Unformatted text preview: T , it is also a lower bound of S . But inf S is the greatest lower bound of S and hence inf T ≤ inf S . 4.13 The equivalence of (a) and (b) follows from Problem 3.7(b). (c)is simply a notation for (b). Remark . The relation sup S ∈ S is a special assumption in Problem 4.5, and it says that namely in this special case max S exists and sup S = max S . Be aware: this is not always true! Counterexample: if S = (0 , 1) then inf S = 0 , sup S = 1 and both are not contained in S ! And S has neither min S , nor max S ! 1...
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- Spring '08
- #, Supremum, Order theory, upper bound, sup, max S