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Theorem 3. 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 VxE S.

Theorem 3. 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 VxE S.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Theorem 3. 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) xSsxeS. (ii) Given.any ɛ> 0, 3 some x E S such that x > s - E.
Transcribed Image Text:Theorem 3. 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) xSsxeS. (ii) Given.any ɛ> 0, 3 some x E S such that x > s - E.
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