Trevor Alexander
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 Feb 19 comment Is it irrational? If the exponent $a$ of the event probability $n^{-a}$ is any number less than $-1$, is the number rational? Or is it required that $a < -2$? Aug 17 comment Why does this “miracle method” for matrix inversion work? When I looked at this question the first thing I thought was "Cayley-Hamilton", but nobody mentioned it. I haven't done matrix algebra in a year, but is there a connection here? Aug 17 comment Why does this “miracle method” for matrix inversion work? Isn't A^n = A idempotency? Apr 21 awarded Popular Question Feb 8 awarded Necromancer Jan 30 awarded Yearling Dec 22 awarded Constituent Dec 9 awarded Caucus Jul 2 awarded Curious Apr 21 comment If there are obvious things, why should we prove them? Elitist much? I wonder how many grossly underpaid but otherwise mathematically apt people are down at walmart right now. (Including adjunct math faculty, even!) Apr 18 comment Proving that the maximum of two convex functions is also convex Does this apply similarly for the maximum of two concave functions? Apr 18 accepted Is a continuously differentiable function convex if all its partial second derivatives are non-negative? Apr 9 comment Pizza theorem with realistic extension The proof sketch you gave requires that the crust be separable from the pizza, though. Apr 3 comment Can a coin with an unknown bias be treated as fair? This is one of my favorite questions from Cover and Joy's info theory text book :) Feb 13 comment Why are the rational numbers not continuous? I sort of get it from the wikipedia article: "An example of a set that lacks the least-upper-bound property is ℚ, the set of rational numbers. Let S be the set of all rational numbers q such that $q^2 < 2$. Then S has an upper bound but no least upper bound in ℚ: If we suppose p ∈ ℚ is the least upper bound, a contradiction is immediately deduced because between any two reals x and y (including √2 and p) there exists some rational p', which itself would have to be the least upper bound (if p > √2) or a member of S greater than p (if p < √2)." Feb 13 comment Why are the rational numbers not continuous? one more question: when you say, "You've so just obtained ℝ!" here, does your argument assert that $\mathbb{Q}$ does not contain non-empty bounded above sets with a least upper bound? I'm having trouble understanding why not. Couldn't you just choose the largest element of a set contained in $\mathbb{Q}$ as its upper bound? I guess I'm really asking what situation yields a supremum not in $\mathbb{Q}$ but in $\mathbb{R}$. Feb 12 comment Why are the rational numbers not continuous? Can you state briefly what the Archimedian property exactly is for completeness' sake? Feb 9 comment Find integral when $dx$ is in the numerator So sick of that "non-standard" term tacked on to this significantly more intuitive interpretation. Feb 3 comment What's a good class of functions for bounding/comparing ratios of complicated logarithms? That's a good one. Closer to home for me is visual/auditory senses, which give you great sensitivity at low ranges without causing a seizure when a truck passes :) Feb 3 comment What's a good class of functions for bounding/comparing ratios of complicated logarithms? Geez, I should have seen that. My head was still spinning from the amount of algebra it took to get everything else out of the way. Thanks.