# Supremum of Subset of Real Numbers/Examples/Example 3

## Example of Supremum of Subset of Real Numbers

The subset $V$ of the real numbers $\R$ defined as:

$V := \set {x \in \R: x > 0}$

## Proof

Aiming for a contradiction, suppose $x \in \R$ is a supremum for $V$.

Then we have that:

$x + 1 \in V$

and it is seen that $x$ is not a supremum after all.

$\blacksquare$