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 Feb 26 comment Proving closure and $x*y = -1$ iff $x(1+y) = -(1+y)$. Does it ring a bell? Feb 5 awarded Critic Jan 21 revised (Fast) eigen decomposition of $DXD$ where $D$ is diagonal, $X$ is symmetric with known eigen decomposition deleted 1 character in body Jan 21 asked (Fast) eigen decomposition of $DXD$ where $D$ is diagonal, $X$ is symmetric with known eigen decomposition Dec 18 awarded Yearling Dec 18 awarded Yearling Dec 18 awarded Yearling Jan 7 awarded Nice Answer Jan 6 comment Asymptotic equivalent of the law of lotto minimal value Oh god. I was pretty sure that using your $\ell$ trick it was possible to prove $$1 - \left( 1 - {m\over n-\ell} \right)^\ell <\mathbb P(X\le \ell) < 1-(1-p)^\ell.$$ I’am missing something, I’ll have to go back on this later. Jan 6 awarded Scholar Jan 6 accepted Asymptotic equivalent of the law of lotto minimal value Jan 6 comment Asymptotic equivalent of the law of lotto minimal value In fact, $\left(1-\frac m{n-l}\right)^{k-1}\frac m{n-l} < \mathbb P(X=k) < (1-p)^{k-1} p$, so you get easily a framing of $\mathh b \P(X \le \ell)$ that allows to conclude with the squeeze theorem. This is nice. Jan 6 comment Asymptotic equivalent of the law of lotto minimal value My question was more general, but I think in this way it will be possible to concludre concerning $\mathbb P(X \le k)$... the $\ell$ trick is beautiful, many thanks. Jan 6 comment Probability of an odd number in 10/20 lotto You might be interested by this question I asked today, related to this problem... Jan 6 revised Asymptotic equivalent of the law of lotto minimal value typo Jan 6 asked Asymptotic equivalent of the law of lotto minimal value Jan 4 revised Probability that n numbered objects placed in random order have p objects in the correct position typo Jan 4 revised Probability that n numbered objects placed in random order have p objects in the correct position notation clarified + asymptotics Jan 4 answered Probability that n numbered objects placed in random order have p objects in the correct position Jan 4 comment About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$ This is homework, right? Starting point: show that $f(0) = 1$. Try to continue with integers, then with rationals of the form $1\over q$, finish with $\mathbb Q$.