product

en-noun

product (countable and uncountable, plural products)

From Middle English product, from Latin prōductus, perfect participle of prōdūcō, first attested in English in the mathematics sense.

The product of 2 and 3 is 6.  The product of 2, 3, and 4 is 24.

(arithmetic) A quantity obtained by multiplication of two or more numbers.


abacus

From Late Middle English abacus, abagus, agabus (“abacus; art of counting with an abacus”), from Latin abacus, abax (“sideboard or table with a slab at the top; slab at the top of a column; counting board, sand table; board for playing games”) (compare Late Latin abacus (“art of arithmetic”)), from Ancient Greek ἄβαξ (ábax, “slab, counting board; board covered with sand for drawing; plate; dice-board”). Doublet of abaque.
The plural form abaci is reinforced from Latin abacī.

der

Harvard University
Houghton Library
Roman abacus

I’ve heard merchants still use an abacus for adding things up in China.

Before leaving the question of early arithmetic I should mention that for practical purposes the almost universal use of the abacus or swan-pan rendered it easy to add or subtract, or even to multiply and divide, without any knowledge of theoretical mathematics. [...] [I]t will be sufficient here to say that they afford a concrete way of representing a number in the decimal scale, and enable the results of addition and subtraction to be obtained by a merely mechanical process.

1888, Walter W[illiam] Rouse Ball, “Egyptian and Phœnecian Mathematics”, in A Short Account of the History of Mathematics, London, New York, N.Y.: Macmillan and Co., →OCLC, page 6:

The computer is but another vehicle to employ in helping people learn, a cousin of books, films, blackboards, chalk, gerbils, abacuses. Like each of these devices, it can be well used or misused.

1974, Theodore R[yland] Sizer, “Foreword”, in Allan B. Ellis, The Use & Misuse of Computers in Education, New York, N.Y.: McGraw-Hill Book Company, →ISBN, page ix:

Take another look at the abacus to see how useful it is. Each row represents a successively higher counting group, or register, by 10 times. Thus, with only 6 rows you can count to one million (actually, up to 999,999, which is 1 short of one million).

1999, Stan Gibilisco, Norman Crowhurst, “From Counting to Addition”, in Mastering Technical Mathematics, 2nd edition, New York, N.Y.: McGraw-Hill, →ISBN, part 1 (Arithmetic as an Outgrowth of Learning to Count), page 10:

Before Pythagoras it was necessary to see the thing before counting it, like children who learn on abacuses, with balls sliding along rods: children learn to add and subtract by sliding stones.

2001, Augusto Boal, “The Impossible Return and the Strangeness of the Familiar”, in Adrian Jackson, Candida Blaker, transl., Hamlet and the Baker’s Son: My Life in Theatre and Politics, London, New York, N.Y.: Routledge, →ISBN, page 342:

Each rod in the bottom deck of an abacus has 5 beads. The value of each bead depends on which rod it is on. Each bead on the ones rod in the bottom deck equals 1. Each bead on the tens rod in the bottom deck equals 10. Each bead on the hundreds rod in the bottom deck equals 100.

2004, Patricia J. Murphy, “The Bottom Deck”, in Counting with an Abacus: Learning the Place Values of Ones, Tens, and Hundreds, New York, N.Y.: The Rosen Publishing Group, →ISBN, page 8:

She was sitting at the parlour table with a small abacus in front of her. [...] Peter still recorded weights of fleeces and pounds of cabbages and bushels of grain by cutting notches in tally sticks, but Liza would translate them into figures on paper and have them totted up on the abacus the very same day.

2007, Valerie Anand, “Hope and Fear”, in The House of Lanyon (The Exmoor Saga), Richmond, London: Mira, published 2008, →ISBN, page 209:

A device used for performing arithmetical calculations; (rare) a table on which loose counters are placed, or (more commonly) an instrument with beads sliding on rods, or counters in grooves, with one row of beads or counters representing units, the next tens, etc.

abakus

device for performing arithmetical calculations


number

numbers (plural)
nummer (alternative dialectal)
numbre (alternative obsolete)

Tok Pisin: namba

→ Brunei Malay: numbur

→ Burmese: နံပါတ် (nampat)

→ Hindustani: नंबर (nambar) / نمبر (nambar)

→ Japanese: ナンバー (nanbā)

→ Kikuyu: namba

→ Malay: nombor

Indonesian: nomor

→ Maori: nama

→ Navajo: námboo

→ Papiamentu: number

→ Palauan: lambang

→ Swahili: nambari, namba

→ Yoruba: nọ́ḿbà

From Middle English number, nombre, numbre, noumbre, from Anglo-Norman noumbre, Old French nombre, from Latin numerus (“number”), ultimately from Proto-Indo-European *nem- (“to divide”). Compare Saterland Frisian Nummer, Nuumer, West Frisian nûmer, Dutch nummer (“number”), German Nummer (“number”), Danish nummer (“number”), Swedish nummer (“number”), Icelandic númer (“number”). Replaced Middle English ȝetæl and rime, more at tell, tale and rhyme.

رَقْم

used to show the rank of something in a list or sequence

The equation e#123;i#92;pi#125;#43;1#61;0 includes the most important numbers: 1, 0, #92;pi, i, and e.

hypercomplex numbers
hypercomplex numbers

(countable, mathematics) An element of one of several sets: natural numbers, integers, rational numbers, real numbers, complex numbers, and sometimes extensions such as hypercomplex numbers, etc.


Roman numeral

Roman numerals (plural)
roman numeral (alternative US)

A numeral represented using a Roman system involving the letters I, V, X, L, C, D, and M.


cube

en-verb

cube (third-person singular simple present cubes, present participle cubing, simple past and past participle cubed)

cubes (present singular third-person)
cubing (participle present)
cubed (participle past)
cubed (past)

From Old French cube, from Latin cubus, from Ancient Greek κύβος (kúbos).

Three cubed can be written as 3³, and equals twenty-seven.

From this severe trial Mr. Nackybal emerged with distinction, having in his cubing made only twenty-five slight mistakes out of the forty-six cubes demanded, and in his rooting, out of the fifty-three extractions propounded, committed a mere matter of four trifling errors!

1953, Samuel Beckett, Watt, [Paris]: Olympia Press, →OCLC:

(transitive, arithmetic) To raise to the third power; to determine the result of multiplying by itself twice.


rational

en-adj

rational (comparative more rational, superlative most rational)

more rational (comparative)
most rational (superlative)
rationall (alternative obsolete)

From Old French rationel, rational, from Latin rationalis (“of or belonging to reason, rational, reasonable; having a ratio”), from ratio (“reason; calculation”).

der

/ˈɹæʃ(ə)nəl/

¾ is a rational number, but √2 is an irrational number.

(mathematics, not comparable) Comprising, or expressible as, a ratio

(arithmetic) Of a number, capable of being expressed as the ratio of two integers.


irrational

en-adj

irrational (comparative more irrational, superlative most irrational)

more irrational (comparative)
most irrational (superlative)

From Latin irratiōnālis, from ir- + ratiōnālis.

The number π is irrational.

(mathematics, arithmetic, number theory, not comparable) Of a real number, that cannot be written as the ratio of two integers.


to

From Middle English to, from Old English tō, from Proto-Germanic *tō ~ *ta, from Proto-Indo-European *de ~ *do (“to”). Cognate with Scots tae, to (“to”), North Frisian to, tö, tu (“to”), Saterland Frisian tou (“to”), Low German to (“to”), Dutch toe, te (“to”), German zu (“to”), West Frisian ta (“to”). Non-Germanic cognates include Albanian ndaj (“towards”), Irish do (“to, for”), Breton da (“to, for”), Welsh i (“to, for”), Russian до (do, “to”). Doublet of too.

uses the dative case or նկատմամբ (nkatmamb)

(first number in genitive case) suhde (second number in illative case) (e.g. yhden suhde yhteen ~ one to one)

(ordinal number of the exponent in illative case)

ב־

written together with the following word

(ordinal number of the exponent in superessive case)

-ஆக

Rarely used, in contrast with "time following" words such as quarter past and half past.

Three squared or three to the second power is nine.

Three to the power of two is nine.

Three to the second is nine.

(arithmetic) Used to indicate that the preceding term is to be raised to the power of the following value; indicates exponentiation.


ordinal number

ординал

generalized kind of number to denote the length of a well-order on a set

In the expression a₃, the "3" is an ordinal number.

