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'.

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- Oct 26th 2009, 10:47 AMtigergirlLeast 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'.

- Oct 26th 2009, 11:00 AMPlato
In general if $\displaystyle t=\text{lub}(A)$ and $\displaystyle s<t$ then this must be true $\displaystyle \left( {\exists x \in A} \right)\left[ {s < x \leqslant t} \right]$

If $\displaystyle b\ne b'$ then $\displaystyle b<b'\text{ or }b'<b$.

There are contradictions either way.