Originally Posted by
alexandrabel90 can someone explain to me what the below means?
consider the set S= (a,b). here b= sup S. let ε > 0, find x ∈ S such that b-ε ≤ a. I think this should be b-ε ≤ x.
to solve this, there are two cases
case 1:
ε≥ b-a. then b-ε≤ a and thus we can take any x of the interval (a,b).
case 2:
ε ≤ b-a then b- ε ∈ (a,b). we can take for x to be the midpt of (b-ε, b). clearly, x ∈ (a,b) and b-ε < x.
can someone explain to me what does the cases talk about becos i have no idea why it works..
thanks!