(arithmetic) A natural number used to denote position in a sequence.

числително редно

grammar: word used to denote relative position in a sequence

пореден номер

arithmetic: number used to denote position in a sequence


calculator

[ˈkʰæɫ.kjəˌleɪ̯.ɾɚ]

In the sense of a person, from Middle English calkelatour (“mathematician, astrologer”), borrowed from Latin calculātor, equivalent to calculate + -or. The other meanings arose in Modern English.

inh

electronic calculator;   pocket calculator

The calculator on a bookkeeper's desk in the 1950s was an adding machine with mechanical guts.

I told him to hand me a calculator and he jokingly placed an adding machine at my side.

A mechanical or electronic device that performs mathematical calculations; sometimes, an electronic one specifically.

គណិតចរ

kĕəʼnetaʼ cɑɑ

ܚܲܫܘܼܒ݂ܘܿܢܵܐ

mechanical device that performs mathematical calculations


draw

en-verb

draw (third-person singular simple present draws, present participle drawing, simple past drew, past participle drawn or (colloquial and nonstandard) drew)

draws (present singular third-person)
drawing (participle present)
drew (past)
drawn (participle past)
drew (colloquial nonstandard participle past)
draw (infinitive)
draw (first-person present singular)
drew (first-person past singular)
draw (present second-person singular)
drawest (archaic present second-person singular)
drew (past second-person singular)
drewest (archaic past second-person singular)
draws (present singular third-person)
draweth (archaic present singular third-person)
drew (past singular third-person)
draw (plural present)
drew (past plural)
draw (present subjunctive)
drew (past subjunctive)
draw (imperative present)
drawing (participle present)
drawn (participle past)

The verb is derived from Middle English drauen, drawen, draȝen, dragen (“to drag, pull; to draw (out); to attract; to entice, lure; to lead; to make a drawing; to move, travel; etc.”), from Old English dragan (“to drag, draw”), from Proto-West Germanic *dragan (“to carry; to haul”), from Proto-Germanic *draganą (“to carry; to pull, draw”); further etymology uncertain, often said to be from Proto-Indo-European *dʰregʰ- (“to pull, draw”), but possibly from a non-Indo-European substrate root which is also the source of Latin trahō (“to pull, draw; etc.”). Doublet of drag and draught.
The noun is derived from Middle English drau, draue (“action of shooting with a bow”), from drauen, drawen (verb).
cognates
* Albanian dredh (“to turn, spin”)
* Danish drage
* Dutch dragen
* German tragen (“to carry”)
* Old Armenian դառնամ (daṙnam, “to turn”)
* Sanskrit ध्रजस् (dhrájas, “gliding course or motion”)
* West Frisian drage

vyluhovávat

of drinks: to leave temporarily so as to allow the flavour to increase

изтеглям

cardgames: to take the top card of a deck into hand

every miller draws water to his own mill

one hair of a woman can draw more than a hundred pair of oxen

arithmetic operation
arithmetic operation

Senses relating to exerting force or pulling.

(transitive, arithmetic) To subject (a number) to an arithmetic operation.


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”).

(uncountable, arithmetic) The arithmetic operation of adding.

remainder left over if divisor does not divide dividend


rate

rate (countable and uncountable, plural rates)

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

der

Postal rates here are low.

A set price or charge for all examples of a given case, commodity, service etc.

This textbook is first-rate.

(nautical) A class into which ships were assigned based on condition, size etc.; by extension, rank.


integer

en-noun

integer (plural integers or (rare) integri)

[ˈɪn.tʰə.d͡ʒɚ]

[ˈɪn.ɾ̃ə.d͡ʒɚ]

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

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

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

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

when understood to include negative numbers and zero


multiplication

multiplication (countable and uncountable, plural multiplications)

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

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

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

(countable, arithmetic) A calculation involving multiplication.


subtraction

subtraction (countable and uncountable, plural subtractions)

subtractions (plural)
substraction (alternative obsolete)

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

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

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

(arithmetic, countable) A calculation involving subtracting.


division

division (countable and uncountable, plural divisions)

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

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

deel

arithmetic: process of dividing a number by another

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

(arithmetic) A calculation that involves this process.

deel

arithmetic: calculation involving this process


fraction

Etymology tree
Middle English fraccioun
English fraction
From Middle English fraccioun (“a breaking”), from Anglo-Norman, Old French fraccion, from Medieval Latin fractio (“a fragment, portion”), from earlier Latin fractio (“a breaking, a breaking into pieces”), from fractus, past participle of frangere (“to break”) (whence English frangible), from Proto-Indo-European *bʰreg- (English break). Doublet of frazione.

der

Appendix:Roget MICRA thesaurus/Class I § 100a. Fraction

Gasoline prices show the mill as a fraction, for example $3.59+⁹⁄₁₀.

(arithmetic) A ratio of two numbers (numerator and denominator), usually written one above the other and separated by a horizontal bar called the vinculum or, alternatively, in sequence on the same line and separated by a solidus (diagonal bar).


Arabic numeral

Arabic numerals (plural)
arabic numeral (alternative US)

A calque of Medieval Latin numerus Arabicus, from its gradual adoption in Europe from Arabic sources.

calque

A number represented using an Indian and Arabic system involving the symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, representing digits.


exponentiation

en-noun

exponentiation (countable and uncountable, plural exponentiations)

Ultimately from exponent + -i- + -ation. Perhaps from exponential + -ation.

In 5⁴ the base is 5 and the power is 4, so there are 4 identical factors of 5, and exponentiation gives 625 as the result.

"The remarkable fact about the system is that it achieves such a high level of security with only six exponentiations," Boneh said, referring to the calculations used to raise numbers to a power. Other systems do exponentiation once, suggesting that this system may be about six times slower because exponentiation is the most time-consuming step in encrypting the data.

1998 August 25, Peter Wayner, “IBM Says Encryption System Prevents Hacker Attack”, in The New York Times:

(mathematics, arithmetic) The process of calculating a power by multiplying together a number of equal factors, where the exponent specifies the number of factors to multiply.

berreketa

the process of calculating a power by multiplying together a number of equal factors

(mathematics, arithmetic, countable) A mathematical problem involving exponentiation.


borrow

en-verb

borrow (third-person singular simple present borrows, present participle borrowing, simple past and past participle borrowed)

borrows (present singular third-person)
borrowing (participle present)
borrowed (participle past)
borrowed (past)
borrow (infinitive)
borrow (first-person present singular)
borrowed (first-person past singular)
borrow (present second-person singular)
borrowest (archaic present second-person singular)
borrowed (past second-person singular)
borrowedst (archaic past second-person singular)
borrows (present singular third-person)
borroweth (archaic present singular third-person)
borrowed (past singular third-person)
borrow (plural present)
borrowed (past plural)
borrow (present subjunctive)
borrowed (past subjunctive)
borrow (imperative present)
borrowing (participle present)
borrowed (participle past)
boro (alternative)

carry

the equivalent reverse procedure in the inverse operation of addition

From Middle English borwen, borȝien, Old English borgian (“to borrow, lend, pledge surety for”), from Proto-West Germanic *borgōn, from Proto-Germanic *burgōną (“to pledge, take care of”), from Proto-Indo-European *bʰergʰ- (“to take care”).
Cognate with Dutch borgen (“to borrow, trust”), German borgen (“to borrow, lend”), Danish borge (“to vouch”). Related to Old English beorgan (“to save, preserve”). More at bury.

cog

(arithmetic) In a subtraction, to deduct (one) from a digit of the minuend and add ten to the following digit, in order that the subtraction of a larger digit in the subtrahend from the digit in the minuend to which ten is added gives a positive result.


carry

en-verb

carry (third-person singular simple present carries, present participle carrying, simple past and past participle carried)

carries (present singular third-person)
carrying (participle present)
carried (participle past)
carried (past)

borrow

the equivalent reverse procedure in the inverse operation of subtraction

→ Cantonese: carry

From Middle English carien, from Anglo-Norman carier (modern French charrier); from a derivative of Latin carrus (“four-wheeled baggage wagon”), ultimately of Gaulish origin.

tīhei

on the back but held in place with hands

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

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

one can't carry two watermelons under one arm

Five and nine are fourteen; carry the one to the tens place.

(transitive, arithmetic) In an addition, to transfer the quantity in excess of what is countable in the units in a column to the column immediately to the left in order to be added there.


vinculum

From Latin vinculum (“bond, link”), from vinciō (“bind, fetter, tie”) + -ulum.

