Symbols:N

The Set of Natural Numbers
$$\mathbb{N}$$

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

Its LaTeX code is \mathbb{N}.

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

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

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

Subsets of Natural Numbers
$$\mathbb{N}_n$$, $$\mathbb{N}^*_n$$

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

Its LaTeX code is \mathbb{N}_n.

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

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

= Deprecated Usages =

Older literature tends to use $$\mathbb{N}$$ 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 $$\tilde {\mathbb{N}}$$.

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