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Theorem 4. If S is a non-empty subset of R which is bounded below, then a real number t is the infimunm of S iff the following two conditions hold : (i) x2t xe S. (ii) Given any ɛ> 0, some x e S such that x

Theorem 4. If S is a non-empty subset of R which is bounded below, then a real number t is the infimunm of S iff the following two conditions hold : (i) x2t xe S. (ii) Given any ɛ> 0, some x e S such that x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Theorem 4. If S is a non-empty subset of R which is bounded below, then a real number t is the infimum of S iff the following two conditions hold : (i) X2 V x S. (ii) Given any ɛ> 0, 3 some x e S such that x<t+ E.
Transcribed Image Text:Theorem 4. If S is a non-empty subset of R which is bounded below, then a real number t is the infimum of S iff the following two conditions hold : (i) X2 V x S. (ii) Given any ɛ> 0, 3 some x e S such that x<t+ E.
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