(arithmetic, obsolete) Any symbol used to group some of the terms in an expression, indicating that that part of the calculation should be done before other parts, or that the Roman numeral underneath should be multiplied by 1,000.

(arithmetic) A horizontal line over the top of some of the terms in an expression, indicating that that part of the calculation is to be done before other parts.

(arithmetic) Specifically, the horizontal line between the numerator and denominator in a fraction.


surd

First attested in the mid 16th century from Latin surdus (“deaf, mute”), used in mathematics for “irrational,” reflecting ἄλογος (álogos, “irrational, speechless”) as found in Euclid, apparently transmitted via Arabic جِذْر أَصَمّ (jiḏr ʔaṣamm, “deaf root”). The phonetic sense, “voiceless,” emerged in the 18th century. Doublet of surdo.

جِذْر أَصَمّ

(arithmetic) An irrational number, especially one expressed using the √ symbol.


root

en-noun

root (countable and uncountable, plural roots)

→ Irish: rúta

PIE word
 *wréh₂ds
From Middle English rote, root, roote (“the underground part of a plant”), from late Old English rōt, from Old Norse rót (Icelandic rót), from Proto-Germanic *wrōts, from Proto-Indo-European *wréh₂ds (“root”); Doublet of wort, radish, and radix.

the love of money is the root of all evil

The cube root of 27 is 3.

(arithmetic) Of a number or expression, a number which, when raised to a specified power, yields the specified number or expression.

wortel

arithmetic: number or expression which when raised to a power gives the specified number or expression

Multiply by root 2.

1899, Dante Gabriel Rossetti (transl.), The New Life (La Vita Nuova) of Dante Alighieri, Siddall edition, page 122.
The number three is the root of the number nine; […] being multiplied merely by itself, it produceth nine, as we manifestly perceive that three times three are nine.

(arithmetic) A square root (understood if no power is specified; in which case, "the root of" is often abbreviated to "root").


binary

en-adj

binary (comparative more binary, superlative most binary)

more binary (comparative)
most binary (superlative)

From Late Latin bīnārius (“consisting of two”), from Latin bīnī (“two-by-two, pair”). By surface analysis, bin- + -ary.

двайко́вы

being in a state of one of two mutually exclusive conditions such as on or off

en:in or concerning the base-2 number system

(arithmetic, computing) Concerning numbers and calculations using the binary number system.


expand

en-verb

expand (third-person singular simple present expands, present participle expanding, simple past and past participle expanded)

expands (present singular third-person)
expanding (participle present)
expanded (participle past)
expanded (past)
expand (infinitive)
expand (first-person present singular)
expanded (first-person past singular)
expand (present second-person singular)
expandest (archaic present second-person singular)
expanded (past second-person singular)
expandedst (archaic past second-person singular)
expands (present singular third-person)
expandeth (archaic present singular third-person)
expanded (past singular third-person)
expand (plural present)
expanded (past plural)
expand (present subjunctive)
expanded (past subjunctive)
expand (imperative present)
expanding (participle present)
expanded (participle past)

contract

antonym(s) of “to change from a smaller form/size to a larger one”

contract

antonym(s) of “to increase the extent, number, volume or scope of”

factor

to rewrite as an equivalent sum of terms

Recorded in Middle English since 1422 (as expanden, expaunden), from Anglo-Norman espaundre, from Latin expandere (“to spread out”), itself from ex- (“out, outwards”) + pandō (“to spread”). Doublet of spawn.

وَسَّعَ

(transitive) to increase the extent, number, volume or scope of

فَصَّلَ

(transitive) to express at length or in detail

разяснявам се

(intransitive) to speak or write at length or in detail

enlarge

Expanding 4#47;7 by 3 gives 12#47;21.

(transitive, arithmetic) To multiply both the numerator and the denominator of a fraction by the same (non-zero) number (which yields a fraction of equal value).

laventaa

(transitive, arithmetic) to multiply the numerator and denominator of a fraction by the same number


evenly divisible

From the concept of dividing a group of objects into subgroups of even (that is, the same) size.

15 is evenly divisible by 3 but 16 isn't.

(arithmetic) Leaving no remainder when divided by.


plus sign

(arithmetic) The symbol + used to denote the operation of addition, to indicate that a number is positive, and so on.


minus sign

(arithmetic) The symbol −, used to denote the operation of subtraction or to indicate that a number is negative.

نَاقَص

symbol used to denote the operation of subtraction and to indicate that a number is negative


radical

PIE word
 *wréh₂ds
Inherited from Middle English radical, from Latin rādīcālis (“of or pertaining to the root, having roots, radical”).

radicale

ring theory: ideal of elements of a ring sharing a certain given property

radicale

ring theory: intersection of maximal submodules of a module

(arithmetic) A root (of a number or quantity).

корен

arithmetic: root (of a number or quantity)


decimal

Borrowed from Late Latin, Medieval Latin decimalis, from Latin decimus, from decem (“ten”) + adjective suffix -alis.

(arithmetic, computing) Concerning numbers expressed in decimal or mathematical calculations performed using decimal.

عَشْرِيّ

concerning numbers expressed in decimal or calculations using decimal


hexadecimal

en-noun

hexadecimal (countable and uncountable, plural hexadecimals)

1952. hexadeca- + decimal; see the Wikipedia article for more information.

(arithmetic, computing, uncountable) A number system with base sixteen, using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, most used in computing as a hexadecimal digit can represent four bits, half a standard byte, and thus a single byte can be represented conveniently with two digits.


raise

en-verb

raise (third-person singular simple present raises, present participle raising, simple past and past participle raised)

raises (present singular third-person)
raising (participle present)
raised (participle past)
raised (past)

From Middle English reysen, raisen, reisen, from Old Norse reisa (“to raise”), from Proto-Germanic *raisijaną, *raizijaną (“to raise”), causative form of Proto-Germanic *rīsaną (“to rise”), from Proto-Indo-European *h₁rey- (“to rise, arise”). According to Kroonen (2013), from Proto-Indo-European *h₃er- (“to stir, rise”).
Cognate with Old English rāsian (“to explore, examine, research”), Old English rīsan (“to seize, carry off”), Old English rǣran (“to raise”). Doublet of rear.

whakahī

Referring to lifting the pitch of a musical note

hāpai

Of lifting an object to a higher elevation

hī

Refers to raising an eyebrow in scepticism

raise oneself up by one's own bootstraps

Two raised to the fifth power equals 32.

(arithmetic) To exponentiate, to involute.


position

From Middle English posicioun, from Old French posicion, from Latin positiō (“a putting, position”), from positus (“placed, situated”), past participle of pōnō (“to place”); see ponent. Compare apposition, composition, deposition; see pose.

позиция

finance: amount of financial instruments held by someone

emergency position indicating radio beacon

emergency position indicating radio-beacon

emergency position indicating radiobeacon

(arithmetic) A method of solving a problem by one or two suppositions; also called the rule of trial and error.

метод на предположението

arithmetic: method of solving a problem by one or two suppositions


quotient

Dividing 12 by 4 yields a quotient of 3.

(arithmetic) The number (either a fraction or an integer) resulting from the division of one number by another.


divide

en-verb

divide (third-person singular simple present divides, present participle dividing, simple past and past participle divided)

divides (present singular third-person)
dividing (participle present)
divided (participle past)
divided (past)

PIE word
 *dwóh₁
From Middle English dividen, from Latin dīvidere (“to divide”). Displaced native Old English tōdǣlan.

dividend

the sum being divided, the upper term in a fraction

divisor

the number of parts in a division, the lower term in a fraction

If you divide 6 by 3, you get 2.

(transitive, arithmetic, with by) To calculate the number (the quotient) by which you must multiply one given number (the divisor) to produce a second given number (the dividend).

3 divides 6.

(transitive, arithmetic) To be a divisor of.


augend

In "4 + 5", 4 is the augend

(arithmetic) A quantity to which another is added.


extract

extract (third-person singular simple present extracts, present participle extracting, simple past extracted, past participle extracted or (archaic) extraught)

extracts (present singular third-person)
extracting (participle present)
extracted (past)
extracted (participle past)
extraught (archaic participle past)

Borrowed from Latin extractum, neuter perfect passive participle of extrahō, from ex- (“out of”) + trahō (“I drag”).

Please extract the cube root of 27.

