Greatest Element is Supremum/Examples/Example 2

Example of Use of Greatest Element is Supremum
Let $V$ be the subset of the real numbers $\R$ defined as:
 * $V := \set {x \in \R: x > 0}$

From Supremum of Subset of Real Numbers: Example 3, $V$ has no supremum.

It follows from Greatest Element is Supremum that $V$ has no greatest element either.