Numeral system
notation for expressing numbers
A numeral system is a writing system for expressing numbers without words; that is, a mathematical notation for representing numbers of a given set, using digits (in positional notation) or other symbols (in sign-value notation) in a consistent manner.
The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral system (used in tallying scores).
The number the numeral represents is called its value. Additionally, not all number systems can represent the same set of numbers; for example, Roman, Greek, and Egyptian numerals all lack an official representation of the number zero.
Ideally, a numeral system will:
Represent a useful set of numbers (e.g. all integers, or rational numbers)
Give every number represented a unique representation (or at least a standard representation)
Reflect the algebraic and arithmetic structure of the numbers.
For example, the usual decimal representation gives every nonzero natural number a unique representation as a finite sequence of digits, beginning with a non-zero digit.
Numeral systems are sometimes called number systems, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of real numbers, the system of complex numbers, various hypercomplex number systems, the system of p-adic numbers, etc. Such systems are, however, not the topic of this article.
“Numeral system” enters the record as notation for expressing numbers. Crown Archives preserves that source wording while asking what Numeral, system and notation can confirm, complicate or overturn.
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This entry incorporates text from “Numeral system” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.