heyghoge; equivalent to hedge + hog. Eclipsed non-native Middle English yrchoun, irchoun (“hedgehog”), from Old French hirchoun, herichon (“hedgehog”); and Middle English il, from Old English īl, iġil (“hedgehog”).

(differential geometry) A type of plane curve; see Hedgehog (geometry).


mole

Calqued from German Mol; spelled as if it had come directly from molecule or Latin moles (the ultimate source of Mol and molecule in any event).

International System of Units
International System of Units

(chemistry, physics) In the International System of Units, the base unit of amount of substance; the amount of substance of a system which contains exactly 6.02214076×10²³ elementary entities (atoms, ions, molecules, etc.). Symbol: mol. The number of atoms is known as Avogadro’s number. [from 1897]


URL

/ˌjuːˌɑːɹˈɛl/

ΟΕΠ

ομοιόμορφος εντοπιστής πόρων (omoiómorfos entopistís póron)

Coordinate term: LRL

(medicine, statistics) Initialism of upper reference limit.


nit

This brightness of this LCD screen is between 900 and 1000 nits.


heart

en-noun

heart (countable and uncountable, plural hearts)

Torres Strait Creole: at

→ Bengali: হার্ট (harṭ)

→ Cantonese: heart

→ Cebuano: Heart

→ Irish: hart

→ Japanese: ハート (hāto); ハツ (hatsu) (from hearts)

→ Korean: 하트 (hateu)

→ Tagalog: Heart

PIE word
 *ḱḗr
From Middle English herte, from Old English heorte (“heart”), from Proto-West Germanic *hertā, from Proto-Germanic *hertô (“heart”), from Proto-Indo-European *ḱérd (“heart”). Doublet of cardia; see also core.
Most of the modern figurative senses (such as passion or compassion, spirit, inmost feelings, especially love, affection, and courage) were present in Old English. However, the meaning “center” dates from the early 14th century.
The verb sense “to love” is from the 1977 I ❤ NY advertising campaign.

the way to a man's heart is through his stomach

I know almost every Beatles song by heart.

(obsolete, except in the phrase "by heart") Memory.

"Aw. Thank you." The Cherub kissed the air between them and sent a small cluster of tiny red hearts at her.

1998, Pat Cadigan, Tea From an Empty Cup, page 106:

A conventional shape or symbol used to represent the heart, love, or emotion: ♥.

(cartomancy) The twenty-fourth Lenormand card.


heart

en-verb

heart (third-person singular simple present hearts, present participle hearting, simple past and past participle hearted)

hearts (present singular third-person)
hearting (participle present)
hearted (participle past)
hearted (past)

We're but the sum of all our terrors until we heart the dove.

2001 April 6, Michael Baldwin, “The Heart Has Its Reasons”, in Commonweal:

2006, Susan Reinhardt, Bulldog doesn't have to rely on the kindness of strangers to draw attention, Citizen-Times.com
I guess at this point we were supposed to feel elated she'd come to her senses and decided she hearts dogs after all.

The further we delve into this "story", the more convinced we become of one thing: We heart the Goss.

2008 January 30, “Cheese in our time: Blur and Oasis to end feud with a Stilton”, in The Guardian, London:

2008 July 25, "The Media Hearts Obama?", On The Media, National Public Radio

Lots of people say they love their hometown, but no one hearts NY quite like Milton Glaser.

2019 July 4, John Leland, “Why This Famous Graphic Designer, at 90, Still ♥s NY”, in New York Times:

(transitive, humorous, informal) To be fond of. Often bracketed or abbreviated with a heart symbol.


logic

en-noun

logic (countable and uncountable, plural logics)

→ Chinese: 邏輯 /逻辑 (luójí)

From Middle English logik, from Old French logike, from Latin logica, from Ancient Greek λογική (logikḗ, “logic”), from feminine of λογικός (logikós, “of or pertaining to speech or reason or reasoning, rational, reasonable”), from λόγος (lógos, “speech, reason”). Displaced native Old English flitcræft (literally “art of arguing”).

ncog

(uncountable, mathematics) The mathematical study of relationships between rigorously defined concepts and of mathematical proof of statements.

