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Jun
20
comment Interesting Number Game
This is just one example of a class of game that you see a lot, but which as far as I know isn't very well studied. Describing the span of a set under some operations tends to be quite easy, however, adding restrictions on how many times those operations can be done seems make the problem very difficult.
Jun
20
revised Interesting Number Game
edited tags
Jun
19
comment Category-theoretic description of the real numbers
Your question body seems to be at odds with the title. The title seems to be asking for practical or philosophical reasons why we should study the real numbers, but the question body seems to be asking "How do the real numbers fit into category theory?". In particular, I think when you say "from a mathematician's point of view" you mean "from a category theorist's point of view".
Jun
19
revised Validity of a trigonometric proof that $2 = 0$.
edited tags
Jun
19
comment Validity of a trigonometric proof that $2 = 0$.
What's going on with these downvotes? This is a legitimate non-duplicate question asking where the fallacy is in a particular argument.
Jun
18
revised Questions on limit superiors
edited title
Jun
18
comment Proof of the derivative of $a^x$
@user157789 Some people would take it as the definition of $a^x$.
Jun
17
revised Why do the negative-exponent terms vanish in this proof of the Residue theorem?
edited body
Jun
17
comment Why do the negative-exponent terms vanish in this proof of the Residue theorem?
@NateEldredge I see it now, thanks.
Jun
17
comment Why do the negative-exponent terms vanish in this proof of the Residue theorem?
@ThomasAndrews So for the sake of intuition, the reason the $n=-1$ case is "special" here is the same reason it's special in elementary calculus when you want to derive $x^{-n}$?
Jun
17
asked Why do the negative-exponent terms vanish in this proof of the Residue theorem?
Jun
17
comment Did I calculate $\text{Res}(\frac z {\sin z}, n\pi)$ correctly?
@DanielFischer Sorry, I have a mnemonic for the trig derivatives that sometimes bites me in the rear when I forget you have to go clockwise rather than anticlockwise, so I thought $\sin'=-\cos$ for a second and forgot to edit the rest of the comment.
Jun
17
comment Did I calculate $\text{Res}(\frac z {\sin z}, n\pi)$ correctly?
@DanielFischer $\sin'n\pi=\cos n\pi$ is $1$ if $n$ is odd and $-1$ if $n$ is even?
Jun
17
comment Group theoretical characterization of $\mathbb Q$ and $\mathbb Q^\star$
Oh, it's the set of all sequences of almost-all-zero integers‌​?
Jun
17
asked Did I calculate $\text{Res}(\frac z {\sin z}, n\pi)$ correctly?
Jun
17
revised If $10^{80}=2^x$, what is the value of $x$?
added 2 characters in body
Jun
17
comment Group theoretical characterization of $\mathbb Q$ and $\mathbb Q^\star$
Is that isomorphic to the set of all sequences of integers under component-wise addition?
Jun
17
comment Group theoretical characterization of $\mathbb Q$ and $\mathbb Q^\star$
What does $\bigoplus_p$ mean?
Jun
17
accepted Group theoretical characterization of $\mathbb Q$ and $\mathbb Q^\star$
Jun
17
comment $1.99999999…$ periodic number is really $2$?
That demonstration is not "child's play", it depends on a specific not-necessarily-obvious definition of what the notation "1.999..." means, as well as the justification that that definition allows multiplication and addition to be manipulated in that way.