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1h
comment Definition of exponential function -
If you have covered the relevant results about power series, then it could go as follows. Let $M>0$ be a (large) constant. Ratio test shows that your series converges at $x=M$. Weierstrass M-test then implies that the convergence is uniform in the interval $[-M,M]$. Therefore you can differentiate termwise in that interval. Because $M$ was arbitrary, you can do this on the whole line.
6h
comment Does $\tan (x)$ equal $\frac{-1}{x-\frac{\pi}{2}}+\frac{-1}{x+\frac{\pi}{2}}+\frac{-1}{x-\frac{3\pi}{2}}+\frac{-1}{x+\frac{3\pi}{2}}+…$?
See the formulas here.
6h
comment What's wrong with my math in this function to update the position of a planet near a star?
IOW I think your physics is incorrect.
9h
comment What's wrong with my math in this function to update the position of a planet near a star?
Would it be easier to keep the speed as a vector as well? xSpeed and ySpeed instead of velocity and direction. Then update those using the acceleration by the force of gravity. That's how I always code gravity sims.
9h
comment Find radius of Circle
Locked for now. The answers deleted to prevent peeking. Ping me or another moderator to undelete after the deadline.
9h
comment What is Haar Measure?
@Pro-er-Sciencer (I assumed that you wanted to comment this answer, so I moved it here): Correct. In $\Bbb{R}_{-}$ we should use $-dx/x$ (or, possibly more naturally use reverse orientation).
9h
comment Functions $f$ such that $f(z+1)-f(z)$ is holomorphic
If $f(z)=\sin 2\pi z$, then $f(z+1)-f(z)$ is a polynomial but $f$ is not. :-)
12h
revised How many integral ideals $\mathfrak{a}$ are there with the given norm $\mathfrak{N}(\mathfrak{a})=n$?
edited body
18h
comment Spectral Measures: Scale Spaces (II)
12 edits in a relatively short span raise an eyebrow again. Were they necessary?
18h
comment Application of the structure theorem for finitely generated modules over a PID
Looks like you were putting the matrix in the Smith normal form, which is, indeed, a very good way of finding the structure of the quotient group. One way of finding an actual isomorphism need you to keep track of the row/column operatiions that you performed while getting there. I tried to explain the process in this old answer. I'm not sure I did a good job there.
18h
comment Dirichlet characters with values in a finite field
The group $\Bbb{F}_q^*$ is cyclic of order $q-1$. Therefore homomorphisms from any group to $\Bbb{F}_q^*$ are (more or less) the same thing as homomorphisms to $\langle e^{2\pi i/(q-1)}\rangle$. I don't know what you mean by a separable Gauss sum.
18h
comment number of distinct necklaces made with n beads and m colors
@SalvadorDali: Source/link ?
18h
answered Explicitly compute the trace for the tautological representation of $D_4$ of $\mathbb{R}^2$.
1d
comment Galois group isomorphic to $\mathfrak{S}_5$.
A quadratic extension corresponds to an index two subgroup of the Galois group. How many index two subgroups are there in $\mathfrak{S}_5$?
1d
answered If $x_{n+1}\leq x_n + 1/n^2$ then $x_n$ converges
1d
comment Why are some branches of mathematics called 'theory' and others not?
IMHO this is a question about language rather than math. In the listed examples the word theory is paired with an object. The roots of the words algebra and analysis describe (IIRC) something like a methodology, and work well as stand alone words. This is a bit fuzzy. I lack the proper linguistic terms to phrase this well, sorry.
1d
comment generating orthogonal parity check matrix, from a random generator matrix
I describe the process for finding $H$ in my answer to your other question.
1d
answered How to find orthogonal vectors in GF(2)
1d
awarded  Great Answer
1d
revised Prove that two non-bald residents of NYC have exactly the same number of hairs.
edited tags; edited title