(countable, mathematics) A formal or informal language together with a deductive system or a model-theoretic semantics.


join

From Middle English joinen, joynen, joignen, from Old French joindre, juindre, jungre, from Latin iungō (“join, yoke”, verb), from Proto-Indo-European *yewg- (“to join, unite”). Cognate with Old English iucian, iugian, ġeocian, ġyċċan (“to join; yoke”). More at yoke.

der

(algebra) The lowest upper bound, an operation between pairs of elements in a lattice, denoted by the symbol ∨.


low

en-adj

low (comparative lower, superlative lowest)

lower (comparative)
lowest (superlative)

From Middle English lowe, lohe, lāh, from Old Norse lágr (“low”), from Proto-Germanic *lēgaz (“lying, flat, situated near the ground, low”), from Proto-Indo-European *legʰ- (“to lie”).
Cognate with Scots laich (“low”), Low German leeg (“low, feeble, bad”), Danish lav (“low”), Icelandic lágur (“low”), West Frisian leech (“low”), North Frisian leeg, liig (“low”), Dutch laag (“low”), obsolete German läg (“low”). More at lie.

laag

in a position comparatively close to the ground

слаб

lacking health or vitality; feeble; weak

could eat the arse out of a low flying duck

could eat the crotch out of a low flying duck

could eat the crutch from a low flying duck

mackerel sky and mare's-tails make lofty ships carry low sails

mackerel sky and mare's-tails make tall ships carry low sails

diets low in vitamin A

made from low-carbon steel

Small, not high (in amount or quantity, value, force, energy, etc).

Having a small or comparatively smaller concentration of (a substance, which is often but not always linked by "in" when predicative).

running low on cash

When silica is in low supply other classes of algae dominate the phytoplankton composition.

2002, V.N. Bashkin, Robert W. Howarth, Modern Biogeochemistry, →ISBN, page 151:

Depleted, or nearing deletion; lacking in supply.

My credit union charges a low interest rate. Jogging during a whiteout, with such low temperatures and low visibility, is dangerous. The store sold bread at low prices, and milk at even lower prices. The contractors gave a low estimate of the costs. low cholesterol a low voltage wire a low number

Unfortunately, low winds were the rule over the local waters and this craft was no better, if as good, as ordinary sailboats under such conditions.

1989, Bernard Smith, Sailloons and Fliptackers: The Limits to High-speed Sailing, →ISBN:

The ability to shift profits to low-tax countries by locating intellectual property in them, which is then licensed to related businesses in high-tax countries, is often assumed to be the preserve of high-tech companies. […] current tax rules make it easy for all sorts of firms to generate […] “stateless income”: profit subject to tax in a jurisdiction that is neither the location of the factors of production that generate the income nor where the parent firm is domiciled.

2013 June 22, “T time”, in The Economist, volume 407, number 8841, page 68:


long

From Middle English long, lang, from Old English long, lang (“long, tall, lasting”), from Proto-West Germanic *lang, from Proto-Germanic *langaz (“long”), from Proto-Indo-European *dlongʰos (“long”).
Cognate with Scots lang (“long”), North Frisian long, lung (“long”), Saterland Frisian loang (“long”), Norwegian, West Frisian, Dutch and German lang (“long”), Swedish lång (“long”), Icelandic langur (“long”), Portuguese longo (“long”), Spanish luengo (“long”), French long, Latin longus (“long”), Russian дли́нный (dlínnyj), до́лго (dólgo), Sanskrit दीर्घ (dīrgha, “long”).
The word exceptionally retains the Old English darkening of -a- before nasals. Though there are other such examples in Middle and Modern English (e.g. bond, song, throng, wrong), the o-form may have been reinforced by Old French long, from Latin longus, from the same Indo-European word. Doublet of lungo and lunge.

A long is typically 64 bits in a 32-bit environment.

(programming) A long integer variable, twice the size of an int, two or four times the size of a short, and half of a long long.


tall

en-adj

tall (comparative taller, superlative tallest)

taller (comparative)
tallest (superlative)

