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Show that if m ∈ A is the maximum of A, then m = sup A.

Show that if m ∈ A is the maximum of A, then m = sup A.

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Answer #1

Given is the maximum of .

Since is the maximum of so ,

  

is an upper bound for the set .

Let be given .

Then   and .

So for all there an element of which is such that .

Hence .

.

.

.

If you have any doubt or need more clarification at any step please comment .

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