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Lily@pie
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Homework Statement
Let A be a set of real numbers that is bounded above and let B be a subset of real numbers such that A (intersect) B is non-empty.
Show that sup (A(intersect)B) <= sup A
The Attempt at a Solution
I don't know how to start but tried this...
Let C = A (intersect) B
So sup C = sup (A (intersect) B)
Then I thought of trying to prove it by contradiction,
show sup C > sup A leads to a contradiction.
Since for all a in A, a <= sup A.
a < sup C,
can I say that this leads to a contradiction as there exist an a that is larger than c because not all elements in A are in C...
but it seems a bit weak...