→ Welsh: tal

From Middle English tall, talle, tal (“seemly, becoming, handsome, good-looking, excellent, good, valiant, lively in speech, bold, great, large, big”), from Old English *tæl, ġetæl (“swift, ready, having mastery of”), from Proto-Germanic *talaz (“submissive, pliable, obedient”), from Proto-Indo-European *dol-, *del- (“to aim, calculate, adjust, reckon”).
Cognate with Scots tal (“high, lofty, tall”), Old Frisian tel (“swift”), Old Saxon gital (“quick”), Old High German gizal (“active, agile”), Gothic 𐌿𐌽𐍄𐌰𐌻𐍃 (untals, “indocile, disobedient”).
The Oxford English Dictionary notes: "The sense development [of tall] is remarkable, but is paralleled more or less by that of other adjectives expressing estimation, such as buxom, canny, clean, clever, cunning, deft, elegant, handsome, pretty, proper; German klein, as compared with English clean, presents the antithesis to modern tall as compared to tall in early Middle English. It has been conjectured that in the sense 'high of stature' it is a different word, adopted from the Welsh tal in some sense; but the latter is, according to Professor Rhŷs, merely a 16th-century borrowing of the English word (in Owen Pughe's Dictionary erroneously mixed up with the genuine Welsh word tal (“end, brow, forehead”), with which it has no possible connection.)"

cog

Being tall is an advantage in basketball.

Then came a maid with hand-bag and shawls, and after her a tall young lady. She stood for a moment holding her skirt above the grimy steps,[…], and the light of the reflector fell full upon her.

1897 December (indicated as 1898), Winston Churchill, chapter V, in The Celebrity: An Episode, New York, N.Y.: The Macmillan Company; London: Macmillan & Co., Ltd., →OCLC:

He′d been packed in with all the other journos, standing out only in that he was taller than most and didn′t make as much noise.

2000, Robert Bingham, Lightning on the Sun, page 34:

(of a person) Having a vertical extent greater than the average. For example, somebody with a height of over 6 feet would generally be considered to be tall.

"That's tall talk."
"Not an inch taller than the truth."

1870, The Cornhill Magazine, volume 21, page 9:

(of a story) Hard to believe, such as a tall story or a tall tale.

(chiefly US, of a cup of coffee) Smaller than grande, usually 8 ounces (~ 230 ml).


tall

Do you have this in a tall?

A tall serving of a drink, especially one from Starbucks, which contains 12 ounces.


narrow

en-adj

narrow (comparative narrower, superlative narrowest)

narrower (comparative)
narrowest (superlative)

From Middle English narow, narowe, narewe, narwe, naru, from Old English nearu (“narrow, strait, confined, constricted, not spacious, limited, petty; limited, poor, restricted; oppressive, causing anxiety (of that which restricts free action of body or mind), causing or accompanied by difficulty, hardship, oppressive; oppressed, not having free action; strict, severe”), from Proto-West Germanic *naru, from Proto-Germanic *narwaz (“constricted, narrow”), from Proto-Indo-European *(s)ner- (“to turn, bend, twist, constrict”).
Cognate with Scots naro, narow, narrow (“narrow”), North Frisian naar, noar, noor (“narrow”), Saterland Frisian noar (“bleak, dismal, meager, ghastly, unwell”), Saterland Frisian Naarwe (“scar”), West Frisian near (“narrow”), Dutch naar (“dismal, bleak, ill, sick”), Low German naar (“dismal, ghastly”), German Nehrung (“spit, narrow peninsula”), Norwegian norve (“a clip, staple”), Icelandic narrow- (“njörva-”, in compounds).

cog

a narrow hallway

She was like a Beardsley Salome, he had said. And indeed she had the narrow eyes and the high cheekbone of that creature, and as nearly the sinuosity as is compatible with human symmetry.

1921, Ben Travers, chapter 1, in A Cuckoo in the Nest, Garden City, N.Y.: Doubleday, Page & Company, published 1925, →OCLC:

Just under the ceiling there were three lunette windows, heavily barred and blacked out in the normal way by centuries of grime. Their bases were on a level with the pavement outside, a narrow way which was several feet lower than the road behind the house.

1963, Margery Allingham, chapter 14, in The China Governess: A Mystery, London: Chatto & Windus, →OCLC:

Not long ago, it was difficult to produce photographs of tiny creatures with every part in focus. That’s because the lenses that are excellent at magnifying tiny subjects produce a narrow depth of field. A photo processing technique called focus stacking has changed that.

2013 July-August, Catherine Clabby, “Focus on Everything”, in American Scientist:

Having a small width; not wide; having opposite edges or sides that are close, especially by comparison to length or depth.

