Suppose SCR is nonempty and bounded. Let A S also be nonempty. Prove that A is...

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Suppose SCR is nonempty and bounded. Let A ≤S also be nonempty. Prove that A is bounded, then prove that sup(A) ≤ sup(S) (meaning prove that the least upper bound property of A is the least upper bound property of S), and inf(S) ≤ inf(A) (meaning proof that the greatest lower bound property of S is the greatestlower bound property of A). Show every step and write the justification for each step using axioms, theorems, or definitions Suppose SCR is nonempty and bounded. Let A ≤S also be nonempty. Prove that A is bounded, then prove that sup(A) ≤ sup(S) (meaning prove that the least upper bound property of A is the least upper bound property of S), and inf(S) ≤ inf(A) (meaning proof that the greatest lower bound property of S is the greatestlower bound property of A). Show every step and write the justification for each step using axioms, theorems, or definitions

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Answer 0 S4 and to show that clearly In and bonded Ass is nonempty and bo... View the full answer