- #1
Kinetica
- 88
- 0
Homework Statement
Let S be a nonempty subset of R that is bounded below. Prove that inf S = - sup {-s: s in S}
The Attempt at a Solution
Let a0 = inf S. Thus, for all s in S, a0 is less or equal to s; or -a0 greater or equal to -s.
If u is any upper bound for -S, u is greater or equal to -a0; or -u less or equal to a0.
and here I have difficulty proceeding further. I don't quite see the logic anymore :-(
Any help is greatly appreciated.