(phonetics) Formed (as a vowel) by a close position of some part of the tongue in relation to the palate; or (according to Bell) by a tense condition of the pharynx; distinguished from wide.

suppea

phonetics: formed (as a vowel) by a close position of some part of the tongue in relation to the palate

a narrow character; a narrow stream

(computing) Of or supporting only those text characters that can fit into the traditional 8-bit representation.


narrow

en-verb

narrow (third-person singular simple present narrows, present participle narrowing, simple past and past participle narrowed)

narrows (present singular third-person)
narrowing (participle present)
narrowed (participle past)
narrowed (past)

From Middle English narwen (“to narrow”); see there for more details, but ultimately derived from the noun.

to narrow an int variable to a short variable

(transitive, programming) To convert to a data type that cannot hold as many distinct values.


wide

en-adj

wide (comparative wider or more wide, superlative widest or most wide)

wider (comparative)
more wide (comparative)
widest (superlative)
most wide (superlative)

PIE word
 *dwóh₁
From Middle English wid, wyd, from Old English wīd (“wide, vast, broad, long; distant, far”), from Proto-Germanic *wīdaz, from Proto-Indo-European *h₁weydʰh₁- (“to separate, divide”), a dissimilated univerbation from *dwi- (“apart, asunder, in two”) + *dʰeh₁- (“to do, put, place”).
Cognate with Scots wyd, wid (“of great extent; vast”), West Frisian wiid (“broad; wide”), Dutch wijd (“wide; large; broad”), German weit (“far; wide; broad”), Danish vid (“wide”), Swedish vid (“wide”), Icelandic víður (“wide”), Latin dīvidō (“separate, sunder”), Latin vītō (“avoid, shun”). Related to widow.

compound

We walked down a wide corridor.

Over a wider region either side of the path of totality, a partial eclipse is seen.

1993, Jacqueline Mitton, The Penguin Dictionary of Astronomy, 2nd edition (paperback), Penguin Books, →ISBN, page 127:

Having a large physical extent from side to side.

wyd

having a large physical extent from side to side

The inquiry had a wide remit.

The single-imaging optic of the mammalian eye offers some distinct visual advantages. Such lenses can take in photons from a wide range of angles, increasing light sensitivity. They also have high spatial resolution, resolving incoming images in minute detail.

2013 July-August, Fenella Saunders, “Tiny Lenses See the Big Picture”, in American Scientist:

Three-way girls offered the widest array of services. One twenty-two-year-old prostitute declared to an undercover vice investigator in New York City, "I am a three-way girl."

2014, Jessica R. Pliley, Policing Sexuality, page 192:

The wide, lifeless expanse.

(Scotland, Northern England, now rare) Vast, great in extent, extensive.

a wide character; a wide stream

(computing) Of or supporting a greater range of text characters than can fit into the traditional 8-bit representation.

But the first visitor to penetrate from the outside world proved to be Sergeant Williams; large and pink and scrubbed-looking; and for a little while Grant forgot about battles long ago and considered wide boys alive today.

1951, Josephine Tey, The Daughter of Time, page 31:

(British, slang, only in "wide boy") Sharp-witted.


high

en-adj

high (comparative higher, superlative highest)

higher (comparative)
highest (superlative)

Sranan Tongo: hei

From Middle English high, heigh, heih, from Old English hēah (“high, tall, lofty, high-class, exalted, sublime, illustrious, important, proud, haughty, deep, right”), from Proto-West Germanic *hauh (“high”), from Proto-Germanic *hauhaz (“high”), from Proto-Indo-European *kewk- (“to elevate, height”). Cognate with Scots heich (“high”), Saterland Frisian hooch (“high”), West Frisian heech (“high”), Dutch hoog (“high”), Low German hoog (“high”), German hoch (“high”), Swedish hög (“high”), Norwegian høy (“high”), Icelandic hár (“high”), Lithuanian kaukas (“bump, boil, sore”).

der

My bank charges me a high interest rate.

I was running a high temperature and had high cholesterol.

high voltage high prices high winds a high number

Can heavenly minds such high resentment show?

1697, Virgil, “The First Book of the Æneis”, in John Dryden, transl., The Works of Virgil: Containing His Pastorals, Georgics, and Æneis. […], London: […] Jacob Tonson, […], →OCLC:

Ignition voltage needs to be high enough to overcome the high resistance created by the air gap.

2005, Tracy Martin, How To Diagnose and Repair Automotive Electrical Systems, page 16:

Anyone can determine for himself whether certain wire is high carbon or not. Heat a piece of the wire red hot and while red plunge into water till cold.