[…] Mr. Nackybal was thoroughly examined, both in cubing and extracting, from the table that Louit had provided.

(transitive, arithmetic) To determine (a root of a number).


reciprocal

From Latin reciprocus, possibly from a phrase such as reque proque (“back and forth, to and fro”), from re- (“back”), prō (“forwards”) and -que (“and”).

0.5 is the reciprocal of 2.

(arithmetic) The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.


decimal point

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

(arithmetic, proscribed) A decimal place.


indivisible

divisible

antonym(s) of “incapable of being divided, arithmetic”

incombinable

antonym(s) of “incapable of being combined”

PIE word
 *dwóh₁
From Middle French indivisible, from Late Latin indivisibilis.

неделим

incapable of being divided by a specific integer

(arithmetic) Incapable of being divided by a specific integer without leaving a remainder.


ratio

→ Portuguese: rácio

/ˈɹeɪ.ʃi.əʊ/

/ˈɹeɪ.ʃiˌoʊ/

Borrowed from Latin ratiō. Doublet of ration and reason.

(arithmetic) The relative magnitudes of two quantities (usually expressed as a quotient).

отношение

arithmetics: relative magnitude of two quantities expressed as quotient


working

en-noun

working (countable and uncountable, plural workings)

From Middle English werking, werkynge, warkynge, worchinge, from Old English wyrċing (“working”), verbal noun of wyrċan (“to work”), equivalent to work + -ing. Cognate with Scots wirking, warking, Dutch werking, German Wirkung.

Be sure to check your working.

(arithmetic) The incidental or subsidiary calculations performed in solving an overall problem.


times

en-verb

times (third-person singular simple present timeses, present participle timesing, simple past and past participle timesed)

timeses (present singular third-person)
timesing (participle present)
timesed (participle past)
timesed (past)

Multiplication sense from the idea that something is repeated or added together a given number of times.

I've taken the calories and the amount of food . . . and it's 410 calories per portion timesed by 6 portions which ^([sic]) the answer was 2460 calories...

1994, Harvey Mellar, Learning with artificial worlds: computer-based modelling in the curriculum:

A student as junior as Year 4 informed me that he made a forward estimate of cheeses in 100 trials by 'timesing both numbers by 10' […]

1995, Mathematical Association, The Australian mathematics teacher, Volumes 51-53:

Alex: Yeah - if you're timesing that distance there by this height, it will disappear.

1998, Psychology of mathematics education, Volume 2:

[…] when the denominator was timesed by three, the same had to be done to the numerator; and so on.

1998, W. M. Roth, Designing Communities, Kluwer Academic Publishers, page 31:


arithmetic

/æɹɪθˈmɛtɪk/

From French arithmétique, from Latin arithmēticus, from Ancient Greek ἀριθμητῐκός (arithmētĭkós).

der

List of terms used in arithmetic in English

arithmetic progression

(arithmetic) Of a progression, mean, etc, computed solely using addition.


multiply

en-verb

multiply (third-person singular simple present multiplies, present participle multiplying, simple past and past participle multiplied)

multiplies (present singular third-person)
multiplying (participle present)
multiplied (participle past)
multiplied (past)

From Old French multiplier, from Latin multiplicō, from multi (“many”) + plicō (“I fold”).
The noun presumably derives from the verb.

when you multiply 3 by 7, you get 21; he multiplied several numbers

But that can be ignored, because the USTR has set ε at 4 and φ at 0.25, so when computed give an overall multiplier of 1 for the imports number. And multiplying by 1 makes no difference at all.

2025 April 3, Felix Salmon, “How to read the White House's tariff formula”, in Axios:

(transitive, arithmetic, with by) To perform multiplication on (a number).

shumëzoj

transitive: perform multiplication on (a number)

He had been multiplying, but it occurred to him he needed to resolve the exponents, first.

(intransitive, arithmetic) To perform multiplication.


vigesimal

From Latin vīcēsimus (“twentieth”) (from *vīcēnssos, from Proto-Indo-European *wi(h₁)ḱm̥ttós, with the -imus ending of decimus (“tenth”)) + -al (suffix forming an adjective). Compare Latin vīgintī (“twenty”), from Proto-Indo-European *h₁wih₁ḱm̥ti, from *dwi(h₁)dḱm̥ti(h₁), *dwi(h₁)dḱm̥ti (“two tens; two decades”).

To go on by hands and feet to 20, and thence to reckon by twenties, is a vigesimal notation. Now though in the larger proportion of known languages, no distinct mention of fingers and toes, hands and feet, is observable in the numerals themselves, yet the very schemes of quinary, decimal and vigesimal notation remain to vouch for such hand-and-foot counting having been the original method on which they were founded.

1871, Edward B[urnett] Tylor, “The Art of Counting”, in Primitive Culture: Researches into the Development of Mythology, Philosophy, Religion, Art, and Custom. … In Two Volumes, volume I, London: John Murray, Albemarle Street, →OCLC, page 236:

The most remarkable vigesimal scale of numeration is that of the Mexicans. The decimal scale is adopted as far as twenty; that is to say, after ten the primitive digits are repeated, but from twenty onwards the numbers are taken by twenties. Thus 34 is canlahhutukal, literally fourteen and twenty.

1875, James A[llanson] Picton, “On the Origin and History of the Numerals”, in Proceedings of the Literary and Philosophical Society of Liverpool, volume XXIX, London: Longmans, Green, Reader, & Dyer; Liverpool: D. Marples & Co. Limited, Lord Street, →OCLC, page 87:

With regard to the Danish numeral-words founded on the vigesimal system of numeration, it must be admitted that here the explanation fails which has been given for the divergence of the forms representing 70, 80 and 90 from the forms representing the lower numerals of 10 in the case of some other languages, since in the present case the forms for 50 and 60 also depart from the decimal system; […]

1923, Melius de Villiers, “Aryan Numeral-words”, in The Numeral-words: Their Origin, Meaning, History and Lesson, London: H. F. & G. Witherby, 326 High Holborn, London, W.C.; Cape Town; Johannesburg; Port Elizabeth: Juta & Co., →OCLC, page 93:

[I]t is not known whether they [the Maya] progressed beyond a "vigesimal point" to negative powers of 20, i.e. to vigesimal fractions.

1970, Petr Beckmann, “The Belt”, in A History of π (Pi), Boulder, Colo.: The Golem Press, →ISBN; republished New York, N.Y.: St. Martin's Press, 1971, →ISBN, page 34:


successor

successors (plural)
successour (alternative obsolete)

predecessor

person or thing that immediately follows another

From Anglo-Norman successour, from Latin successor.

A limit ordinal is not the successor of any ordinal.

(arithmetic, set theory) The integer, ordinal number or cardinal number immediately following another.

наследник

integer or cardinal immediately following another


numerator

/ˈnuː.məɹˌeɪ̯.təɹ/

Learned borrowing from Late Latin numerātor.

lbor

(arithmetic) The number or expression written above the line in a fraction (such as 1 in ½).


denominator

Learned borrowing from Late Latin dēnōminātor (“that which names”).

common denominator

lowest common denominator

(arithmetic) The number or expression written below the line in a fraction (such as 2 in ½).


round up

en-verb

round up (third-person singular simple present rounds up, present participle rounding up, simple past and past participle rounded up)

rounds up (present singular third-person)
rounding up (participle present)
rounded up (participle past)
rounded up (past)

събирам

to collect or gather (something) together

The total is $24,995 — let's round it up to $25,000.

(transitive, arithmetic) To round (a number) to the smallest integer that is not less than it, or to some other greater value, especially a whole number of hundreds, thousands, etc.


round down

round down (third-person singular simple present rounds down, present participle rounding down, simple past and past participle rounded down)

rounds down (present singular third-person)
rounding down (participle present)
rounded down (participle past)
rounded down (past)

The total is $25,715, but to keep the figures simple, I'll round it down to $25,000.

(transitive, arithmetic) To round (a number) to the greatest integer that is not greater than it, or to some other lower value, especially a whole number of hundreds, thousands, etc.

