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May
20
comment A question on logic - where intuition can fail
Is $\bigwedge_{x\in\{\}}P(x)$ true? And what about $\bigvee_{x\in\{\}}P(x)$? It is supposed to be false, isn't it? But thank you for that answer. It helped me quite much.
May
19
comment Is there an algorithm to find the roots of high-order polynomials?
My question was, if the polynomial is expressable in terms of radicals, is it possible to give an algorithm to find them?
May
18
comment Is there an algorithm to find the roots of high-order polynomials?
I read the article and think, that you can certainly show that a polynomial's roots are describable in terms of radicands using the Galois Theory, but it doesn't explains you how to find them.
May
10
comment Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
I just tried to understand this answer again, but I didn't understood, why $2n+1+\sum_{0\le k<n}a_k^{-2}=2n+1+o(n)$
May
10
comment Find a number $b$ such that $a\cdot b\equiv 1\mod m$
@Asag Karagila: Yes.
May
3
comment Need a result of Euler that is simple enough for a child to understand
Good idea. How about euler tours?
Apr
12
comment Solving a scrambled $3 \times 3 \times 3$ Rubik's Cube with at most 20 moves!
I would suggest looking on Wikipedia And also here
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
Thank you. Great answer.
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
@Arturo Magidin: Thank you very much.
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
@quanta: Please don't cheat. I want to get an answer I can use to understand the derivation. But anyway, thanks for the definition.
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
Ah... Okay. And how to show, that $\lim_{\delta\to\infty}\ln\left(1-\frac1{x\delta}\right)^\delta = x^{-1}?$
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
@Fabian: In our school, we are doing l'Hôpital in grade 11, I don't want to wait that long ;)
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
@Arturo Magidin: Yes. Sorry. Got confused by myself.
Apr
4
comment Common algorithm with an order of Θ(2^n)
Hm... I'm not a mathematician. Thank you.
Mar
29
comment Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
That's still only an asymptotic.
Mar
8
comment How to prove that a polynomial of degree $n$ has at most $n$ roots?
@Moron: Okay. Thank you for this.
Mar
8
comment How to prove that a polynomial of degree $n$ has at most $n$ roots?
@Moron: It's a part of the fundamental theorem. Consider this question as answered.
Mar
8
comment How to prove that a polynomial of degree $n$ has at most $n$ roots?
@Moron: I'm not (yet) in university. This isn't homework. Just asking this as a part to proof my last question. I'm asking this because I didn't knew, that this is a fundamental theorem of algebra.
Mar
5
comment How to prove the equality $\sum_{j=0}^n (x)^j (-1)^{n-j} \left\{{n \atop j}\right\} = x^n$?
Is your $(x)^j$ the same as $x^\overline{j}?$
Mar
5
comment Equality of polynomials: formal vs. functional
@Harry Stern: Yes :)