Feanor

Krakow, Poland

Age: 25

Jul
21
comment What is ethics really about? (the goal or the means)
Your claim strikes me as false. Suppose I say that world peace would be a good thing. I can make sense of this statement without first figuring out how to stop all wars, so here is a goal that can be understood with no reference to means. Or I could tell a child (and a god could tell a person, presumably) how to behave, and it would then know the means without knowing the goal. What am I missing?
Jul
7
comment Prove $\operatorname{func}(f)=\sum_{i=1}^{m}\frac{n_i}{f^2}\left(1-\frac{1}{f}\right)^{n-n_i}$ has a maximal value.
To clarify: do you want to prove a maximum exists with respect to $f$ exists for fixed $n_i,m $, or do you want to prove that a maximum exists with respect to $f,n_i,m$?
Jul
6
revised For $a_n,b_n\uparrow$ and $\sum \frac{1}{a_n}$, $\sum \frac{1}{b_n}$ divergent is the series $\sum \frac{1}{a_n+b_n}$ also divergent?
added 136 characters in body
Jul
6
answered For $a_n,b_n\uparrow$ and $\sum \frac{1}{a_n}$, $\sum \frac{1}{b_n}$ divergent is the series $\sum \frac{1}{a_n+b_n}$ also divergent?
Jul
5
comment Given $d$, for how many $m$'s is $d$ a quadratic residue mod $m$?
e.g. take $d \equiv 1 \pmod{4}$ prime, $m = p^{d-1}$, where $p \equiv 1 \pmod{4}$ and $d$ is not a quadratic residue modulo $p$. Then $d$ is not quadratic residue modulo $m$, but if $q \equiv m \pmod{4d}$ is a prime then $d$ is a quadratic residue modulo $d$.
Jul
5
comment Given $d$, for how many $m$'s is $d$ a quadratic residue mod $m$?
I'm not sure about the step where you reduce the condition that $d$ is a quadratic residue modulo $m$ to a congruence condition on $m$. This works if $m$ is prime, but it seems to fail when $m$ is composite. (Apparently, you need a condition on each prime factor of $m$).
Jul
5
asked Given $d$, for how many $m$'s is $d$ a quadratic residue mod $m$?
Jul
4
comment Solve functional equation $f(f(f(x)))+f(x)=2x$
@user161621 Best I can think of is to tell the same story, except with a different sequence (you can replace $z^n + w^n$ by something like $\sqrt{2}^n \cos(\alpha n)$ where $\alpha$ is a real number, but I am not sure which). My suspicion is that there should be some extra assumptions on $f$ that rule out the examples like above.
Jul
4
answered Solve functional equation $f(f(f(x)))+f(x)=2x$
Jul
4
comment Solve functional equation $f(f(f(x)))+f(x)=2x$
Any assumptions on $f$? What's the domain?
Jul
3
asked A generalisation of Roth's result on Diophantine approximation?
Jul
3
awarded Revival
Jul
2
awarded Inquisitive
Jul
2
awarded Curious
Jul
1
answered Why do we define functions to be set theoretic objects?
Jul
1
awarded Teacher
Jul
1
comment Representing a higher degree polynomial as product of smaller degree polynomials?
Are you basically asking for a way to factor a polynomial of a high degree? Surely, there is much a lot of literature on that...
Jul
1
awarded Editor
Jul
1
revised Why is Sauron always portrayed as being stronger than Gandalf
added 320 characters in body
Jul
1
answered Why is Sauron always portrayed as being stronger than Gandalf
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