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Ted123
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Homework Statement
Homework Equations
The Attempt at a Solution
I've done the first 3 parts. I've come to the bit on Cauchy sequences at the end. How do I show [itex]x_n = n[/itex] is/isn't a Cauchy sequence in the 2 metrics?
[itex](x_n)[/itex] is a Cauchy sequence in a metric space [itex](X,d)[/itex] if for any [itex]\varepsilon >0[/itex] there exists [itex]N\in \mathbb{N}[/itex] such that if [itex]m,n > N[/itex] then [itex]d(x_m , x_n ) < \varepsilon[/itex].
The metric space [itex](X,d)[/itex] is complete if every Cauchy sequence in [itex](X,d)[/itex] converges to a limit in [itex]X[/itex].