How do I prove that If S is bounded then there exist a positive real number M such that |x| ≤ M for all x ∈ S ?

Answer 1

w/o the absolute value, it would be:
−M≤x≤M

Answer 2

ok and?

Answer 3

Sorry Raban, unfortunately I can't help, I've done way too much math today and that question is giving me headache. I hope you figure it out.

Answer 4

looks like that is the very definition of boundedness.