prometheus54
New member
- Joined
- Mar 7, 2011
- Messages
- 5
I need to prove the following. Let S be a nonempty subset of R that is bounded below. Then inf S = -sup{ -s : s is in S}
So i started by proof by contradiction and said we will assume inf S < -sup{ -s : s is in S}. then there exists an x in S such that x< -sup{ -s : s is in S},
so - x > -sup{ -s : s is in S}. Which is a contradiction. Now this is where i got lost in now proving the second case that we assume inf S > -sup{ -s : s is in S}.
Also i am not sure if i did the first case correctly, and thoughts or help would be much appreciated. Thanks
So i started by proof by contradiction and said we will assume inf S < -sup{ -s : s is in S}. then there exists an x in S such that x< -sup{ -s : s is in S},
so - x > -sup{ -s : s is in S}. Which is a contradiction. Now this is where i got lost in now proving the second case that we assume inf S > -sup{ -s : s is in S}.
Also i am not sure if i did the first case correctly, and thoughts or help would be much appreciated. Thanks