(Mathematics, other places where you need to talk about the real numbers:)

An *interval* is a subset I⊆**R** of the real numbers with the property that if x,y∈I and z is between x and y, then z∈I too.

It's just a "contiguous" segment of the line (which may or may not be bounded on either end). Or, if you like, it's a convex subset of **R** -- 1-dimensional convexity is boring.

Here are an open interval, a closed interval, a half-open interval (which is also half-closed) and 2 unbounded intervals:

(-2,3) = {x: -2<x<3}

[4,7] = {x: 4≤x≤7}

[11,17) = {x: 11≤x<17}

(-∞,9] = {x: x≤9}

(-∞,+∞) = **R**

**Note:** The symbol "∞" in an unbounded interval means precisely *nothing*: the only meaning here is carried by the entire symbol "(-∞,9]".