# Least Upper bound 61.1

• October 26th 2009, 10:47 AM
tigergirl
Least Upper bound 61.1
Prove that if A has a least upper bound, then it is unique. Thus prove: If b and b' are both least upperbound of A, then b = b'.
• October 26th 2009, 11:00 AM
Plato
Quote:

Originally Posted by tigergirl
Prove that if A has a least upper bound, then it is unique. Thus prove: If b and b' are both least upperbound of A, then b = b'.

In general if $t=\text{lub}(A)$ and $s then this must be true $\left( {\exists x \in A} \right)\left[ {s < x \leqslant t} \right]$

If $b\ne b'$ then $b.