Please state the problem!
We don't know what you are to prove,
S is a nonempty set of real numbers bounded from below.
Here is what I have done so far:
x=inf S=glb S
Since x=glb S, there cannot be an x+epsilon that is a lower bound. This implies there exists a elemt of S such that x-epsilon<a<x<x+epsilon.
My problem is that I think I went wrong somewhere in the 2nd sentence. I can do the rest of my problem if I can get this cleared up, but I'm not entirely sure where I went wrong.
here is a sketch of the proof
if S has a minimum, then inf(S) = min{S} and so is in the set
now suppose S does not have a minimum, and let x = inf(s)
then there is some so that . let . then by the denseness of , there is some , so that and . continue this logic by induction to create a sequence that converges to