Proving open 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, infinity) is an open set

 

[daon]

Let \(\displaystyle x\in(a,\infty)\) then \(\displaystyle x>a \implies x>\frac{x+a}{2}>a\).

Find an open set contained in that set centered at x now.