Problem 1:

Let S be a non-empty set bounded by the subset of real numbers. Prove that sup S is unique.

Problem 2:

Let S and T be non-empty bounded subsets of real numbers were S is a subset of T. Prove that

inf T <= inf S <= sup S <= sup T

Problem 3:

A) prove: if x and y are real numbers with x < y, then there are infitely many rational numbers in the interval [x,y]

B) repeat part A for irrational numbers