Two standard proofs
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Text Book: - Taylor & Menon
1.) Prove that a compact set is bounded.
2.) Prove that if the sequence {xn} converges, than the sequence {IxnI} also converges. Is the converse true as well?
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The solution comprises approximately 1 page written in Word with mathematical expressions in Mathtype explaining step by step the full solutions to the two questions asked.
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I am going to assume you are talking about subsets of and sequences in . If this is not the case, please let me know and I will adjust the solution accordingly.
1) Prove that any compact set of is bounded.
A subset S of is bounded if there exists such that .
A set is called compact if every open cover has a finite subcover.
Let . In other words, is ...
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