Proving closed sets

[summerset353]

A set S of real numbers is defined to be an open set if it has the following property: for each xEs, there exists a positive number r such that (x-r, x+r) is a subset of S. The set S is closed if the set R(real numbers)\S is open.

Prove the interval [a,b] is a closed set

 

[daon]

You need to show \(\displaystyle (\infty, a) \cup (b,\infty)\) is open.

Where are you stuck?