**EXPERT ANSWER**

# The Completeness Axiom only asserts something about sets that arebounded above. Use the Completeness Axiom to prove that everynonempty set of real numbers that is bounded below has aninfimum. Completeness Axiom: Each nonempty set of real numbersthat is bounded above has a supremum. a)If y is a rational number such that y2 >2, then y is an upper bound of S. b)Every rational number that is an upper bound of S is greater than1. c)The number q is rational.

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