# Basic topology proof

1. Aug 21, 2012

### bedi

1. The problem statement, all variables and given/known data

Let E be a nonempty set of real numbers which is bounded above. Let y=sup E. Then y $\in$ E closure. Hence y $\in$ E if E is closed.

2. Relevant equations

E closure = E' $\cup$ E where E' is the set of all limit points of E.

3. The attempt at a solution

By the definition of closure, y is either in E' or E (maybe in both). If E is closed, E' $\subset$ E and we know that the union of a set and its subset is the set itself. Therefore E closure = E.

Is this a valid proof?

2. Aug 22, 2012

### clamtrox

Shouldn't you be proving that if y=sup(E), then y ∈ E closure?