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It is well known that natural numbers start in 1.

However, sometimes people work with a "widened set" of natural numeres plus zero, $\mathbb{N}\cup\lbrace 0\rbrace$. That is, all non-negative integers.

Is there a specific symbol for this set? such as $\mathbb{N}^{*}$, $\mathbb{Z}^+$ or anything similar? Thank you

FGSUZ
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    It's actually pretty common to take $\mathbb{N}$ to include zero. I'm not sure which convention is more common; if anything, I think it's a bit more common to include zero. – Daniel Hast Dec 22 '20 at 01:50
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    "It is well known that natural numbers start in 1" No... it is a disagreed upon definition. Many authors have the natural numbers starting from $0$, not $1$. Starting from $1$ happens to also be done by some other authors, but to say that the natural numbers start from $1$ with no further clarification as though it is a universal fact is just flat wrong. – JMoravitz Dec 22 '20 at 01:51
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    It's been many years since I've seen the naturals defined without including $0$. – CyclotomicField Dec 22 '20 at 01:51
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    As another aside, the plus sign, $+$, does not have the meaning you intend. You mean to have the union which is represented by $\cup$, so you should have said $\Bbb N\cup {0}$ – JMoravitz Dec 22 '20 at 01:52
  • A union symbol would be preferable to $+$, like this: $\mathbb N \cup { 0 }$ or $\mathbb Z^+ \cup { 0 }$. I also agree with @DanielHast that many authors use the convention that $\mathbb N$ includes $0$. – littleO Dec 22 '20 at 01:53
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    As yet another aside... $\Bbb Z^+$ is a choice of notation for the strictly positive integers and as such would not include zero, not the set you are after. Asterisks are commonly used to denote the nonzero elements of whatever set though admittedly is not often seen with $\Bbb Z$ or $\Bbb N$. It is seen more commonly with $\Bbb R^$ or $\Bbb Q^$ to mean the nonzero reals or nonzero rationals respectively. – JMoravitz Dec 22 '20 at 01:53
  • So true, it's been too long without sleep, I was feeling weird about writing the + symbol but I wasn't coming up with the union symbol, for some reason. Edited – FGSUZ Dec 22 '20 at 01:55
  • @JMoravitz I've seen $Z^+$ as non-negative and $Z^{++}$ for strictly possitive, but I don't know if that's a rare choice of someone or something more general – FGSUZ Dec 22 '20 at 01:56
  • Shall I delete the question? As I see it's a dupe, altough it didn't show me when I stated the question... – FGSUZ Dec 22 '20 at 01:58
  • $\mathbb Z^{\geq 0}$ or $\mathbb Z_{\geq 0}$ is reasonably common and, unlike most of the alternatives, is unambiguous. –  Dec 22 '20 at 02:14

2 Answers2

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$\mathbb{N}_0$ is the most common choice.

Noah Solomon
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I've seen $\mathbb{N}_0$. But saying $n\ge 0$ is not heavy lifting.

ncmathsadist
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