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visits | member for | 5 years, 3 months |
seen | Jan 21 at 3:21 | |
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If I like your problem, I'll think of it in honest. However, if the question is badly posed or the information is incomplete, I'll vote to close it when in a bad mood and waste several hours of your and my time asking for clarification, pointing out trivial counterexamples, etc., when in a good mood. In both cases, the most likely outcome is that I'll finally switch my attention to something else. ;)
Jan 13 |
awarded | Guru |
Dec 30 |
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What is the reason that $\sigma$-algebra replaced $\sigma$-ring in introductory measure theory?
Oh, my! So it is "sigma-ring", not "semiring"? I was totally perplexed with that typo in the post. Then there is not much difference, really. It is just convenient to assume that the whole space is always measurable and to be able to pass to the complement freely, but otherwise it is more a question about terminology than about substance unless I misunderstand something. |
Dec 29 |
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A version of Wald identity
@HMPanzo Indeed. Thank you! It doesn't look like their approach is any easier than mine (or even substantially different)... :-) |
Dec 29 |
revised |
A version of Wald identity
deleted 5 characters in body |
Dec 29 |
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A version of Wald identity
@user57639 OK, see if it works now. Either I am missing some obvious approach, or it can make one of the trickiest problems about the Brownian motion on the probability exam. Where did you get this question from? |
Dec 29 |
answered | A version of Wald identity |
Dec 28 |
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A version of Wald identity
@Nate Elderedge Ah, indeed. OK, let me try to answer properly then :-) |
Dec 28 |
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A version of Wald identity
The (now deleted) example of Bjorn shows that at most one of those is true for the hitting time of $1$, in which case $EW_T=EW_T^2=1$, i.e., neither $0$, nor $\infty$ ;-) |
Dec 28 |
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A bilinear estimate in Lp space
Let $u^2$ be the Dirac mass (yeah, impossible as written, but quite possible as an approximation). Then $u_n\to 0$ in $L^p$ with $p<2$ but whatever non-zero operator you apply to $u_n^2$, the result tends to something nontrivial. |
Dec 28 |
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Why is it hard to prove that the Euler Mascheroni constant is irrational?
Philosophically, there is essentially only one way to prove that a number is irrational/transcendental, which is to use the fact that there is no integer between 0 and 1 In a sense, yes, but then what (non-existence) statement about integers does not fall into that category? I mean, what you say is true, but how far is it from a tautology? |
Dec 27 |
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Two (strictly related) proofs by induction of inequalities
Now it looks a bit better :-). However I'm still a bit perplexed by the notation $a_n$ and the phrase $n\to\infty$ because there is no running $n$ anywhere else. Also, what on Earth is $p_{m+1}$ in this case? |
Dec 27 |
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Which universities teach true infinitesimal calculus?
@katz Neither was it my intention (the main purpose of my comment was to prevent this thread from being closed), so let us stop that side discussion here (though I would gladly talk about it somewhere else) :-). |
Dec 27 |
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Two (strictly related) proofs by induction of inequalities
Let's get the notation straight before talking about anything else: the opening phrase "Let $p_m$ be the largest prime factor of $a_n$" puts me in such a beautiful state of blissful ignorance about the indexation in the following three story formulae, that the proverbial ram looking at the new gate is an example of perfect comprehension and deep understanding compared to me looking at them ;-) |
Dec 27 |
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lower-bound for $Pr[X\geq EX]$
@Gil Kalai Mark Rudelson told me that another (in the sense of "independent", not necessarily in the sense of "different") short proof of Feige's theorem was found by Oleshkevich, though, like me, he didn't bother to ever publish it. Unfortunately, Mark had absolutely no memories about what that proof was, but you may want to investigate a bit. :-). |
Dec 26 |
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Any way to prove Prime Number Theorem using Hyperbolic Geometry?
There is very little difference (if any) between the result for the van Mangoldt function you stated and the PNT without the error term estimate. As to the main question, I have no idea (in the sense of getting a simpler than usual approach from some standard geometry, not in the sense of restating the result in fancy artificial terms shedding no light on anything whatsoever) |
Dec 26 |
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Which universities teach true infinitesimal calculus?
The obvious observation is: "Very few places do", so, definitely, it makes more sense to ask this question on the professional mathematician forum than on the general teaching forum (just to throw my weight to keep it open here). I would never do it in the undergraduate curriculum myself (unless the standard epsilon-delta language is taught in parallel) for the simple reason that very few texts in analysis are written in this language, so, alas, I don't know much as far as the main question is concerned. |
Dec 25 |
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How to solve this differential equation with an infinite sum?
@Bertrand If $a_n$ are just bounded and $f$ grows, how do you understand the sum? (formally the series diverges in this case). |
Dec 24 |
reviewed | Leave Open Regular paths along surface of sphere |
Dec 24 |
awarded | Nice Answer |
Dec 23 |
awarded | Nice Answer |