# Definition:Strictly Positive/Natural Number

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## Definition

The **strictly positive natural numbers** are the set defined as:

- $\N_{>0} := \set {x \in \N: x > 0}$

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

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

## Also known as

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

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