Definition:Initial Segment of Natural Numbers/One-Based

Definition
Let $n \in \N$ be a natural number. The initial segment of the non-zero natural numbers determined by $n$:
 * $\set {1, 2, 3, \ldots, n}$

is denoted $\N^*_{\le n}$.

Also denoted as
The usual notation for this is $\N^*_n$, but the notation $\N^*_{\le n}$ is less ambiguous.

Some sources use the notation of integers, and denote $\set {1, 2, 3, \ldots, n}$ as $\map \Z n$.

Some sources use $P$ or a variant, for example by, who uses $\mathbf P_n$.

There does not seem to be any notation for this concept which is neither ambiguous nor cumbersome, so on it is commonplace to select a simple notation and define it at point of use.

Also see

 * Definition:Initial Segment of Zero-Based Natural Numbers