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.