1907, The American Exporter, volume 60, page 101:

Large, great (in amount or quantity, value, force, energy, etc).

Carrots are high in vitamin A. made from a high-copper alloy

Having a large or comparatively larger concentration of (a substance, which is often but not always linked by "in" when predicative).


solid

From Middle English solid, from the adjective, Middle French solide, or Latin solidum. Doublet of solidum.

(geometry) A three-dimensional figure (as opposed to a surface, an area, or a curve).


salt

en-noun

salt (countable and uncountable, plural salts)

Bislama: sol

Tok Pisin: sol

PIE word
 *séh₂ls
From Middle English salt, from Old English sealt, from Proto-West Germanic *salt, from Proto-Germanic *saltą, from Proto-Indo-European *séh₂ls (“salt”). Doublet of sal, ultimately from Latin sāl (“salt”), which it superseded as the general term for "salt".

(cryptography) A sequence of random data added to plain text data (such as passwords or messages) prior to encryption or hashing, in order to make brute force decryption more difficult.

sůl

additional bytes inserted into an encryption


salt

en-verb

salt (third-person singular simple present salts, present participle salting, simple past and past participle salted)

salts (present singular third-person)
salting (participle present)
salted (participle past)
salted (past)

(cryptography) To add filler bytes before encrypting, in order to make brute-force decryption more resource-intensive.


tail

Sranan Tongo: tere

From Middle English tail, tayl, teil, from Old English tæġl (“tail”), from Proto-West Germanic *tagl, from Proto-Germanic *taglą (“hair, fiber; hair of a tail”), from Proto-Indo-European *doḱ- (“hair of the tail”), from Proto-Indo-European *deḱ- (“to tear, fray, shred”). Cognate with Scots tail (“tail”), Saterland Frisian Tail (“tail, end”), West Frisian teil (“tail”), Dutch teil (“tail, haulm, blade”), Low German Tagel (“twisted scourge, whip of thongs and ropes; end of a rope”), German Zagel (“tail”), dialectal Danish tavl (“hair of the tail”), Swedish tagel (“hair of the tail, horsehair”), Norwegian tagl (“tail”), Icelandic tagl (“tail, horsetail, ponytail”), Gothic 𐍄𐌰𐌲𐌻 (tagl, “hair”). In some senses, apparently by a generalization of the usual opposition between head and tail.

hali

of cattle, in addition to reptiles, amphibians, and basically all animals that do not fall into the other categories; also used for inanimate objects and figuratively

have the world by the tail on a downhill pull

the cow knows not the worth of its tail till it loses it

trust someone as far as one could fling a bull by the tail

(statistics) The part of a distribution most distant from the mode; as, a long tail.

häntä

statistics: part of a distribution most distant from the mode

A sequence (a#95;n) is said to be frequently 0 if every tail of the sequence contains 0.

(mathematics) All the last terms of a sequence, from some term on.

häntä

math: last terms of a sequence, from some term on


blade

From Middle English blade, blad, from Old English blæd (“leaf”), from Proto-West Germanic *blad, from Proto-Germanic *bladą, from Proto-Indo-European *bʰl̥h₃-o-to-m, from *bʰleh₃- (“to thrive, bloom”).
See also West Frisian bled, Dutch blad, German Blatt, Danish blad, Irish bláth (“flower”), Welsh blodyn (“flower”), Tocharian A pält, Tocharian B pilta (“leaf”), Albanian fletë (“leaf”). Similar usage in German Sägeblatt (“saw blade”, literally “saw leaf”). Doublet of blat. More at blow.

teh

typically sharp-edged working end of a knife or other cutting tool

Holonym: multivector

(mathematics) An exterior product of vectors. (The product may have more than two factors. Also, a scalar counts as a 0-blade, a vector as a 1-blade; an exterior product of k vectors may be called a k-blade.)


brass

From Portuguese braça and Spanish braza, from Old Galician-Portuguese and Old Spanish braça, from Latin brachia, variant of bracchium (“arm, cubit”), from Ancient Greek βραχίων (brakhíōn, “upper arm”).

der

(historical, obsolete) Synonym of brace, a traditional unit of measure equivalent to a fathom (6 feet) or about 1.6 m, especially as the Spanish braza and Portuguese braça, also French brasse.


