0
integer number zero; neutral element for the addition
0 (zero, ) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently dividing by 0 is generally considered to be undefined in arithmetic. Additionally, any number raised to the power of 0 is equal to 1, with exception of 0 to the power of 0 which is sometimes undefined.
As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya.
Common names for the number 0 in English include zero, nought, naught (), and nil.
This brief starts where responsible research should: with the source description of “0” as integer number zero; neutral element for the addition. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as integer number zero; neutral element for the addition. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Sep 18, 2026. The linked authority identifier is Q204. The Library of Congress control number is sh85149761. None of the 1 selected statements returned an explicit reference.
The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
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- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
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This entry incorporates text from “0” 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.