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Concerning Problem 1.2 in HW2

Concerning Problem 1.2 in HW2

av Shamiur Rahman Ramim -
Antal svar: 6

Hi! I might have found something wrong with 1.2. I hope my reasoning below isn't all wrong, but here goes: 

A part of 1.2 is to prove that if a sequence is Cauchy in (X, d_1), then it is convergent in (X, d_2), where d_1 and d_2 are equivalent metrics. But d_1 is equivalent to itself. So a corollary would be that if sequence is Cauchy in X, then it is convergent in X. Which is not the always the case? 

Som svar till Shamiur Rahman Ramim

Re: Concerning Problem 1.2 in HW2

av Sofia Tirabassi -
Hello,

The problem should ask you to show that if a sequence is Cauchy with d1 then it is Cauchy with respect to d2

And the same for convergent instead of cauchy.

I will look at the text and fix it 

Mvh

Sofia