Definition:Initial Segment of Natural Numbers

Definition
Let $$n \in \N$$ be a natural number.

The subset of the natural numbers less than $$n$$:
 * $$\left\{{0, 1, 2, \ldots, n-1}\right\}$$

is denoted $$\N_n$$.

The subset of the non-zero natural numbers less than or equal to $$n$$:
 * $$\left\{{1, 2, 3, \ldots}\right\}$$

is denoted $$\N^*_n$$.

Some sources consider $$n$$ as an integer and use the symbology:
 * $$\Z \left({n}\right) = \left\{{1, 2, \ldots, n}\right\} = \left\{{z \in \Z: 1 \le z \le n}\right\}$$

but this is rare.