S.O.S. Mathematics CyberBoard

hi,
can someone please help me with those two sequences

Let T be the collection of all U subset R such that U is open using the usual
metric on R.Then (R; T ) is a topological space. The topology T could also be described as
all subsets U of R such that using the usual metric on R, R \ U is closed and
bounded.

Does {1/n} n=1 to infinity converge? Why or why not?

I think it does converge...it converges to 1 for example...am I right?

Does {n} n=1 to infinity converge? Why or why not?

I dont think that this sequence converges in a topological space?

thanks

Don't you know the definition of convergence? If not, you have no hope of solving these, and with the definition, I'm not sure what the problem is. Topologies are defined so that you understand what convergence means, so the response to your last remark is: topological spaces are where one talks about convergence, if you say "it doesn't converge in a topological space" you're saying "it doesn't converge in the only context where it makes sense to talk about convergence."

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I 'm sorry, I meant to say that "it does not converge in usual topology on R^n"

Yes, that is true because the sequence is not Cauchy.

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Also, for the first sequence I meant to say it converges to 0 not 1 in usual topology.

This is accurate.

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