# Definition:Initial Segment of Natural Numbers/One-Based

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## Contents

## 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 *Undergraduate Topology* by Robert H. Kasriel, who uses $\mathbf P_n$.

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

## Also see

## Sources

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): $\S 1.1$. Sets: Example $7$ - 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Chapter $1$: Mappings: $\S 15$ - 1971: Robert H. Kasriel:
*Undergraduate Topology*... (previous) ... (next): Notation for Some Important Sets