sharp

en-adj

sharp (comparative sharper, superlative sharpest)

sharper (comparative)
sharpest (superlative)

bland

antonym(s) of “having an intense and acrid flavour”

From Middle English scharp, from Old English sċearp, from Proto-West Germanic *skarp, from Proto-Germanic *skarpaz, from Proto-Indo-European *(s)kerb-, from *(s)ker- (“to cut”).
Cognate with West Frisian skerp, Low German scharp, Dutch scherp, German scharf, Danish skarp. Compare Irish cearb (“keen; cutting”), Latin acerbus (“tart, bitter”), Tocharian B kärpye (“rough”), Latvian skârbs (“sharp, rough”), Russian щерба (ščerba, “notch”), Polish szczerba (“gap, dent, jag, chip, nick, notch”), Albanian harb (“rudeness”). More at shear.

better than a poke in the eye with a sharp stick

Sure, any planar graph can be five-colored. But that result is not sharp: in fact, any planar graph can be four-colored. That is sharp: the same can't be said for any lower number.

(mathematics, of a statement) Said of as extreme a value as possible.


smooth

smooth (comparative smoother, superlative smoothest)

smoother (comparative)
smoothest (superlative)

From Middle English smothe, smethe, from Old English smēþe, smōþ, both from Proto-West Germanic *smanþī, of unknown origin. Cognate with Scots smuith (“smooth”), Low German smood and smödig (“smooth, malleable, ductile”), Dutch smeuïg (“smooth”) (from earlier smeudig).

a smooth sea never made a skilled sailor

the course of true love never did run smooth

Any ANALYTIC FUNCTION is smooth. But a smooth function is not necessarily analytic.

2003, Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, →ISBN, page 419:

(mathematics, of a function) Having derivatives of all finite orders at all points within the function’s domain.

光滑

mathematics, of a function: Having derivatives of all finite orders at all points within the function’s domain

(mathematics, of a number) That factors completely into small prime numbers.


smooth

A smooth of the potato data set has already been given in Figure 1.2.

1990, Wolfgang Härdle, Applied Nonparametric Regression, →ISBN, page 17:

(statistics) The analysis obtained through a smoothing procedure.

изглаждане

statistics: analysis obtained through a smoothing procedure


smooth

en-verb

smooth (third-person singular simple present smooths, present participle smoothing, simple past and past participle smoothed)

smooths (present singular third-person)
smoothing (participle present)
smoothed (participle past)
smoothed (past)

[…] the 7-month moving averages provide better smoothing of the data in this case than do the 3-month moving averages.

1999, Murray R. Spiegel, Larry J. Stephens, Schaum’s Outline of Theory and Problems of Statistics, →ISBN, page 457:

(statistics, image processing, digital audio) To capture important patterns in the data, while leaving out noise.

image processing; digital audio; image processing; digital audio

изглаждам

statistics: capture important patterns in the data, while leaving out noise


float

float (third-person singular simple present floats, present participle floating, simple past and past participle floated)

floats (present singular third-person)
floating (participle present)
floated (participle past)
floated (past)

From Middle English floten, from Old English flotian (“to float”), from Proto-West Germanic *flotōn, from Proto-Germanic *flutōną (“to float”), from Proto-Indo-European *plewd-, *plew- (“to float, swim, fly”).
Cognate with Saterland Frisian flotje (“to float”), West Frisian flotsje (“to float”), Dutch vlotten (“to float”), Middle Low German vloten, vlotten (“to float, swim”), German flötzen, flößen (“to float”), Swedish flotta (“to float”), Icelandic fljóta, Old English flēotan (“to float, swim”), Ancient Greek πλέω (pléō), Lithuanian plaukti, Russian пла́вать (plávatʹ). Compare flow, fleet.

ভাসানো

to cause something to be suspended in a liquid of greater density

(intransitive, aviation) To remain airborne, without touching down, for an excessive length of time during landing, due to excessive airspeed during the landing flare.

leijua

aviation: to remain airborne for an excessive length of time during landing

To get the footer acting right, you need to float it and clear it on both margins.

2010, Andy Harris, HTML, XHTML and CSS All-In-One For Dummies, page 290:

(computing, publishing, transitive) To cause (an element within a document) to float above or beside others.


flow

en-noun

flow (countable and uncountable, plural flows)

From Middle English flowe, from the verb (see below). The psychology sense “state of focus” was coined by Mihaly Csikszentmihalyi in 1975.

coin

The notion of flow is basic to the study of ordinary differential equations.

