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QUESTION 11 The proof that the real numbers contains the square root of 3 relied upon,just the field of axioms of the reals, just the order axioms of the reals, the field axioms,order axioms and the least upper bounds property of the reals, just the least upper bound property of the reals

The proof that the real numbers contains the square root of 3 relied upon. just the field of axioms of the reals just the order axioms of the reals the field axioms,order axioms and the least upper bounds property of the reals just the least upper bound property of the reals 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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