If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum of S if and only if the following two conditions hold : (i) x 0, 3 some x e S such that x > s- E.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Show that given statement , no typing 

If S is a non-empty set of real numbers which is bounded
above, then a real number s is the supremum of S if and only if the following
two conditions hold :
(i) xSs V xeS.
(ii) Given.any ɛ> 0, 3 some x e S such that x > s - E.
11
Transcribed Image Text:If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum of S if and only if the following two conditions hold : (i) xSs V xeS. (ii) Given.any ɛ> 0, 3 some x e S such that x > s - E. 11
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