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

does not admit a supremum.

Proof
$x \in \R$ 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.