закръглям надолу

to round downwards to the desired accuracy


tetration

en-noun

tetration (usually uncountable, plural tetrations)

/tɛˈtɹeɪʃn̩/

/tɛˈtɹeɪʃən/

PIE word
 *kʷetwóres
From tetra- (prefix meaning ‘four’) + (itera)tion, from the fact that tetration is in fourth place after addition, multiplication, and exponentiation. The word was coined by the English mathematician Reuben Goodstein (1912–1985).

coinage

You don't ordinarily hear much about tetration because it is so powerful an operation that tetrating even very small numbers with each other produces inordinately large numbers. A tetration is worked out below.
⁴²#61;2#123;(2#123;(#123;2²#125;)#125;)#125;
 #61;2#123;(#123;2⁴#125;)#125;
 #61;2#123;16#125;
 #61;64,536

1982 May, Rudy Rucker, “All the Numbers”, in Infinity and the Mind: The Science and Philosophy of the Infinite, Boston, Mass.; Stuttgart, Baden-Württemberg: Birkhäuser, →ISBN, page 69:

Repeated exponentiation—called tetration—is so rare that a shorthand for it is hardly worth the trouble, appealing only to research mathematicians. Most professional engineers and scientists never encounter tetration, and the shorthand for it is seldom taught anywhere but in mathematics departments. But it doesn't stop there, and for the almost-unheard-of "multiple tetration" there is yet a stronger cousin operation, waiting in the wings.

1993, Alexander Humez, Nicholas Humez, Joseph Maguire, “One”, in Zero to Lazy Eight: The Romance of Numbers, New York, N.Y.: Touchstone, Simon & Schuster, →ISBN, page 39:

Tetration is usually symbolized with a number drawn to the upper left of another number, as opposed to the upper right used for exponents. Let's look at an example: what is 2 tetrated to the 4th? We would draw this as a 2 with a little 4 to the upper left side: ⁴². This is equivalent to 2#123;2#123;2²

2016, Erik Seligman, “Simple Surprises”, in Math Mutation Classics: Exploring Interesting, Fun and Weird Corners of Mathematics, New York, N.Y.: Apress, Springer Science+Business Media, →DOI, →ISBN, page 11:

(arithmetic) The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times.


subtract

en-verb

subtract (third-person singular simple present subtracts, present participle subtracting, simple past and past participle subtracted)

subtracts (present singular third-person)
subtracting (participle present)
subtracted (participle past)
subtracted (past)
substract (alternative obsolete)

Borrowed from Latin subtractus, perfect passive participle of subtrahō (“I draw from beneath; withdraw, remove”); from sub (“under”) + trahō (“I draw, pull, drag”).

If you subtract the $100 for gas from the total cost, it was a fairly inexpensive trip.

(transitive, arithmetic) To remove or reduce; especially to reduce a quantity or number


reverse Polish notation

Back in my day, we had reverse Polish notation calculators: You had to write "2 4 3 * +" instead of "2 + 4 * 3".

(arithmetic) An arithmetic notation in which numbers precede the operators to be applied to them.


dividend

From Middle French dividende, from Latin dividendum (“thing to be divided”), future passive participle of divido (“to divide”), by surface analysis, divide + -end.

uder

In "42 ÷ 3" the dividend is the 42.

(arithmetic) A number or expression that is to be divided by another.


divisor

делител

integer that divides another integer an integral number of times

In "42 ÷ 3" the divisor is the 3.

(arithmetic) In an expression involving division, the number by which another number is being divided.


divisibility

en-noun

divisibility (countable and uncountable, plural divisibilities)

combinability（state capable of being combined）

mergeability（state capable of being merged）

indivisibility（state incapable of being divided）

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

قَابِلِيَّةُ الْقِسْمَةِ

or, equivalently الْقَابِلِيَّةُ لِلْقِسْمَةِ f (al-qābiliyyatu lilqismati)

(arithmetic) The property of being divisible by a particular integer.


divisible

combinable

antonym(s) of “capable of being divided”

[dɪˈvɪzɪbəɫ]

PIE word
 *dwóh₁
From Middle English divisible, from Old French, from Late Latin divisibilis, from the verb Latin divido.

12 is divisible by 3.

(arithmetic) Of an integer, that, when divided by another integer, leaves no remainder.

делим

of an integer, that when divided leaves no remainder


duodecimal

6B4 is the duodecimal notation for the decimal number 1000.

(arithmetic) Of a number, expressed in base twelve.

дванадесетичен

expressed in a base-twelve number system


duodecimal

(arithmetic) A number system that uses twelve as its base.


octal

octal (countable and uncountable, plural octals)

(arithmetic, computing, uncountable) The number system that uses the eight digits 0, 1, 2, 3, 4, 5, 6, 7.

(arithmetic, computing, countable) A digit or value in the octal number system.


octal

(arithmetic, computing) Concerning numbers expressed in octal or mathematical calculations performed using octal.

八進制 /八进制

concerning numbers expressed in octal or mathematics calculations performed using octal


number system

(arithmetic) A set of numerals for representing numbers.


multiplicand

In the expression 5 × 3, the "3" is the multiplicand.

(arithmetic) A number that is to be multiplied by another (the multiplier).


multiplier

In the expression 5 × 7, the "5" is a multiplier.

The score multiplier increases each time you complete a level of the video game.

The electron number constraint unlike the idempotency constraint can be represented by a single equation. For this reason, one can properly incorporate this constraint using a Lagrange multiplier and defining an effective chemical potential

1997, Christopher Alan White, The Development of Ab Initio Methods for the Treatment of Large Molecules:

After studying a recursive formulation and the associated Bellman equation, in section 5.5 we analyze a Lagrangian formulation that provides useful insights about how Lagrange multipliers on transition laws relate to gradients of value functions.

2018, Lars Ljungqvist and Thomas J. Sargent, Recursive macroeconomic theory, 4th edition, MIT Press, page 129:

But that can be ignored, because the USTR has set ε at 4 and φ at 0.25, so when computed give an overall multiplier of 1 for the imports number. And multiplying by 1 makes no difference at all.

(arithmetic) A number by which another (the multiplicand) is to be multiplied.


multiplication table

multiplication table (plural multiplication tables)

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

It was not till animated by some discussion, based upon the multiplication-table, that you saw how keen and shrewd those large, dull, gray eyes could become.

1837, L[etitia] E[lizabeth] L[andon], “Alteration”, in Ethel Churchill: Or, The Two Brides. […], volume II, London: Henry Colburn, […], →OCLC, page 21:

I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall never get to twenty at that rate! However, the Multiplication Table doesn’t signify: let’s try Geography.

1865 November (indicated as 1866), Lewis Carroll [pseudonym; Charles Lutwidge Dodgson], “The Pool of Tears”, in Alice’s Adventures in Wonderland, London: Macmillan and Co., →OCLC, pages 19–20:

(arithmetic) A table showing the products of each of the integers from 1 to 10 (or, especially formerly, 12) with each of the integers from 1 to 10 (or 12).


minuend

From Latin minuendus (“something to be diminished”), gerundive of minuō (“decrease, diminish”), by surface analysis, minus + -end.

der

In the subtraction 10 − 4, 10 is the minuend and 4 is the subtrahend.

(arithmetic) A number or quantity from which another is to be subtracted.


subtrahend

1670s, from Latin subtrahendus numerus (“number to be subtracted”), form of subtrahō (“I pull out from under, I subtract”) (English subtract).
By surface analysis, subtract + -end (“patient (recipient) of action”).

surf

In the subtraction 10 − 4, 4 is the subtrahend.

(arithmetic) A number or quantity to be subtracted from another.


osculate

en-verb

osculate (third-person singular simple present osculates, present participle osculating, simple past and past participle osculated)

osculates (present singular third-person)
osculating (participle present)
osculated (participle past)
osculated (past)

From Latin ōsculāt-, past participial stem of ōsculor (“to kiss”), from ōsculum (“kiss”) + -or (verbal suffix), from ōs (“mouth”) + -culus (diminutive suffix). Doublet of oscillate.

(Vedic arithmetic) To perform osculation.


times sign

(arithmetic, informal) A multiplication sign.


Euclidean algorithm

en-noun

Euclidean algorithm (plural Euclidean algorithms)

Euclidean algorithms (plural)
Euclid's algorithm (alternative)

1985, Erich Kaltofen, Heinrich Rolletschek, Arithmetic in Quadratic Fields with Unique Factorization, Bob F. Caviness (editor), EUROCAL '85, European Conference on Computer Algebra, Linz, Proceedings, Volume 2, Springer, LNCS 204, page 279,
In a quadratic field Q (√), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known. We prove that for D<-19 even remainder sequences with possibly nondecreasing norms cannot determine the GCD of arbitrary inputs.

