Prove that $\min(S)$ does not exist for $S=(0,1)$

Question

Prove that $\min(S)$ does not exist for $S=(0,1)$.

I'm taking the proof by contradiction route i.e. assuming m = min(S) then trying to find some sort of contradiction.

I've tried take m=2m-1 and take m = (m-1)/2 but neither seem to work?

score 5 · Answer 1 · answered Oct 27 '15 at 16:44

5

Hint: If $m \in S$ is your candidate minimum, consider $m/2$.

answered Oct 27 '15 at 16:44

Ben Grossmann

Consider m1 = m/2. then 0<m1<1 there m1 is in S. But clearly m1<m....contradiction! – Mals T Oct 27 '15 at 21:19
Right!${}{}{}{}$ – Ben Grossmann Oct 27 '15 at 22:00

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