# Talk:Natural number

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The current version of this paper uses two slightly different definitions of the natural numbers. First it defines the natural numbers as the set

N = {0, 1, 2, 3, ...}

which includes zero. Then it constructs the Peano axioms for the whole numbers

W = {1, 2, 3, ...}

which excludes zero. The term “natural numbers” is used to refer to both sets, N and W. This can be confusing, since Lemma 1 in the section titled “ordering” fails if y happens to be zero. --173.206.237.178 21:59, 19 June 2011 (UTC)