Preferred Notation for Indexing the Naturals from $0$

Asked Dec 08 '13 at 23:56

Active Dec 08 '13 at 23:56

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Depending on circumstantial factors, I occasionally want to index the natural numbers $\mathbb{N}$ from $0$, and at other times, from $1$: i.e. $\mathbb{N} = \{0,1,2,3,\ldots\} \text{ or } \{1,2,3,\ldots\}$, respectively.

Here's my question: is there a preferred or conventional way of denoting the index? For example, for the positive integers, I usually write $\mathbb{Z}_+$. I've seen $\mathbb{N}_0$ to denote the naturals indexed from $0$, but this seems a little ambiguous (especially when we would conversely write $\mathbb{N}_1$). I've thought about writing $\mathbb{N}\cup \{0\}$ to denote the naturals indexed from $0$ unambiguously, but this seems a little heavy-handed.

asked Dec 08 '13 at 23:56

Newb

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People seem to like $\mathbb N_{\ge 0}$. I like $\mathbb N_0$. – Git Gud Dec 08 '13 at 23:58
I'd play it safe and define $\mathbb{N}_0 = \mathbb{N}\cup{0}$ at the start. – genepeer Dec 09 '13 at 00:00
My convention is that $\Bbb N$ includes $0$, and $\Bbb Z^+$ does not. If I think that it’s likely to be understood, I use $\omega$ rather than $\Bbb N$. (I have also been known to use $\omega\setminus 1$ instead of $\Bbb Z^+$.) – Brian M. Scott Dec 09 '13 at 00:23
I've seen Brian's notation quite frequently. – Jemmy Dec 09 '13 at 00:31
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@BrianM.Scott At $\omega\setminus 1$ I had to stare for half a minute until it clicked, but now I love it! ;-) – fgp Dec 09 '13 at 00:39
What is the set $\omega$? – Newb Dec 09 '13 at 00:49

Preferred Notation for Indexing the Naturals from $0$

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