(mathematics) A formalization of the idea of the motion of particles in a fluid, as a group action of the real numbers on a set.


dust

en-noun

dust (countable and uncountable, plural dusts)

→ Russian: дуст (dust)

From Middle English dust, doust, from Old English dūst (“dust, dried earth reduced to powder; other dry material reduced to powder”), from the fusion of Proto-Germanic *dustą (“dust”) and *dunstą (“mist, dust, evaporation”), both from Proto-Indo-European *dʰewh₂- (“to smoke, raise dust”).
Cognate with Scots dust, dist (“dust”), Dutch duist (“pollen, dust”) and dons (“down, fuzz”), German Dust (“dust”) and Dunst (“haze”), Swedish dust (“dust”), Icelandic dust (“dust”), Latin fūmus (“smoke, steam”). Also related to Swedish dun (“down, fluff”), Icelandic dúnn (“down, fluff”). See down.

der

(countable, mathematics) A totally disconnected set of points with a fractal structure.

(cryptocurrencies) Tiny amounts of cryptocurrency left over after a transaction due to rounding error.


dust

en-verb

dust (third-person singular simple present dusts, present participle dusting, simple past and past participle dusted)

dusts (present singular third-person)
dusting (participle present)
dusted (participle past)
dusted (past)

(cryptocurrencies) To attempt to identify the owner of (a cryptocurrency wallet) by sending tiny amounts of cryptocurrency.


stone

stone (third-person singular simple present stones, present participle stoning, simple past and past participle stoned)

stones (present singular third-person)
stoning (participle present)
stoned (participle past)
stoned (past)

From Middle English ston, stone, stan, from Old English stān, from Proto-West Germanic *stain, from Proto-Germanic *stainaz, from Proto-Indo-European *steyh₂- (“to stiffen”).
See also West Frisian stien, Saterland Frisian Steen, Dutch steen, German Stein, Danish and Swedish sten, Norwegian stein; also Russian стена́ (stená, “wall”), Ancient Greek στία (stía, “pebble”), στέαρ (stéar, “tallow”), Albanian shtëng (“hardened or pressed matter”), Sanskrit स्त्यायते (styāyate, “it hardens”)). Doublet of stein.

cog

I was stoning the whole of today.

2003, Roger, Joy, Vera and Amanda Loh, Facts about Singapore: Differences between Ohio and Singapore:

Resume writing class lesson 2, stoning.

2011 November 2, Shermaine Ong, (Please provide the book title or journal name):

The Marina Barrage is a reservoir, but everyone goes there because the spacious greenery at the top is the perfect place for stoning, which is Singlish for hanging out and chilling.

2015 April 8, Becky Osawa, Trekking with Becky: Stoning at the Marina Barrage, Singapore:

(intransitive, Singapore, slang) To do nothing, to stare blankly into space and not pay attention when relaxing or when bored.


space

en-noun

space (countable and uncountable, plural spaces)

From Middle English space, from Anglo-Norman space, variant of espace, espas et al., and spaze, variant of espace, from Latin spatium, from Proto-Indo-European *(s)peh₂- (“to stretch, to pull”).

مَسَافَة

gap between written characters, lines etc.

ala

figuratively: field, area, or sphere of activity or endeavour — see also area, domain, field, sector, sphere

Fully Automated Luxury Queer Space Communism

(heading) A bounded or specific extent, physical or otherwise.

(geometry) A set of points, each of which is uniquely specified by a number (the dimensionality) of coordinates.

Functional analysis is best approached through a sound knowledge of Hilbert space theory.

(countable, mathematics) A generalized construct or set whose members have some property in common; typically there will be a geometric metaphor allowing these members to be viewed as "points". Often used with a restricting modifier describing the members (e.g. vector space), or indicating the inventor of the construct (e.g. Hilbert space).

espai

mathematics: generalized construct or set


volume

en-noun

volume (countable and uncountable, plural volumes)

From Middle English volume, from Old French volume, from Latin volūmen (“book, roll”), from volvō (“roll, turn about”).

The room is 9×12×8, so its volume is 864 cubic feet.

The proper products can improve your hair's volume.

Volatiles of kecap manis and its raw materials were extracted using Likens-Nickerson apparatus with diethyl ether as the extraction solvent. The extracts were then dried with anhydrous sodium sulfate, concentrated using a rotary evaporator followed by flushing using nitrogen until the volume was about 0.5 ml.

