Least Upper Bound Property

Theorem
Let $S \subset \R$ be a non-empty subset of the set of real numbers such that $S$ is bounded above.

Then $S$ admits a supremum in $\R$.

This is known as the least upper bound property of the real numbers.

Also known as
The least upper bound property of $\R$ is also known as:
 * the supremum principle.
 * the continuum property (although this is also used to encompass the Greatest Lower Bound Property, a complementary result)

Also see

 * Greatest Lower Bound Property
 * Continuum Property