Definition:Positive/Real Number

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Definition

The positive real numbers are the set:

$\R_{\ge 0} = \set {x \in \R: x \ge 0}$

That is, all the real numbers that are greater than or equal to zero.


Thus, in Wirth interval notation:

$\R_{\ge 0} = \hointr 0 \to$


Also known as

In order to remove all confusion as to whether positive real number is intended to mean strictly positive real number, the use of the term non-negative real number (or nonnegative real number) is often recommended instead.


The $\mathsf{Pr} \infty \mathsf{fWiki}$-specific notation $\R_{\ge 0}$ is actually non-standard.

The conventional symbols to denote this concept are $\R_+$ and $\R^+$, but these can be confused with the set $\set {x \in \R: x > 0}$.


Also see

  • Results about positive real numbers can be found here.


Sources

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