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2d
revised Topological groups, why need them?
edited tags
2d
comment Is it possible that “A counter-example exists but it cannot be found”
Given the tags, I think the OP wants situations in which a counter-example provably cannot be found. Is that the case here?
Apr
15
comment Characterizing the Galois group using permutations of roots
Thanks. Okay, so now replace $S_4$ with an arbitrary subgroup $G\leq S_n$. If $G$ satisfies that property, must $G$ be the Galois group? In other words, does that property characterize the Galois group?
Apr
15
comment Characterizing the Galois group using permutations of roots
I edited my question title in the hopes of avoiding an XY problem.
Apr
15
revised Characterizing the Galois group using permutations of roots
added 134 characters in body; edited title
Apr
15
comment Word problem number theory
@labbhattacharjee This is a nitpick, but that doesn't follow directly, does it? I mean, I agree that the LCM divides every common multiple, but you can't deduce that instantly from the fact that it's the smallest one, can you?
Apr
15
comment Word problem number theory
You're using the fact that the LCM divides every common multiple, aren't you?
Apr
15
revised Characterizing the Galois group using permutations of roots
added 448 characters in body
Apr
15
comment Characterizing the Galois group using permutations of roots
@mt__ I think I may have badly formulated my converse. I'll edit in some more details.
Apr
15
revised Word problem number theory
added 34 characters in body
Apr
15
comment Word problem number theory
You're sure of it, but you don't know the reasoning behind it?
Apr
15
comment Characterizing the Galois group using permutations of roots
@mt_ So you're saying the converse is in fact true for the full symmetric group?
Apr
15
comment Does this integral have any closed form? $\displaystyle\int\frac{1}{x+\sin(x+1)}\mathop{\mathrm dx}$
Your substitution will turn it into a rational function in $x$ and $\sin(x)$, but I don't think that such a thing is guaranteed to have an elementary closed form.
Apr
15
asked Characterizing the Galois group using permutations of roots
Apr
15
comment Why is $sinx$ the imaginary part of $e^{ix}$?
@EamesCobb Do you at least understand why the trig functions turn up here in the first place?
Apr
15
comment Why is $sinx$ the imaginary part of $e^{ix}$?
Do you specifically want to know why the imaginary part isn't $\cos$?
Apr
15
comment Why is $sinx$ the imaginary part of $e^{ix}$?
Not to be rude, but what does this add that wasn't contained in the other answer?
Apr
15
comment Why is $sinx$ the imaginary part of $e^{ix}$?
The best explanation I've seen goes that since the derivative of $e^{ix}$ is $ie^{ix}$, we have a curve which starts at $1$ and has a "velocity vector" always orthogonal to itself, pointing left, and of magnitude $1$. So naturally, it draws a circle. But I don't know how to make this rigorous.
Apr
14
comment Show that there is no integer n with $\phi(n)$ = 14
(Also, your argument for the prime case is a bit complicated. Assume $n$ is prime, then $n=15$, contradiction!).
Apr
14
comment Show that there is no integer n with $\phi(n)$ = 14
I don't see at all what "similar argument" you're implying for the case when $n$ isn't prime, could you explain?