Let A be a non-empty subset of R that is bounded above. (a) Let U =...

Question

Question

Let A be a non-empty subset of R that is bounded above.

(a) Let U = {x ∈ R : x is an upper bound for A}, the set of all upper bounds for A. Prove that there exists a u ∈ R such that U = [u, ∞).

(b) Prove that for all ε > 0 there exists an x ∈ A such that u − ε < x ≤ u. This u is one shown to exist in Part (a).

Answer 1

Answer #1

and is mont of v is gone as a Afo) C Risebounded aboven o. - U={X ER: x is an upper bound for A}. since A is bounded above v

Answer 2

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