2003, Ali Akhavi, Brigitte Vallée, Average Bit-Complexity of Euclidean Algorithms, Ugo Montanari, Jose D.P. Rolim, Emo Welzl (editors), Automata, Languages and Programming: 27th International Colloquium, Proceedings, Springer, LNCS 1853, page 373,
In this paper, we provide new analyses that characterize the precise average bit-complexity of a class of Euclidean algorithms.
We consider here five algorithms that are all classical variations of the Euclidean algorithm and are called Classical (𝒢), By-Excess (ℒ), Centered (𝒦), Subtractive (𝒯) and Binary (ℬ).

The general behavior of lattice reduction algorithms is far from being well understood.[…]We explain how a mixed methodology has already proved fruitful for small dimensions p, corresponding to the variety of Euclidean algorithms (p = 1) and to the Gauss algorithm (p = 2).

2009, Brigitte Vallée, Antonio Vera, “3: Probabilistic Analyses of Lattice Reduction Algorithms”, in Phong Q. Nguyen, Brigitte Vallée, editors, The LLL Algorithm: Survey and Applications, Springer, page 71:

greatest common divisor
greatest common divisor

(arithmetic, number theory) Specifically, a method, based on a division algorithm, for finding the greatest common divisor (gcd) of two given integers; any of certain variations or generalisations of said method.


greatest common divisor

greatest common divisor (plural greatest common divisors)

least common multiple

antonym(s) of “largest number that divides each of a set of positive integers”

LL-Q1860 (eng)-Pvanp7-greatest common divisor.wav

The greatest common divisor of 66, 30 and 18 is 6.

1974, John M. Peterson, Basic Concepts of Elementary Mathematics, Prindle, Weber & Schmidt, page 148,
Euclid's algorithm is a process for finding the greatest common divisor of any two whole numbers.

Suppose (a#95;0,a#95;1,#92;dots,a#95;n)#92;in#92;Z we say (a#95;0,a#95;1,#92;dots,a#95;n) is primitive if the greatest common divisor of a#95;0,a#95;1,#92;dots,a#95;n is 1.

2006, W. B. Vasantha Kandasamy, Florentin Smarandache, Neutrosophic Rings, Hexis, page 53:

This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm.[…]As one of the fundamental algebraic problems with a long history, finding the greatest common divisor (GCD) of univariate polynomials is an indispensable component of many algebraic computations besides being an important problem in its own right.

2011, Zhonggang Zeng, “The Numerical Greatest Common Divisor of Univariate Polynomials”, in Leonid Gurvits, Philippe Pébay, J. Maurice Rojas, David Thompson, editors, Randomization, Relaxation, and Complexity in Polynomial Equation Solving, American Mathematical Society, page 187:

(arithmetic, number theory) The largest positive integer (respectively polynomial, element of a given ring) that is a divisor of each of a given set of integers (respectively polynomials, elements of a given ring).


fellowship

fellowship (countable and uncountable, plural fellowships)

From Middle English felowschipe, felawshipe, felaȝschyp, equivalent to fellow + -ship; or perhaps adapted from Old Norse félagskapr, félagsskapr (“fellowship”). Compare Icelandic félagsskapur (“companionship, company, community”), Danish fællesskab (“fellowship”), Norwegian fellesskap (“fellowship”), and Old Swedish fælaghskap (“fellowship”)

cog

(arithmetic, archaic) The proportional division of profit and loss among partners.


Polish notation

After the nationality of the logician Jan Łukasiewicz

In Polish Notation, the connectives are placed before the wffs. The virtue of this sentence is that its grammar is simpler, for it has no need for parentheses. Sider’s examples: (P ∧ Q) → R and P ∧ (Q → R) become → ∧PQR and ∧P → QR.
If you actually look at a text in this tradition, you’ll find something slightly different. “C” stands for “consequence”, i.e., implication (→) and “N” for negation (∼).
So,consider the following from Tarski and Łukasiewicz’s Investigations into the Sentential Calculus. The claim there is that there are three axioms:
 ‘CCpqCCqrCpr’
 ‘CCNppp’
 ‘CpCNpq’

2009, Brandon C. Look, “Symbolic Logic II, Lecture 6”, in www.uky.edu/~look, archived from the original on 2011-11-09:

(arithmetic, logic) A notation for arithmetic (and logical) formulae in which operations (respectively, quantifiers and operands) are written immediately before their operands, used to avoid the need for parentheses; for example, 3 * (4 + 7) is written as * 3 + 4 7 and A AND B is written as AND A B.


cast out nines

en-verb

cast out nines (third-person singular simple present casts out nines, present participle casting out nines, simple past and past participle cast out nines)

casts out nines (present singular third-person)
casting out nines (participle present)
cast out nines (participle past)
cast out nines (past)

(arithmetic) To apply a procedure for verifying whether an arithmetic operation is probably correct or certainly incorrect using modulo characteristics of the digit 9.


rabdology

(arithmetic) The practice of performing arithmetic using Napier's bones.


Napier's bones

(arithmetic) A set of numbered rods used for multiplication and division (see the Wikipedia article for a fuller explanation).

àbac neperià

a set of numbered rods used for multiplication and division


promptuary

(arithmetic) A device described in Napier's treatise Rabdologiæ, consisting of a large set of strips used to multiply multi-digit numbers more easily than Napier’s bones.


location arithmetic

Calque of Latin arithmeticae localis, coined by Scottish landowner and mathematician John Napier (1550–1617) in his 1617 treatise Rabdologiæ (written in Latin).

(arithmetic) A device and technique described in Napier's treatise Rabdologiæ for performing multiplication, division and extraction of square roots by using counters to represent numbers in binary.

John Napier
Rabdology
location arithmetic

arithmeticæ localis

device and technique to aid in performing arithmetic calculations


empty product

(arithmetic) The result of multiplying no numbers, conventionally defined to equal one.


empty sum

(arithmetic) The result of adding no numbers, conventionally defined to equal zero.


nullary sum

These concepts are expressed by sum types, specifically the binary sum, which offers a choice of two things, and the nullary sum, which offers a choice of no things.

2012, Robert Harper, Practical Foundations for Programming Languages, →ISBN, page 86:


improper fraction

en-noun

improper fraction (plural improper fractions)

(arithmetic) A vulgar fraction of which the numerator has a greater magnitude than the denominator, such as 3/2.


proper fraction

proper fraction (plural proper fractions)

(arithmetic) A vulgar fraction in which the magnitude of the numerator is less than or equal to that of the denominator, such as 2/3.


vulgar fraction

vulgar fraction (plural vulgar fractions)

Calque of New Latin fractiō vulgāris, from Latin vulgāris (“common”), originally in contrast to specialised forms such as “astronomical” (sexagesimal) fractions.

(arithmetic) A fraction in the form of one integer divided by another, non-zero, integer.


common fraction

common fraction (plural common fractions)

Originally a calque of New Latin fractiō vulgāris. See vulgar fraction.


binary arithmetic

binary arithmetic (usually uncountable, plural binary arithmetics)

Note that all correctly rounding arithmetics satisfy property A1, as do those with properly truncating addition. All faithful binary arithmetics and all arithmetics with either properly truncating or correctly chopping addition satisfy property A2.

1992, Douglas M. Priest, On Properties of Floating Point Arithmetics, University of California, Berkeley, page 17:

(arithmetic) arithmetic using binary numbers


decimal arithmetic

(arithmetic) Arithmetic using decimal numbers.


lowest common denominator

lowest common denominator (plural lowest common denominators)

LL-Q1860 (eng)-Flame, not lame-lowest common denominator.wav

The lowest common denominator of ¹⁄₆ and ³⁄₁₀ is 30.

(mathematics) The smallest positive integer which is a multiple of every denominator of several fractions.

mínimu común denominaor

smallest multiple of several denominators


osculation

osculation (countable and uncountable, plural osculations)

From Latin ōsculātiō (“a kissing”), from ōsculor (“I kiss”). By surface analysis, osculate + -ion.

(Vedic arithmetic) The determination of whether a number is divisible by another by means of certain operations on its digits.


decimal place

The answer is 1.245, to three decimal places

(arithmetic) The position of a digit to the right of the decimal point in a decimal number.

小數位 /小数位

position of digit to the right of the decimal point


place of decimals

place of decimals (plural places of decimals)

It will always be better to calculate one place of decimals more than are required by the question.

