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.
Any advice? Thanks in advance.
Hello jzelltLet $\displaystyle m_1$ and $\displaystyle m_2$ be two minima of $\displaystyle U$. Then
$\displaystyle \forall x \in U, m_1 \le x \wedge m_2 \le x$
$\displaystyle \Rightarrow m_1 \le m_2 \wedge m_2 \le m_1 $
$\displaystyle \Rightarrow m_1 = m_2$
Same with maxima.
Grandad