**EXPERT ANSWER**

# Use the completeness axiom for sups to prove the analogous result for infs: if S is a subset of Real Numbers, S ≠ Ø, and S is bounded below, then there is a α existent in REAL NUMBERS such that α = inf(S). (Hint: Given a nonempty set S, look at the new set -S defined by -S = {-s|s is existent in S}. Apply the completeness axiom to -S and interpret the result.)

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