# Symbols:N

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## nano-

$\mathrm n$

The Système Internationale d'Unités metric scaling prefix denoting $10^{\, -9 }$.

Its $\LaTeX$ code is \mathrm {n} .

## The Set of Natural Numbers

$\N$

The set of natural numbers:

$\N = \left\{{0, 1, 2, 3, \ldots}\right\}$.

The $\LaTeX$ code for $\N$ is \N  or \mathbb N or \Bbb N.

## The Set of Non-Zero Natural Numbers

$\N_{> 0}$ or $\N_{\ne 0}$
$\N_{> 0} = \left\{{1, 2, 3, \ldots}\right\}$.

The $\LaTeX$ code for $\N_{> 0}$ is \N_{> 0}  or \mathbb N_{> 0} or \Bbb N_{> 0.}

The $\LaTeX$ code for $\N_{\ne 0}$ is \N_{\ne 0}  or \mathbb N_{\ne 0} or \Bbb N_{\ne 0.}

### Deprecated

$\N^*$
$\N^* = \left\{{1, 2, 3, \ldots}\right\}$.

The $\LaTeX$ code for $\N^*$ is \N^*  or \mathbb N^* or \Bbb N^*.

## Initial Segment of Natural Numbers

$\N_n$, $\N^*_n$

The set $\N_n$ is the set of all natural numbers which are less than $n$:

$\N_n = \left\{{x \in \N: x < n}\right\} = \left\{{0, 1, 2, \ldots, n-1}\right\}$.

The $\LaTeX$ code for $\N_n$ is \N_n  or \mathbb N_n or \Bbb N_n.

Similarly, the set $\N^*_n$ is the set of all non-zero natural numbers which are less or equal to $n$:

$\N^*_n = \left\{{x \in \N^*: x \le n}\right\} = \left\{{1, 2, \ldots, n}\right\}$.

The $\LaTeX$ code for $\N^*_n$ is \N^*_n  or \mathbb N^*_n or \Bbb N^*_n.

# Deprecated Usages

Older literature tends to use $\N$ to mean $\left\{{1, 2, 3, \ldots}\right\}$.

Consequently, the set $\left\{{0, 1, 2, 3, \ldots}\right\}$ needs another symbol to denote it. The usual technique is to use $\tilde {\N}$.

The $\LaTeX$ code for $\tilde \N$ is \tilde \N .