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3h
comment Integral along real axis by integrating along contours above and below axis
@user2582713: Your epsilon is fixed, so your deformation has an error that depends only on the global properties of $f$ and on $\epsilon$. So once you have control over that error, you take $\epsilon\rightarrow 0$.
4h
comment How to show this equality
Don't forget that $n=p_1\cdots p_k$ for distinct primes $p_k$ since it's squarefree.
4h
comment Integral along real axis by integrating along contours above and below axis
@user2582713: This is why you're looking at the integral up to $-\kappa-\epsilon$, so it doesn't hit the singularity.
4h
comment Intuitively, how do you explain the concept of Flux?
Read "Div,Grad,Curl and all That" by Schey: amazon.com/Div-Grad-Curl-All-That/dp/0393925161
4h
answered How to get the inverse function of this one?
4h
comment Minimizing sample variance of $n$ functions
So you have a discrete list of pairs $(x_i,f_i(x_i))$?
4h
comment How to show this equality
Try showing it first for $n=p$, a prime. Then use the fact that it's multiplicitive.
4h
answered Proving that the sum of a sequence of lower semicontinuous functions is lower semicontinuous.
5h
comment Integral along real axis by integrating along contours above and below axis
@user2582713: Perhaps I did bad job of explaining. If you have a nice continuous functionf $f(x)$, with integral $\int_{\mathbb{R}}f(x)dx$, then it's going to be close to $\int_{\mathbb{R}+i\delta}f(z)dz$, for $\delta$ small. It sounds like Jackson is trying to skirt the issue of having a singularity on the real line by considering the integrals just slightly above, which sounds like considering first the principle part and then doing the integrals mentioned.
5h
answered Integral along real axis by integrating along contours above and below axis
7h
comment Why is the expression $\underbrace{n\cdot n\cdot \ldots n}_{k \text{ times}}$ bad?
Perhaps it's because you'll have calculus students doing the following: $\frac{d}{dx}(x^2)=\frac{d}{dx}\underbrace{(x+\cdots+x)}_{x}=1+\cdots+1=x$, :)
7h
comment My understanding of “$\sigma-$algebra represents information”.
If you're inclined to physical meanings, read the first chapter of William's "Probability with Martingales" along with some of the later chapters where he talks about filtrations: amazon.com/…
7h
comment Proof of convergence in distribution
Do you mean for all $\epsilon>0$ or just for a particular one?
2d
comment Is $d(x,y) = (x-y)^2$ a metric on $\Bbb R$?
That's why Euclidean distance has an extra square root, which makes the triangle inequality work out (think of the reals as a one dimensional vector space)
Sep
12
answered Show $E$ is a valid expectation operator
Sep
12
comment An Integral and its limit
If $g=f$, with $f>0$, then the integral is 0. As well, there's no mention of how to define this integral outside the support of $f,g$.
Sep
12
comment Evaluating $\lim_{n \to \infty} \left ( \sqrt[n]{n} + \frac 1 n \right )^{\frac n {\ln n}}$
this is a common trick for logarithms: factor out the biggest piece and taylor expand.
Sep
12
answered Evaluating $\lim_{n \to \infty} \left ( \sqrt[n]{n} + \frac 1 n \right )^{\frac n {\ln n}}$
Sep
11
comment Is really mathematics the mother of all science subjects ?
Can you rephrase this question without resorting to meaningless metaphors like "mother" and "father?" It sounds like you're interested in whether mathematics subsumes other fields but perhaps you could clarify.
Sep
11
revised Concluding that a function is not analytic at a point?
edited body