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

## Definition

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

The initial segment of the natural numbers determined by $n$:

$\set {0, 1, 2, \ldots, n - 1}$

is denoted $\N_{< n}$.

## Also denoted as

The usual notation for this is $\N_n$, but the notation $\N_{< n}$ is less ambiguous.

The notation $\Z_n$ is often see, for the set of least positive residues of the set of residue classes modulo $n$:

$\Z_n = \set {0, 1, \ldots, n - 1}$

which of course is exactly the same thing.