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 $n$:
 * $\left\{{1, 2, 3, \ldots, n}\right\}$

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.