Etymology
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number (v.)

c. 1300, "to count," from Old French nombrer "to count, reckon," from nombre (n.) "number" (see number (n.)). Meaning "to assign a distinctive number to" is late 14c.; that of "to ascertain the number of" is from early 15c. Related: Numbered; numbering.

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system (n.)
1610s, "the whole creation, the universe," from Late Latin systema "an arrangement, system," from Greek systema "organized whole, a whole compounded of parts," from stem of synistanai "to place together, organize, form in order," from syn- "together" (see syn-) + root of histanai "cause to stand," from PIE root *sta- "to stand, make or be firm."

Meaning "set of correlated principles, facts, ideas, etc." first recorded 1630s. Meaning "animal body as an organized whole, sum of the vital processes in an organism" is recorded from 1680s; hence figurative phrase to get (something) out of one's system (1900). Computer sense of "group of related programs" is recorded from 1963. All systems go (1962) is from U.S. space program. The system "prevailing social order" is from 1806.
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number (n.)

c. 1300, "sum, aggregate of a collection," from Anglo-French noumbre, Old French nombre and directly from Latin numerus "a number, quantity," from PIE root *nem- "assign, allot; take."

Meaning "written symbol or figure of arithmetic value" is from late 14c. Meaning "single (numbered) issue of a magazine" is from 1795. Colloquial sense of "a person or thing" is by 1894. Meaning "dialing combination to reach a particular telephone receiver" is from 1879; hence wrong number (1886). The modern meaning "musical selection" (1885) is from vaudeville theater programs, where acts were marked by a number. Earlier numbers meant "metrical sound or utterance, measured or harmonic expression" (late 15c.) and, from 1580s, "poetical measure, poetry, verse."

Number one "oneself" is from 1704 (mock-Italian form numero uno attested from 1973); the biblical Book of Numbers (c. 1400, Latin Numeri, Greek Arithmoi) is so called because it begins with a census of the Israelites. Childish slang number one and number two for "urination" and "defecation" attested from 1902. Number cruncher is 1966, of machines; 1971 of persons. To get or have (someone's) number "have someone figured out" is attested from 1853; to say one's number is up (1806) meaning "one's time has come" is a reference to the numbers on a lottery, draft, etc. The numbers "illegal lottery" is from 1897, American English.

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cardinal number (n.)
1590s, "one, two, three," etc. as opposed to ordinal numbers "first, second, third," etc.; so called because they are the principal numbers and the ordinals depend on them (see cardinal (adj.)).
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Dewey Decimal system (n.)

library classification system that organizes information into 10 broad areas subdivided numerically into progressively smaller topics, by 1885, named for Melvil Dewey (1851-1931) who proposed it 1876 while acting librarian of Amherst College. He also crusaded for simplified spelling and the metric system.

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algorithm (n.)
1690s, "Arabic system of computation," from French algorithme, refashioned (under mistaken connection with Greek arithmos "number") from Old French algorisme "the Arabic numeral system" (13c.), from Medieval Latin algorismus, a mangled transliteration of Arabic al-Khwarizmi "native of Khwarazm" (modern Khiva in Uzbekistan), surname of the mathematician whose works introduced sophisticated mathematics to the West (see algebra). The earlier form in Middle English was algorism (early 13c.), from Old French. Meaning broadened to any method of computation; from mid-20c. especially with reference to computing.
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numerical (adj.)

"pertaining to or relating to number, denoting number," 1620s, from Latin numerus "a number" (see number (n.)) + -ical. Perhaps by influence of French numérique "of a number or numbers." Related: Numerically.

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numerate (v.)

"to count, enumerate," 1721, from Latin numeratus, past participle of numerare "to count, to number," from numerus "a number" (see number (n.)). Related: Numerated; numerating.

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numerosity (n.)

"state of being numerous," 1610s, from Latin numerositatem (nominative numerositas) "a great number, a multitude," from numerosus "numerous," from numerus "a number" (see number (n.)).

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outnumber (v.)

"to number more than, exceed in number," 1660s, from out- + number (v.). Related: Outnumbered; outnumbering.

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