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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

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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

(6)(a)(4pts) state the completeness axiom for the real numbers (b)(6 pts). use the completeness axiom to prove that the integers z , r are bounded above by any real number.

Use the completeness axiom to show that every non empty subset of R (real numbers) that is bounded below has an infimum in R

1. prove that every nonempty set of real numbers that is bounded below has an infimum .suggested strategy: your argument will use the the completeness axiom.

Prove using the axioms and properties of real numbers that for any real numbers x and y, if x is greater than or equal to y, then -y greater than or equal to -x.

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

Five the precise definition or statement for the following. 1. Let S be a nonempty subset of the real numbers. a. An upper bound for S. b. The supremum for S. c. The completeness axiom for the real numbers.

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