Question: a) Prove that if x is an upper bound of a set E R and x E, then x is the supremum of

a) Prove that if x is an upper bound of a set E ⊂ R and x ∈ E, then x is the supremum of E.
b) Make and prove an analogous statement for the infimum of E.
c) Show by example that the converse of each of these statements is false.

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a Let x be an upper bound of E and x E If M is any upper bound of E then M x Hence ... View full answer

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