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Jun
13
comment Count number of colorings of tetrahedron, where colorings are indistinguishible if one can be reached from another by rotation
Try googling Burnside's Lemma or searching for answers on this site that apply it to counting problems. I've written a couple, but can't write out a full hint/toy example now.
Jun
13
comment The disc of convergence of a power series
"Geometrically" is alluding to a limit comparison test (or similar) with a geometric series which is known to converge.
Jun
11
comment Principle of mathematical induction
Roughly: Induction is an axiom if you use PA to define the natuals, and a theorem if you're using a set theoretical basis. The fact that there are different axiom systems that can make sense and lead to a certain conclusion you find obvious is a fact of life in mathematics.
Jun
10
comment Trajectories in orthogonal systems
The orbits are only circles in 2d when the eigenvalues have zero real part. Nonreal eigenvalues isn't enough.
Jun
5
comment Why can the transformation derived from a list of points and a list of their transformed counterparts not be affine or linear?
@null Absolutely right. As long as the three initial points don't lie on the same straight line, you will be able to solve the 6 equations for the 6 unknowns.
Jun
5
revised Why can the transformation derived from a list of points and a list of their transformed counterparts not be affine or linear?
deleted 1 character in body
Jun
5
comment Why can the transformation derived from a list of points and a list of their transformed counterparts not be affine or linear?
It might be good to edit in more of the context so that your question does not depend on those links never breaking.
Jun
5
answered Why can the transformation derived from a list of points and a list of their transformed counterparts not be affine or linear?
May
31
comment Find least numerator and denominator for a given sequence of numbers in decimal form
If there is a nice algorithm, it may be related to continued fractions. If you just want a handful of specific cases, things like wolframalpha.com/input/?i=Rationalize%5B0.1234444%2C.0000001%5D might work for you.
May
28
awarded  Revival
Mar
31
comment Can $[0,1]$ be partitioned with the following property?
I may be misreading something. If the measure of A is less than 1/2, isn't there no hope?
Mar
30
comment Infinite number of Derivatives
@user31415 My confusion was because my comment was about a different theorem. But as I said above, I now notice it's not needed for that other theorem either. I thank you for pointing that out.
Mar
30
comment Infinite number of Derivatives
@user31415 I didn't post an answer, nor did I use the word smooth. But nonetheless you're right. I think the proof I linked to doesn't make use of infinite differentiability in any way.
Mar
30
comment Infinite number of Derivatives
@user31415 I don't think you meant to @ me, but I agree.
Mar
29
comment Infinite number of Derivatives
And it's a bit less easy to prove that any function which is infinitely differentiable and has some derivative equal to zero at each point is still a polynomial. See the MathOverflow question
Mar
29
answered Derivatives of $\sin x$ and $\exp x$ using differentials / dual numbers
Mar
29
comment What's the difference between hyperreal and surreal numbers?
Things get a little hairy when dealing with class-sized hyperreal fields, but Keisler is quoted with a precise statement of "the surreals are the biggest version of the hyperreals" and proof sketch in Ehrlich's "The absolute arithmetic continuum and the unification of all numbers great and small"
Mar
29
comment Numerical system that includes the limit targets such as $0^+$, $0^-$, $1^+$ etc
You have listed the "limit targets", and I don't see why you want numerical operations on them, nor do I have much of an intuition about how they should be defined. Why must it be that $1^+=1+0^+$? As an aside (to complicate matters), a good way of thinking about limits is in terms of limsup and liminf from the left and right. Then at each real number $a$, a function defined on, say, $(a-h,a+h)$ has four "limits", which are extended reals.
Mar
29
answered Clifford algebra over non-Archimedean field
Mar
28
revised The Fundamental group of Klein Bottle
added dollar signs for math