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Is 0 a natural number?

There seems to be no consensus, although perhaps one is gathering over the centuries to say yes to the first question and identify $\mathbb{N}$ with $\omega$ : the set of finite Von Neumann ordinal numbers. That leaves $\textbf{N}$ = {$1$, $2$, ...} for the counting numbers (who counts with $0$?). You can dodge the issue by writing $\mathbb{Z}_{\geq0}$, $\mathbb{Z}_+$, etc., but it seems awkward to use derived and complicated notation for something so basic.

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    [Oh boy...](http://math.stackexchange.com/questions/283)2010-12-12
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    "who counts with 0?" - C/++ programmers?2010-12-12
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    @J.M:Probably you meant C/C++ but actually there is no such language,contiguous array indexing start from $0$ not only in C and C++ but also in D,Java and probably in few other languages.2010-12-12
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    @Deb: It's a tic of mine; I'm too lazy to write another C. :) In any event, strings are also indexed at 0 (okay fine, they're arrays too :P ).2010-12-12
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    @J.M: Cool! ;-)2010-12-12
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    @J.M.: Well, it sounds strange to call "0" the "first" number.2010-12-12
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    I agree @Hendrik, I'm just repeating an old lame joke... :)2010-12-12
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    @J.M:In C strings are actually null terminated character arrays but yes they are also indexed from $0$.2010-12-12
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    The only programming language known to me that does _not_ count from 0 is the one used in Matlab. In fact, indexing arrays from 1 makes little to no sense. In CS, typically $\mathbb{N} = \{0, 1, \dots\}$ is used.2010-12-12

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