Symbols:N

The Set of Natural Numbers
$$\N$$

The set of natural numbers:
 * $$\N = \left\{{0, 1, 2, 3, \ldots}\right\}$$.

Its LaTeX code is \mathbb{N} or \N.

The Set of Non-Zero Natural Numbers
$$\N^*$$

The set of non-zero natural numbers:
 * $$\N^* = \left\{{1, 2, 3, \ldots}\right\}$$.

Its LaTeX code is \mathbb{N}^* or \N^*.

Subsets of Natural Numbers
$$\N_n$$, $$\N^*_n$$

The set $$\N_n$$ is the set of all natural numbers which are less than $$n$$:
 * $$\N_n = \left\{{x \in \N: x < n}\right\} = \left\{{0, 1, 2, \ldots, n-1}\right\}$$.

Its LaTeX code is \mathbb{N}_n or \N_n.

Similarly, the set $$\N^*_n$$ is the set of all non-zero natural numbers which are less or equal to $$n$$:
 * $$\N^*_n = \left\{{x \in \N^*: x \le n}\right\} = \left\{{1, 2, \ldots, n}\right\}$$.

Its LaTeX code is \mathbb{N}^*_n or \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 $$\tilde {\N}$$.

Its LaTeX code is \tilde {\mathbb{N}}</tt> or \tilde {\N}</tt>.