Ben Alpert
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 Mar 20 comment Numbers satisfying $\binom{n}{k} = m!$ I just wrote a script and I don't believe there are any others up to 13! (except of course $\binom{n}{0}$ and $\binom{n}{1}$). Mar 20 comment Is $\nu_1\perp\nu_2$ equivalent to $|\nu_1|\perp|\nu_2|$ for complex measure? You may want \perp instead of \bot; the spacing is better with \perp. Feb 17 comment Proving the value of a limit using the $\epsilon$-$\delta$ definition I don't think your sarcastic condescension helps anyone. Feb 13 comment Finding $\int_0^{\pi/2} \sin x\,dx$ @Arturo: Yes, but why is the derivative of $\cos(x)$ equal to $-\sin(x)$ when $x$ is measured in radians? Feb 13 comment Finding $\int_0^{\pi/2} \sin x\,dx$ @Isaac, you're right that that does make more sense. I'll change my question (though I'm not sure it was particularly unclear originally). Feb 13 comment Finding $\int_0^{\pi/2} \sin x\,dx$ So you answered why the integrals give different answers scaled by a the ratio between a degree and a radian, but I already knew this. My question was why radians are special and give the answer of 1 (which you skip entirely when you say, "We know that…"). Sorry if my question was unclear. Feb 13 comment Coloring points on an n-gon Perfect, exactly what I was looking for! Feb 13 comment Coloring points on an n-gon Thanks; I'm accepting Qiaochu's answer because it's more complete (and also was a few seconds before yours). Jan 26 comment I want to put my words into a formula/algorithm but I lack the mathematical fortitude I agree with Yuval here; there's no reason to use any fancy math notation because the words you have currently are already very clear. Adding any symbols would unnecessarily complicate the algorithm. (And anyway, I don't think that there is any standard notation for what you want. Probably the best you can do is just write pseudocode for the algorithm, but that's not particularly mathy.) Jan 24 comment Algorithm for generating integer partitions @Will: Are you sure? I think that should work fine; that's what maxval is for. Jan 22 comment a question related to two competing patterns in coin tossing @PEV: I can't tell if I'm just being really stupid here, but I'm still unsure how that helps. For example, if with a fair coin you're looking for TH vs HH, it's much more likely ($3/4$ vs. $1/4$) that you'll see TH first because once you see a single T, it's impossible to get HH before seeing TH. How do we get the same answer using your method? (Presumably that would be $pq$ vs $p^2$.) Jan 22 comment a question related to two competing patterns in coin tossing @PEV: So if that's a fair coin, you're saying the probability is $1/32$. Of course, that's the probability that a random flip sequence of length 5 is equal to HTHTH but doesn't seem to answer whether HTHTH or HTHH is more likely to appear first. Jan 22 comment a question related to two competing patterns in coin tossing Sorry, but does this actually answer either of the part of the problem? I'm (not very familiar with Markov chains and am) confused about what the mean time tells you. (And I'm assuming $q = 1 - p$; is that right?) Jan 22 comment a question related to two competing patterns in coin tossing I'm also interested to know how to solve this problem; I've seen variations a few times on contests but never knew how to solve it. Sep 16 comment Finding $\lim\limits_{n \to \infty} \sum\limits_{k=0}^n { n \choose k}^{-1}$ Why is the text on this so big? Aug 3 comment Solve an equation with linear and exponential functions, $x=10^{x/10}$ Besides, that's not a complete answer. x ≈ 1.37129 works as well. Jul 30 comment Which average to use? (RMS vs. AM vs. GM vs. HM) Isaac: Thanks, fixed. Jul 30 comment Which average to use? (RMS vs. AM vs. GM vs. HM) Qiaochu Yuan: Can you elaborate a little more? I'm not sure you mean by rotational invariance. How are you rotating the values? Jul 30 comment Which average to use? (RMS vs. AM vs. GM vs. HM) (Couldn't decide whether or not this is appropriate for this site; vote to close at will.) Jul 30 comment Proof that $n^3+2n$ is divisible by 3 Indeed. If you do enough problems like this, then at least tricks like this become second nature.