Theorem 3. If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum of S if and only if the following two conditions hold : (i) xSsxeS. (ii) Given.any ɛ> 0,...

Proof

Extracted text: Theorem 3. If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum of S if and only if the following two conditions hold : (i) xSsxeS. (ii) Given.any ɛ> 0, 3 some x E S such that x > s - E.