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8h
comment How to express the min operator as a binary operator
$\text{min}(A, B) + \text{min}(C, D)$ is fine and moderately standard.
8h
comment Can someone show me why mathematicians use $d\mu$ instead of $dx$ for Lebesgue Integral over $u(x)$
@Michael: look, these notes were written for a reason, and that reason was to teach some students about the dominated convergence theorem, which is a theorem about the Lebesgue integral. There is no intention on the part of the author for the notes to be accessible to a wider audience that doesn't know about the Lebesgue integral: the audience is students in a course involving the Lebesgue integral. If you don't want to learn about the Lebesgue integral, don't read these notes.
10h
comment Can someone show me why mathematicians use $d\mu$ instead of $dx$ for Lebesgue Integral over $u(x)$
@Michael: On page 2 the notes clarify that $\mu$ is Lebesgue measure. I think you should not replace the $d\mu$ with $dx$ everywhere it appears; it's important to recognize the difference between the Lebesgue and Riemann integrals. Even if they ultimately give the same answer in familiar situations, they're built very differently, and the way you prove theorems about them is different.
11h
revised An interesting property of binomial coefficients that I couldn't prove
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11h
comment Can someone show me why mathematicians use $d\mu$ instead of $dx$ for Lebesgue Integral over $u(x)$
@Keba: again, by "Lebesgue integral" I mean the measure-theoretic integral with respect to some measure, not necessarily the Lebesgue measure.
11h
comment Can someone show me why mathematicians use $d\mu$ instead of $dx$ for Lebesgue Integral over $u(x)$
@quid: by "Lebesgue integral" I mean the measure-theoretic integral with respect to some measure.
11h
answered Can someone show me why mathematicians use $d\mu$ instead of $dx$ for Lebesgue Integral over $u(x)$
11h
revised Recognizing action of semidirect product
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11h
comment An interesting property of binomial coefficients that I couldn't prove
The link you mention describes another property of forward differences which is again analogous to differentiation: the forward difference of a polynomial of degree $d$ is a polynomial of degree $d - 1$. Hence $\Delta^d$ applied to a polynomial of degree $d$ is a constant: in fact it's $d!$ times the leading term of the polynomial. This is also not hard to prove by induction.
11h
answered An interesting property of binomial coefficients that I couldn't prove
12h
comment Under what conditions is a ZG-module torsion-free?
@3005: I don't understand what kind of conditions you want. Say $G$ is the trivial group. Then you're asking when an abelian group is torsion-free. I mean... some abelian groups are torsion-free and others aren't. What kind of answer are you looking for?
13h
comment How do we distinguish between characteristic 0 and characteristic p for very large p?
That doesn't sound right. You can also object to the implicit claim that the axioms you've written down are consistent.
13h
answered Where does the ambiguity in choosing a basis for a Lie algebra come from?
14h
revised Recognizing action of semidirect product
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14h
revised Recognizing action of semidirect product
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14h
answered Recognizing action of semidirect product
1d
awarded  representation-theory
1d
answered Is the Kolmogorov complexity of a number always its logarithm?
Jul
27
awarded  Yearling
Jul
27
comment The algebra of natural transformations of the n-th power tensor functor
@anton: the proof of Schur-Weyl duality in the blog post I link to above doesn't assume this, only that the characteristic is $0$.