1841, Charles Hutton, Thomas Stephens Davies, A Course of Mathematics in Two Volumes, Composed for the Use of the Royal Military Academy, page 56:

Find the positive root of the equation eˣ – 3x = 0, correct to 3 places of decimals.

1980, Michael H. Stone, The Borderline Syndromes: Constitution, Personality, and Adaptation, page 101:

In consequence of the need of Tables of Jₙ (x) with fairly large values of n and x for Astronomical purposes, Hansen constructed a Table of J₀ (x) and Jᵢ (x) to six places of decimals with a range from x = 0 to x = 10.0 with interval 0.1.

1995, G. N. Watson, A Treatise on the Theory of Bessel Functions, page 655:

To round a decimal correct to one place of decimals (1 d.p.) you look at the second place of decimals.

2001, Keith Pledger, Edexcel GCSE Mathematics, page 103:

Use Newton Raphson method to find the values of (i) VT2 and (ii) —, correct to four places of decimals.

2005, Veerarajan & Ramachandran, Numerical Methods: With Programs In C, pages 3–54:

In the application of Simpson's rule, when the number of places of decimals to which the answer is required, is not mentioned, it is usual to calculate the answer correct to three places of decimals.

2006, Bansi Lal, Topics in Integral Calculus, page 272:

(arithmetic, dated, chiefly UK, usually in the plural) A decimal place.


unit fraction

(arithmetic) A fraction whose numerator is 1 and whose denominator is a positive integer; for example, 1/2 or 1/7.

аликвотна дроб

fraction whose numerator is 1 and denominator a positive integer


quinary

From the Latin quīnārius (“containing five each”), from quīnī (“five each”, “five at a time”) + -ārius (whence the English suffix -ary); compare the French quinaire, the Italian quinario, and the Portuguese quinário. Doublet of quinarius.

der

(arithmetic) To the base of five; represented by the numerals 0, 1, 2, 3 and 4.


ternary

From Late Latin ternārius (“consisting of three things”), from ternī (“three each”).

Perhaps the prettiest number system of all is the balanced ternary notation

1999, Donald Knuth, The Art of Computer Programming, 3rd edition, volume 2, →ISBN, page 207:


arithmetic operation

en-noun

arithmetic operation (plural arithmetic operations)

Although Equation 2.45 looks simple, it involves more arithmetic operations as compared to Equations 2.36 and 2.38.

2000, Chang Shu, Differential Quadrature and Its Application in Engineering, Springer, page 38:

A key feature of the IEEE standard is that it requires correctly rounded operations, specifically:
• correctly rounded arithmetic operations (add, subtract, multiply, divide);
• correctly rounded remainder and square root operations;
• correctly rounded format conversions.

2001, Michael L. Overton, Numerical Computing with IEEE Floating Point Arithmetic, SIAM, page 31:

PHP enables you to do arithmetic operations on numbers. You indicate arithmetic operations with two numbers and an arithmetic operator. For instance, one operator is the plus (+) sign, so you can indicate an arithmetic operation like this:
1 + 2

2013, Steve Suehring, Janet Valade, PHP, MySQL, JavaScript & HTML5 All-in-One For Dummies, John Wiley & Sons, page 289:

(arithmetic, computing) Any one of the four basic operations in arithmetic: addition, subtraction, multiplication or division; any one of said operations as implemented on a computer.

аритметична операция

any one of the four basic operations in arithmetic


decimal fraction

decimal fraction (plural decimal fractions)

(arithmetic) A proper or improper fraction the denominator of which is a power of ten and the decimal representation of which is a terminating decimal number.


senary

From the Latin sēnārius (“consisting of six each”), from sēnī (“six each, six at a time”) + -ārius (whence the English suffix -ary).

der

The senary fraction 0.2 is one-third, i.e. two-sixths.

(arithmetic) Of, pertaining to, or based on six.


senary

(arithmetic) The numeral system which uses six as the base.


radicate

en-verb

radicate (third-person singular simple present radicates, present participle radicating, simple past and past participle radicated)

radicates (present singular third-person)
radicating (participle present)
radicated (participle past)
radicated (past)

From Latin radicatus, past participle of radicari (“to take root”), from radix (“root”).

Numbers, arithmetically, can be added, subtracted, multiplied and divided, exponentiated and radicated, […]

1972, Patrick Meredith, Dyslexia and the individual, page 36:

(transitive, arithmetic, rare) To extract the root of a number.


weighted mean

(arithmetic) An average calculated after biasing values according to agreed weightings.


osculator

(Vedic arithmetic) An algorithm for performing osculation.


arithmetic operator

en-noun

arithmetic operator (plural arithmetic operators)

(arithmetic) Any of the four basic operators in arithmetic, namely addition, subtraction, multiplication and division.

թվաբանական օպերատոր

any of the four basic operators in arithmetic


biquadrate

en-verb

biquadrate (third-person singular simple present biquadrates, present participle biquadrating, simple past and past participle biquadrated)

biquadrates (present singular third-person)
biquadrating (participle present)
biquadrated (participle past)
biquadrated (past)

Two biquadrated is equal to sixteen.

(transitive, arithmetic) To raise to the fourth power; to determine the result of multiplying by itself three times.


dozenal

(arithmetic, rare) Of a number, expressed in base 12.


dozenal

(arithmetic, rare) A value in a number system that uses 12 as its base.


vinculate

vinculate (third-person singular simple present vinculates, present participle vinculating, simple past and past participle vinculated)

vinculates (present singular third-person)
vinculating (participle present)
vinculated (participle past)
vinculated (past)

The reason why we typically want to vinculate is we want to deal with small single digit numbers. This means we typically want to vinculate numbers that are larger than 5. When we vinculate numbers like 6, 7, 8, 9 we get 4, 3, 2 and […]

2010, Chandramouli Mahadevan, Basics of Speed Mathematics, Lulu.com, →ISBN, page 24:


carry over

carry over (third-person singular simple present carries over, present participle carrying over, simple past and past participle carried over)

carries over (present singular third-person)
carrying over (participle present)
carried over (participle past)
carried over (past)

Attested since the 17th century; listed for instance in Elisha Coles' 1676 dictionary as a translation of transfer, thereby possibly a calque of Latin transfero; compare Dutch overdragen, German übertragen.

(transitive, arithmetic) To carry; to transfer an excess quantity to the next column of digits.


complex fraction

en-noun

complex fraction (plural complex fractions)

(mathematics, arithmetic) Any fraction in which either or both of the numerator or denominator are themselves fractions.


doubly even

Eight is a doubly even number.

(arithmetic) Leaving no remainder when divided by 4; divisible by 4.


singly even

Six is a singly even number.

(arithmetic) That leaves a remainder of 2 when divided by 4; divisible by 2 but not by 4.


radication

radication (usually uncountable, plural radications)

From Middle English radicacyon, from Medieval Latin rādīcātio.

(arithmetic, rare) The process of extracting a number's root.


Chinese numeral

Chinese numeral (plural Chinese numerals)

From their original development and chief use in China.

A number represented using a Chinese system involving the characters 一, 二, 三, etc.

(in the plural) The system using such numerals, still employed in Chinese- and Japanese-speaking countries and formerly used in Korean- and Vietnamese-speaking ones.


simple fraction

simple fraction (plural simple fractions)

(mathematics, arithmetic) A fraction in which both the numerator and the denominator consist of whole numbers.


GCF

greatest common factor
greatest common factor#English

(arithmetic) Initialism of greatest common factor.


Hindu-Arabic numeral

Hindu-Arabic numeral (plural Hindu-Arabic numerals)


place value

(arithmetic) The value of a digit of numbers. For example, ones, tens, hundreds in the decimal counting; ones, sixes, thirty-sixes in the senary counting.


Suzhou numeral

A calque of Chinese 蘇州碼子 /苏州码子 (Sūzhōu mǎzi), from their use at the formerly important market town of Suzhou in Jiangsu Province. Mistakenly entered into Unicode as "Hangzhou numerals", which Unicode's policy precludes changing.

calque

A system of Chinese numerals based on Southern Song rod numerals.


dot and carry

en-verb

dot and carry (third-person singular simple present dots and carries, present participle dotting and carrying, simple past and past participle dotted and carried)

dots and carries (present singular third-person)
dotting and carrying (participle present)
dotted and carried (participle past)
dotted and carried (past)

(arithmetic) In addition, to set down the units and carry over the tens to the next column.


octodecimal

Octodecimal 1249 is equivalent to decimal 6561 or nonary 10000.

