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According to most modern [[mathematics]] and [[logic]] textbooks a '''natural number''' is a non-negative [[integer]] such as 0, 1, 2, 3,... etc. <ref>Unfortunately, 0 is sometimes also included in the list of "natural" numbers (Bourbaki 1968, Halmos 1974), and there seems to be no general agreement about whether to include it. In fact, Ribenboim (1996) states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 in P." [http://mathworld.wolfram.com/NaturalNumber.html (Wolfram)] </ref>

In [[mathematics]], a '''natural number''' is a a number from the set {0,1,2,...} or (1,2,3...}, depending on the context and the reference.<ref>Unfortunately, 0 is sometimes also included in the list of "natural" numbers (Bourbaki 1968, Halmos 1974), and there seems to be no general agreement about whether to include it. In fact, Ribenboim (1996) states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 in P." [http://mathworld.wolfram.com/NaturalNumber.html (Wolfram)] </ref> Natural numbers were used initially for counting ("there are three cows in this field"), but they took on the purpose of ordering as well ("She is the 2nd fastest person alive). The set of natural numbers is [[countably infinite]]- via [[bijection]], this property can be used to prove the countability of the [[integer]]s and [[rational number]]s.

Older books sometimes exclude [[zero]], as there is a long history of people thinking that zero is unnatural or not really a number.

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