# Basic topology proof

## Homework Statement

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.

## Homework Equations

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

## 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?