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Jul
27
awarded  Yearling
May
18
awarded  Good Question
May
9
comment Why are nodes and nodal sets called this way?
My native language is Hebrew. What do you mean by that they "look like nodes"? What does a node look like?
May
6
comment Why are nodes and nodal sets called this way?
Why the downvote?
May
2
revised Why are nodes and nodal sets called this way?
added 47 characters in body; edited tags
Apr
30
asked Why are nodes and nodal sets called this way?
Apr
28
comment Prove that $371\cdots 1$ is not prime
@HyoyoungJung, if $37\underbrace{1\cdots1}_{n}$ is divisible by one of the primes then so is $37\underbrace{1\cdots1}_{n}000000$, thus so is $37\underbrace{1\cdots1}_{n}111111=37\underbrace{1\cdots1}_{n+6}$, because the difference $111111$ is divisible by all of them.
Apr
24
awarded  Nice Answer
Apr
23
answered A problem that I'm not sure whether to use Weierstrass Approximation Theorem
Apr
22
accepted Haar's theorem for the rotation-invariant distribution on the sphere
Apr
22
answered Haar's theorem for the rotation-invariant distribution on the sphere
Apr
13
comment Haar's theorem for the rotation-invariant distribution on the sphere
Thanks for your comment @user24142, you are right. In fact, the Lebesgue measure on $\mathbb R^n$ splits to $\mu \times$ (a measure on $\mathbb R$ with density $r^{n-2}$) or something like that.
Apr
13
comment Haar's theorem for the rotation-invariant distribution on the sphere
Oh, I like this approach, but I don't understand something. Clearly $\mu \times m$ is invariant under orthogonal transformations. Why is it invariant under translations?
Apr
7
comment Haar's theorem for the rotation-invariant distribution on the sphere
Thanks for the answer, but I am looking for something more elementary, i.e. without Lie theory or the general theory of compact groups, just this case of the sphere and orthogonal-matrix-invariance. Preferably in a book that I can just quote as in "it is a well-known fact that the Lebesgue measure is the unique rotation-invariant measure on the sphere [1]" :)
Apr
6
awarded  Good Answer
Apr
6
answered Stuck on crucial step while computing $\int_{- \infty}^{\infty} e^{-t^2}dt$
Apr
6
comment Stuck on crucial step while computing $\int_{- \infty}^{\infty} e^{-t^2}dt$
It's not a dirty trick, it's one of the most beautiful computations in mathematics :)
Mar
14
comment A functional equation: $4f(x)^3 +f(3x)=3f(x)$
Certainly there are more functions. For instance, $0$ on the rationals and $1/\sqrt 2$ on the irrationals.
Mar
12
revised Haar's theorem for the rotation-invariant distribution on the sphere
added 3 characters in body
Mar
10
asked Haar's theorem for the rotation-invariant distribution on the sphere