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seen Apr 13 at 19:59

Apr
12
revised Looking for a a measure-theoretic treatment of “differential entropy”
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Apr
10
asked What's the name of the quantity $\mathbb{P}(A\cap B)/(\mathbb{P}(A)\mathbb{P}(B))\;$?
Apr
10
asked Looking for a a measure-theoretic treatment of “differential entropy”
Apr
7
awarded  Nice Question
Apr
7
accepted How to recognize adjointness?
Apr
6
asked How to recognize adjointness?
Apr
5
accepted What are integrating factors, really?
Apr
5
awarded  Civic Duty
Apr
5
asked What are integrating factors, really?
Mar
19
awarded  Notable Question
Mar
17
comment Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$
@Sabyasachi: sorry, I had not finished with my comment. Also, on the contrary, I think your proof is extremely elegant. I'm making the case for inelegance here.
Mar
17
comment Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$
$\dots\;\;$ These means that $\nset$ can be partitioned according to the $d$ factor of these products, and the size of each partition is $\varphi(n/d)$. But don't get me wrong: such proofs are OK, as quick ways to convince oneself that something is true, but one needs to go beyond them to get at the essence of why something is true.
Mar
17
comment Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$
What sticks in my craw about this argument is that fractions are really inessential to the problem; they get brought in only because they come with a built-in, widely recognized "simplified to lowest terms" operation. IOW, fractions show up in this theorem only as, basically, a cute hack, and IMO they obscure what's really happening in the theorem, namely that (1) every $m \in \def\nset{\{1,\dots,n\}}\nset$ can be written uniquely as the product $du$ where $d\mid n$ and $\gcd(u, n/d) = 1$, and (2) every such product $du$ belongs to $\nset$. $\;\;\dots$
Mar
16
accepted On proving $n = \sum_{d\mid n}\varphi(d)$
Mar
16
comment On last digit of 4 consecutive primes less than 10 apart
I see. Thanks for the clarifiication!
Mar
16
accepted On last digit of 4 consecutive primes less than 10 apart
Mar
16
comment Artin 2nd Ed. Problem 12.5.3
As a follow-up to Ted Shifrin's comment, you may find this answer useful.
Mar
16
answered Find the point on the y-axis which is equidistant from the points $(6, 2)$ and $ (2, 10)$.
Mar
16
revised Is there any advantage to the $a \equiv b\;\;(\mathrm{mod}\;c)$ notation?
added 320 characters in body
Mar
16
revised Is there any advantage to the $a \equiv b\;\;(\mathrm{mod}\;c)$ notation?
deleted 1 characters in body