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visits member for 1 year, 9 months
seen Aug 24 at 14:11

Jul
2
awarded  Curious
Jun
9
accepted Help with understanding a proof about differentiating a real power series
Jun
9
asked Help with understanding a proof about differentiating a real power series
Jun
4
asked Difference quotient inequality with convex functions
Jun
1
accepted Hyperreals - is there a “boundary” between convergent and divergent series?
May
31
revised Hyperreals - is there a “boundary” between convergent and divergent series?
added 254 characters in body
May
31
comment Hyperreals - is there a “boundary” between convergent and divergent series?
Good point. So we can't find a lower bound on the divergent series. What aboout an upper bound for the convergent ones?
May
31
revised Hyperreals - is there a “boundary” between convergent and divergent series?
added 19 characters in body
May
31
asked Hyperreals - is there a “boundary” between convergent and divergent series?
May
26
comment Complex power series divergent and convergent on dense subsets of the circumference of convergence?
When I first looked at it, it seemed correct. But yes, I should have read it more carefully. I'll unaccept if I see the example is incorrect, right now I only see that Dirichlet test doesn't apply, but the series could be convergent for all I know. Then, the answer would still be alright. Also, someone else upvoted it too, so I'm inclined to believe I'm just missing something more or less obvious.
May
26
accepted Complex power series divergent and convergent on dense subsets of the circumference of convergence?
May
26
comment Complex power series divergent and convergent on dense subsets of the circumference of convergence?
I've now took a while to analyze your example more carefully and something looks wrong to me. The partial sums of $ \sum z^(2^n) $ don't seem bounded, so we can't use Dirichlet test. Am I missing something obvious?
May
23
accepted Examples of decreasing sequences of closed sets with constant diameter and empty intersection in complete metric spaces
May
23
comment Examples of decreasing sequences of closed sets with constant diameter and empty intersection in complete metric spaces
Good point, but what about other metric spaces?
May
23
asked Examples of decreasing sequences of closed sets with constant diameter and empty intersection in complete metric spaces
May
21
accepted Simple examples of proper metric spaces?
May
19
awarded  Yearling
May
19
asked Complex power series divergent and convergent on dense subsets of the circumference of convergence?
May
13
comment Why does $1 \cdot 0=0$ not stand?
1*0 = 0 does stand. The problem is that 0 is not invertible. For every integer a, 0*a = 0. But for (3) to be satisfied we need, in particular, a number x such that x*0 = 1. And there's no such x, obviously.
May
12
comment Simple examples of proper metric spaces?
Unfortunately the examples from David's link seem to require some background knowledge in topological groups/fields, which I don't have, so while I do find the examples quite interesting, I can't really fully understand them. Are there really no easier examples?