Is there complete consensus on which of these is true?
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No. ${}{}{}{}{}$ – user7530 Mar 19 '14 at 16:23
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1I would say ${1,2,\dots}$ otherwise there is no distinction from $\mathbb{N}$. However, I would recommend $\mathbb{Z}_{>0}$ for example. But this is just my opinion. – naslundx Mar 19 '14 at 16:23
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@naslundx no distinction from $\Bbb N$? I have always used $\Bbb N$ to mean ${1,2,3,\cdots}$. For ${0,1,2,3,\cdots}$ I use $\Bbb W$. It's always like this in school here. – Guy Mar 19 '14 at 16:34
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@Sabyasachi Interesting, I would say $0 \in \mathbb{N}$, but I might be wrong. Either way, one of the two alternatives would equal $\mathbb{N}$. – naslundx Mar 19 '14 at 16:40
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@naslundx yes one of the two would. Also it doesn't cause that much confusion, the intended set can almost always be inferred from context. Of course, $0$ should be in $\Bbb N$. There's nothing unnatural about it. – Guy Mar 19 '14 at 16:42
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most of the time $\mathbb{Z}_{+}$ is taken as $\{1,2,3,...\}$...for other the term $non-negative \ integers$ is used.
wanderer
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I'm not saying you're wrong, just that you should include a link to a source that verifies your claim. – naslundx Mar 19 '14 at 16:28
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@naslundx http://mathworld.wolfram.com/NaturalNumber.html or http://en.wikipedia.org/wiki/Natural_number...but again its a matter of convention. – wanderer Mar 19 '14 at 16:30
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These notations haven't an universal agreement and just know for example that the Bourbaki notation for these sets (which's the notation adopted by the French mathematicians among other) is:
- $\Bbb N=\{0,1,2,\ldots\}$
- $\Bbb N^*=\{1,2,\ldots\}$
- $\Bbb Z_+=\Bbb N$