Prove that if a is an upper bound for A, and if a is also an element of A, then it must be that a = sup A.
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Prove that if a is an upper bound for A, and if a is also an element of A, then it must be that a = sup A.

[From: ] [author: ] [Date: 11-09-14] [Hit: ]
Thus, sup(A) = a.......
If a is an upper bound for A, then sup(A) exists, and:

sup(A) <= a

If a is an element of A, then, since sup(A) is an upper bound on A, we have:

a <= sup(A)

Thus, sup(A) = a.
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