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(6) Let A be a bounded set of real numbers. Show that both L.u.b. A and g.l.b. A are in cl A. However, show that each of these need not necessarily be an accumulation point of A.

(6) Let A be a bounded set of real numbers. Show that both L.u.b. A and g.l.b. A are in cl A. However, show that each of these need not necessarily be an accumulation point of A.

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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Help me answer number 6 only.
(6) Let A be a bounded set of real numbers. Show that both l.u.b. A and g.l.b. A are in cl A. However, show that each of these need not necessarily be an accumulation point of A. (7) Let S = { 1 − (−1)″ | n € N}. Determine inf S and sup S. Justify. n
Transcribed Image Text:(6) Let A be a bounded set of real numbers. Show that both l.u.b. A and g.l.b. A are in cl A. However, show that each of these need not necessarily be an accumulation point of A. (7) Let S = { 1 − (−1)″ | n € N}. Determine inf S and sup S. Justify. n
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