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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.


marked as duplicate by Timothy Wagner, Ross Millikan, J. M. is a poor mathematician, Aryabhata, Jonas Meyer Dec 12 '10 at 17:45

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    $\begingroup$ Oh boy... $\endgroup$ – J. M. is a poor mathematician Dec 12 '10 at 15:54
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    $\begingroup$ "who counts with 0?" - C/++ programmers? $\endgroup$ – J. M. is a poor mathematician Dec 12 '10 at 15:56
  • $\begingroup$ @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. $\endgroup$ – Quixotic Dec 12 '10 at 16:06
  • $\begingroup$ @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 ). $\endgroup$ – J. M. is a poor mathematician Dec 12 '10 at 16:08
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    $\begingroup$ 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. $\endgroup$ – Raphael Dec 12 '10 at 18:07

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