Theorem 4. If S is a non-empty subset of R which is bounded below, then a real number t is the infimum of S iff the followving two conditions hold : (i) x>tV xe S. (ii) Given any ɛ> 0, 3 some x e S...

Proof this Theorem

Extracted text: Theorem 4. If S is a non-empty subset of R which is bounded below, then a real number t is the infimum of S iff the followving two conditions hold : (i) x>tV xe S. (ii) Given any ɛ> 0, 3 some x e S such that x