Definition:Strictly Positive/Integer

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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.

Writers whose aim is specialised may refer to the positive integers as just numbers, on the grounds that these are the only type of number they are going to be discussing.

Also see