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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

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    $\begingroup$ 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. $\endgroup$ Dec 22, 2020 at 1:50
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    $\begingroup$ "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. $\endgroup$
    – JMoravitz
    Dec 22, 2020 at 1:51
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    $\begingroup$ It's been many years since I've seen the naturals defined without including $0$. $\endgroup$ Dec 22, 2020 at 1:51
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    $\begingroup$ 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 $\Bbb N\cup \{0\}$ $\endgroup$
    – JMoravitz
    Dec 22, 2020 at 1:52
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    $\begingroup$ 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. $\endgroup$
    – JMoravitz
    Dec 22, 2020 at 1:53

2 Answers 2

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

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

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