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Apr
25
revised $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
deleted 36 characters in body
Apr
25
comment Follow up question about translation of a limit expression
@Didier: yes, I know. I would've left it but I don't want to accumulate down votes : / I'm sorry, I would've kept the comments visible if it had been possible.
Apr
25
comment Fundamental Group of a finite set with discrete topology
@Theo: thank you, now I understand. I didn't understand why it was necessary to pick base points when one can show that every point in $S$ can only have the constant loop. It's necessary because that is how the fundamental group is defined.
Apr
25
comment Follow up question about translation of a limit expression
@david: true but neither does the first line.
Apr
25
asked Follow up question about translation of a limit expression
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Didier: yes, I see the difference.
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Didier: I think I'll have to make my own, follow up question about this "translation". I still don't see what's wrong.
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Didier: Ah! Yes but Martin's comment writes that I'm proving that the limit is zero, which I'm not.
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Nir: No. But as for now you should use david's answer, it seems there might be something wrong in the reasoning with my answer.
Apr
25
revised $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
Clarification added.
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Didier: sorry, can you explain a bit more detailed, I can't find my mistake, even reading your comment above, thank you!
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Didier, @Martin: I'm not proving that the limit is $0$!
Apr
25
revised $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
Clarification added.
Apr
25
answered $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
Apr
25
comment Fundamental Group of a finite set with discrete topology
@Theo: I assume you are using $S^1$ instead of $[0,1]$ because the question is about closed paths. Why do you have to choose a base point in the domain of the paths? Shouldn't you say "...since $S^1$ is connected, it must be mapped to this base point entirely....", where that base point is the one in $S$?
Apr
25
comment Fundamental Group of a finite set with discrete topology
@Theo: what's $S^1$? The unit circle?
Apr
23
comment Homotopy equivalence iff both spaces are deformation retracts
@Theo: thanks, that was a typo. I corrected it.
Apr
23
revised Homotopy equivalence iff both spaces are deformation retracts
added 13 characters in body
Apr
23
comment Simple set exercise seems not so simple
Nice answer!
Apr
23
answered Simple set exercise seems not so simple