Definition:Initial Segment of Natural Numbers

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

The initial segment of the natural numbers determined by $n$:
 * $\left\{{0, 1, 2, \ldots, n-1}\right\}$

is denoted $\N_n$.

The initial segment of the non-zero natural numbers determined by $n$:
 * $\left\{{1, 2, 3, \ldots, n}\right\}$

is denoted $\N^*_n$.

Also defined as
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.

Some sources use $\mathbf P_n$ or similar, for either $\N_n$ or $\N^*_n$, where $\mathbf P$ may stand for positive.

There is considerable inconsistency in the literature.