Prove that inf S = - sup {-s: s in S}

  • Thread starter Kinetica
  • Start date
  • #1
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.


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

Related Threads on Prove that inf S = - sup {-s: s in S}

  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
8
Views
994
Replies
2
Views
4K
  • Last Post
Replies
4
Views
4K
Replies
3
Views
5K
Replies
3
Views
1K
  • Last Post
Replies
14
Views
2K
Replies
4
Views
3K
Top