1997, A. J. Taylor, D. S. Mothram, editors, Flavour Science: Recent Developments, Elsevier, →ISBN, page 63:

A three-dimensional measure of space that comprises a length, a width and a height. It is measured in units of cubic centimeters in metric, cubic inches or cubic feet in English measurement.

(obsolete) A roll or scroll, which was the form of ancient books.

сви́тък

(computing) An accessible storage area with a single file system, typically resident on a single partition of a hard disk.

том

computing: accessible storage area with a single file system

(climbing, bouldering) A modular foothold attached to a climbing wall used for gripping, often in triangular, pyramidal, or angular shapes.

(graph theory) The sum of the degrees of a set of vertices.


meter

meter (countable and uncountable, plural meters)

Senses 1.1, 2, and 3 were borrowed from French mètre and Latin metrum; see metre for more.
Sense 1.2 is a noun derived from mete, from Old English metan (“to measure, mark off”), possibly influencing the other meanings.

inh

(American spelling) Alternative form of metre


lift

en-verb

lift (third-person singular simple present lifts, present participle lifting, simple past lifted or (rare, regional, obsolete) lift, past participle lifted or (rare, regional, obsolete) lift or (obsolete) yleft)

lifts (present singular third-person)
lifting (participle present)
lifted (past)
lift (obsolete past rare regional)
lifted (participle past)
lift (obsolete participle past rare regional)
yleft (obsolete participle past)

From Middle English liften, lyften, from Old Norse lypta (“to lift, air”, literally “to raise in the air”), from Proto-Germanic *luftijaną (“to raise in the air”), related to *luftuz (“roof, air”), perhaps from Proto-Indo-European *lewp- (“to peel, break off, damage”) or from a root meaning roof (see *luftuz). Cognate with Danish and Norwegian Bokmål løfte (“to lift”), Norwegian Nynorsk and Swedish lyfta (“to lift”), German lüften (“to air, lift”), Old English lyft (“air”). See above. 1851 for the noun sense "a mechanical device for vertical transport".
(To steal): For this sense Cleasby suggests perhaps a relation to the root of Gothic 𐌷𐌻𐌹𐍆𐍄𐌿𐍃 (hliftus) "thief", cognate with Latin cleptus and Greek κλέπτω (kléptō)).

der

(category theory, transitive) Given morphisms f and g with the same target: To produce a morphism which the given morphism factors through (i.e. a morphism h such that f=g∘h; cf. lift n.18)

Finally, we can lift a partial function into a regular (total) function that returns an Option or a Some(value) when the partial function is defined for the input argument or None when it isn't.

2021, Dean Wampler, chapter 2, in Programming Scala, 3rd edition, O'Reilly, →ISBN:

(programming) To transform (a function) into a corresponding function in a different context.

nostaa

programming: to transform into a different context


lift

en-noun

lift (countable and uncountable, plural lifts)

→ Cantonese: 𨋢 /䢂 (lip¹)

→ Dutch: lift
→ Papiamentu: left

→ Malay: lif

desctree

→ Russian: лифт (lift)
→ Armenian: լիֆտ (lift)
→ Georgian: ლიფტი (lipṭi)
→ Kazakh: лифт (lift)
→ Mongolian: лифт (lift)
→ Uyghur: لىفت (lift)
→ Uzbek: lift
→ Yakut: лифт (lift)

→ Swahili: lifti

→ Swedish: lift

For a covering space p#58;#92;tildeX#92;toX a path #92;gamma [i.e. a continuous map #91;0,1#93;#92;toX] in X has a unique lift #92;tilde#92;gamma starting at a given point of p#123;-1#125;(#92;gamma(0))

2001, Allen Hatcher, Algebraic Topology, page 69:

(category theory) A morphism which some given morphism factors through; i.e. given a pair of morphisms f:X→Y and g:Z→Y, a morphism h such that f=g∘h. (In this case h is said to be a lift of f via Z or via g).


ether

Gas is not ether–it's a separate virtual currency with its own exchange rate against ether.

2018, Andreas M. Antonopoulos, Gavin Wood, Mastering Ethereum: Building Smart Contracts and DApps, O'Reilly Media, →ISBN:

(cryptocurrencies) Alternative letter-case form of Ether