“A numeral is a symbol for a number — and the most important numeral ever adopted was zero, which Romans never had and which transformed everything.”
Latin numerale meant belonging to a number — from numerus (number). A numeral was originally an adjective: a numeral noun, a numeral adjective. The independent noun numeral — a symbol representing a number — entered English in the 16th century as the distinction between number (the abstract quantity) and numeral (the written symbol) became important.
Roman numerals — I, V, X, L, C, D, M — had no symbol for zero. Roman arithmetic was awkward: you could not easily perform calculations with written Roman numerals, so Romans used abacus beads for calculation and wrote numerals only to record results. There was no Roman way to write the position value that zero enables: no way to distinguish 11 from 101 without zero to mark the empty position.
Hindu-Arabic numerals — 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 — arrived in Europe through Arabic translations of Indian mathematical texts. Al-Khwarizmi's 9th-century treatise on Indian arithmetic (whose Latin translation title began 'Algoritmi de numero Indorum' — Al-Khwarizmi concerning the number of Indians) introduced the system to the Islamic world. Fibonacci's Liber Abaci (1202) promoted the system in Europe.
The adoption of Hindu-Arabic numerals with positional notation and zero was the single most significant change in the history of European mathematics. Without zero and positional notation, calculus and algebra would have been incomparably harder. The numeral — the symbol for the number — is the technology that made mathematical notation possible.
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Today
The numeral and the number are not the same thing. The number 7 exists independently of how you write it — VII in Roman, ٧ in Arabic-Indic, 七 in Chinese, 7 in the Western standard. The numeral is the written symbol; the number is the abstract quantity.
Digital computers operate in binary: 0s and 1s. Every piece of digital information — every document, photograph, and piece of music — is ultimately a sequence of two numerals. The binary numeral system was proposed by Leibniz in 1703, who saw it as a mathematical demonstration of creation from nothing. The computer realizes Leibniz's theological metaphor as engineering.
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