# Math Help - [SOLVED] Proof regarding maximums and minimums of ordered sets

1. ## [SOLVED] Proof regarding maximums and minimums of ordered sets

Let U be an ordered set.

Prove the following:
The minimum of U, if it exists, is unique. The maximum of U, if it exists, is unique.

2. ## Ordered set

Hello jzellt
Originally Posted by jzellt
Let U be an ordered set.

Prove the following:
The minimum of U, if it exists, is unique. The maximum of U, if it exists, is unique.

Let $m_1$ and $m_2$ be two minima of $U$. Then
$\forall x \in U, m_1 \le x \wedge m_2 \le x$
$\Rightarrow m_1 \le m_2 \wedge m_2 \le m_1$
$\Rightarrow m_1 = m_2$