The decimal scheme should have been made a duodecimal, or better a quinquedecimal or octodecimal one; the expansive system would need a more than India-rubber elasticity to include all the whimsical creations of an author's brain.

By studying other number system such as unodecimal (base-11), duodecimal (base-12), tridecimal (base-13), quadrodecimal (base-14), pentadecimal (base-15), heptadecimal (base-17), octodecimal (base-18), nonadecimal (base-19) and vigesimal (base-20), researcher will gain a better understanding of how number systems work in general.

2012 January, Debasis Das, U.A. Lanjewar, “Realistic Approach of Strange Number System from Unodecimal to Vigesimal”, in International Journal of Computer Science and Telecommunications, volume 3, number 1:

Traditional number system — binary, octal, decimal and hexadecimal, in regular use and Strange number system, with an extra edge of memorized information with greater density, zero redundancy problem, avoiding sign problem and reducing complexity of interconnections, - unodecimal, duodecimal, tridecimal, quadrodecimal, pentadecimal, heptadecimal, octodecimal, nona decimal, vigesimal and further are discussed through compliments.

2013 May, “Subtraction in Traditional and Strange Number System by r's and r-1's Compliments”, in International Journal of Computer Applications, volume 70, number 23:

(arithmetic) Using eighteen as the base.


arithmetic geometry

1994, Nancy Childress, John W. Jones (editors), Arithmetic Geometry: Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, American Mathematical Society, back cover,
This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993.

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over nonalgebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory.

2010, Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta, Arithmetic Geometry: Lectures given at the C.I.M.E. Summer School, Springer, page v:

Their^([semistable models']) occurrence in arithmetic geometry is ubiquitous for the study of ℓ-adic or p-adic cohomology, and of Galois representations.

2013, Matthieu Romagny, “Models of Curves”, in Pierre Dèbes, Michel Emsalem, Matthieu Romagny, A. Muhammed Uludağ, editors, Arithmetic and Geometry Around Galois Theory, Springer, page 149:

Arakelov geometry is one of the branches in arithmetic geometry.

2014, Atsushi Moriwaki, Arakelov Geometry, American Mathematical Society, page vii:

(mathematics) A developing branch of mathematics in which techniques of algebraic geometry are applied to number theory, in particular being concerned with schemes of finite type over the spectrum of the ring of integers, Spec(ℤ).


unprimeable

In the year 200 Diophantus, noted Greek mathematician was born. 200 million is approximately 2/3 of the total population of this country we call home. 200 is also the smallest base 10 unprimeable number.

2007 May 26, “Episode #200”, in Game Show Newsnet:

6,292,015 is a composite, Duffinian, odd, semiprime, square-free and unprimeable number.

2015 June 29, “Brain-O Quiz Answers”, in Mathematical Mystery Tour:

200 is the smallest unprimable number

2015 November 1, Adam Spencer, Adam Spencer's World of Numbers, Xoum Publishing, page 200:

There are infinitely many unprimeable numbers, although the first unprimeable number ending in an odd number is not until 212159.

2019, Julia Collins, Numbers in Minutes:

(arithmetic) That cannot be turned into a prime number by changing just one of its digits to any other digit.


tridecimal

(arithmetic, music) Of a number, expressed in base thirteen.


Euclidean division

en-noun

Euclidean division (countable and uncountable, plural Euclidean divisions)

(arithmetic) The process of dividing one integer by another to yield a quotient and a remainder smaller than the divisor.


parentheme

Modeled after the relationship of thesis to theme.

(arithmetic, linguistics) The expression inside a pair of parentheses.


tetrate

en-verb

tetrate (third-person singular simple present tetrates, present participle tetrating, simple past and past participle tetrated)

tetrates (present singular third-person)
tetrating (participle present)
tetrated (participle past)
tetrated (past)


pentate

pentate (third-person singular simple present pentates, present participle pentating, simple past and past participle pentated)

pentates (present singular third-person)
pentating (participle present)
pentated (participle past)
pentated (past)


hexate

hexate (third-person singular simple present hexates, present participle hexating, simple past and past participle hexated)

hexates (present singular third-person)
hexating (participle present)
hexated (participle past)
hexated (past)


root extraction

en-noun

root extraction (plural root extractions)

(arithmetic) The process or result of computing the nth root of a real or complex number.


plus mark

In the left top window, identified as "News Server" you will see the name of all the news groups your server's news feed carries. At the very left of that window are folder icons, if there are subgroups within that folder. If there is a plus mark to the left of the icon, it means there are groups within that folder that you might want to look at. Click on the plus mark to list the subgroups, click on the minus sign to close that folder.

1996 August 15, J Gerber, “News Groups”, in news.newusers.questions (Usenet), retrieved 2022-08-15:

As you probably know, one of the new things in Access 2000 is a Subdatasheet, a grid that shows up when you click on a plus mark next to each record of the table that is in 1-1 or 1-many relationship with table(s). The examples of the pictures taken can be found at http://www.geocities.com/SouthBeach/Palms/9151/ac_slike.zip and now please look at picture 1.jpg
Picture one shows a price list. So, there are groups of products, products themselves and packages of the products. The relation is Groups->Products->Packages. The picture shows packages of the second product in the first group that showed up when the user clicked a plus mark.
The problem can be seen in picture 2.jpg when going to the new group (group no. 3) the packages of the second product of this group are visible even though the user didn't open them by clicking on the plus mark. I think that the best thing would be to remember the state of each datasheet or to collapse all when going to another group.

1999 August 3, this"@sezampro.yu mire, “SubDataSheet problem”, in microsoft.public.access.forms (Usenet), retrieved 2022-08-15:

A machine for drawing/cutting an ellipse is basically a plus mark shaped groove in wood or plastic and a bar with two adjustable points and a holder for a marker/cutter at the end. The distances from the marker/cutter to the first point and from the first pointer to the second determine the size of the ellipse. Keeping the points in the grooves of the plus mark takes practice.

2002 January 11, Mike Firth, “Oval Cutter”, in rec.crafts.glass (Usenet), retrieved 2022-08-15:

Ok.. try this.. your commas, quotation marks, plus marks, etc are all messed up.

2002 May 2, Mike Flynn, “[PHP-WIN] window.open and php...”, in php.windows (Usenet), retrieved 2022-08-15:

Jim,
Open up your address book in OE under the "Tools" menu. In the address book, click on View and make sure there is a check mark next to Folders and Groups. You should be seeing a list on the left side of the address book with at least "Shared Contacts" and Identity contacts. If you click on Identity contacts you should see the name of your group in the list on the right. If there is a plus mark next to your identity contacts on the left, click the plus and you should see the groups drop down under that folder.

2002 June 27, Spider, “In OE: inserting email addresses”, in 24hoursupport.helpdesk (Usenet), retrieved 2022-08-15:


fractional number

fractional number (plural fractional numbers)

(arithmetic) A fraction, such as 1/2 or 3/5.


mental calculation

mental calculation (countable and uncountable, plural mental calculations)

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

Arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator.

حساب ذهني

arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator


hexatrigesimal

hexatrigesimal (countable and uncountable, plural hexatrigesimals)

From hexa- + tri- + decimal; see the Wikipedia article for hexadecimal for more information.

(arithmetic, computing, uncountable) A number system with base thirty-six, using the digits 0–9 and A–Z.


hexavigesimal

hexavigesimal (countable and uncountable, plural hexavigesimals)

From hexa- + vigesimal; see the Wikipedia article Hexadecimal for more information.

(arithmetic, computing, uncountable) A number system with base twenty-six, using the digits 0–9 and A–P (or A-Z without numerals).


quadravigesimal

quadravigesimal (countable and uncountable, plural quadravigesimals)

/ˌkwɒdˈɹɑvaɪd͡ʒɛsɪməl/

(arithmetic, computing, uncountable) A number system with base twenty-four, using the digits 0–9 and A–N (or Greek α-ω without numerals).


Cyrillic numeral

Cyrillic numeral (plural Cyrillic numerals)

Cyrillic numerals (plural)
cyrillic numeral (alternative US)

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-Cyrillic numeral.wav

A numeral represented using a Cyrillic system involving the letters.


(arithmetic, computing) Synonym of binary (“concerning numbers and calculations using the binary number system”).


Indo-Arabic numeral

Indo-Arabic numeral (plural Indo-Arabic numerals)