So far, I've written down the definition of an interval as follows:
There exists a,b in S and c in S such that a < c < b. S
Let S1 = Intersection (-inf,c)
Let S2 = Intersection (c,inf).
Then I've assumed f is not confinuous at a point a and started an epsilon-delta arguement.
I think it has something to do with f(c) + epsilon/2, but I can't complete the proof...