Let A be a bounded subset of R "REAL NUMBERS" B a nonempty subset of A .show that :
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Originally Posted by flower3 Let A be a bounded subset of R "REAL NUMBERS" B a nonempty subset of A .show that : First let's prove inf(B) <= sup(b) For any x in B, by defintion inf(B)<=x<=sup(B) All you need to observe now is inf(A) is lower bound of B and sup(A) upper bound of B. Now invoke the definitions of inf,sup
For all (since and so (as is an upper bound for Hence is an upper bound for and so (since is the least of the upper bounds for A similar argument shows that Finally, as let Then (since and are a lower and an upper bound for respectively).
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