Question: 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

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

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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