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6. Let K be compact in R and let c E R. Prove that there exists a point a € K such that |c – a| = inf{|c – x| : x € K}. -

6. Let K be compact in R and let c E R. Prove that there exists a point a € K such that |c – a| = inf{|c – x| : x € K}. -

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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6. Let K be compact in R and let c e R. Prove that there exists a point a E K such that |c – a| = inf{|c – x| : x E K}.
Transcribed Image Text:6. Let K be compact in R and let c e R. Prove that there exists a point a E K such that |c – a| = inf{|c – x| : x E K}.
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