# Definition:Strictly Positive/Integer

## Definition

The strictly positive integers are the set defined as:

$\Z_{> 0} := \set {x \in \Z: x > 0}$

That is, all the integers that are strictly greater than zero:

$\Z_{> 0} := \set {1, 2, 3, \ldots}$

## Also known as

Some sources to not treat $0$ as a positive integer, and so refer to:

$\Z_{> 0} := \set {1, 2, 3, \ldots}$

as the positive integers.

Consequently the term non-negative integers tends to be used in such sources for:

$\Z_{\ge 0} := \set {0, 1, 2, 3, \ldots}$

Sources which are not concerned with the axiomatic foundation of mathematics frequently identify the positive integers with the natural numbers, which is usually completely appropriate.