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Feb
4
comment For a sequence, why must $\lim _{n→∞} {||x_n||} = ∞$, $\lim _{n→∞} {||x_n||} = 0$, or there exists a convergent subsequence with a nonzero limit?
The example by @LubošMotl not only shows that there was something wrong with how you interpreted the problem. It is in fact a counterexample to the very claim itself.
Feb
4
answered page $102$ from Ahlfors.
Feb
4
comment How can a piece of A4 paper be folded in exactly three equal parts?
@J.G I may often be moderate, but am not a moderator. Those have diamonds next to their name.
Feb
4
comment Order-Preserving Bijection $f:A\to A^*$?
certainly not for finite $A$
Feb
4
answered Number Theory Primes and Rationals
Feb
3
comment Is there any generalization of Riemann Mapping theorem?
There are more shapes and sizes than just annuli $B(0,R)\setminus \overline{B(0,r)}$, but those are conformally equivalent iff they have the same ration $\frac rR$. (Especially, the punctured disk is not equivalent to an annulus with positive $r$ ... IIRC, one can map all regions to "standard" regions consisting of a disk with arc-shaped slits; and those representative shapes are then quit characteristic (there's a choice what to pick as "outer hole", though, and of course only up to rotation)
Feb
3
answered What do $\{ceps_q\}_{q=0}^Q$ and $\{a_q\}_{q=1}^p$ mean?
Feb
3
comment Peano's 3rd axiom -explain
If your personal $\Bbb N$ contains an element $0$ that is not the successor of anything else, then what the author denotes with the symbol $1$ is your $0$. (You probably also use the symbol $1$, but for the diffferent object $s(0)$; in this case confusion between the notations is due to arise; moreover, if the author will define two operations $+$ and $\cdot $ soon, rest assured that those are not your ordinary addition and multiplication). The theory is the same, but it may be easier for you to follow the author if you remove $0$ from $\Bbb N$. ;)
Feb
3
answered Only two groups of order $10$: $C_{10}$ and $D_{10}$
Feb
3
comment Find all pairs of nonzero integers $(a,b)$ such that $(a^2+b)(a+b^2)=(a-b)^3$
$2(b+3)$ in denominator, i suppose?
Feb
3
comment Find all pairs of nonzero integers $(a,b)$ such that $(a^2+b)(a+b^2)=(a-b)^3$
In fact, the discriminat is $(b+1)^2(1-8b)$, hence $1-8b$ must be a perfect square
Feb
3
comment Find all pairs of nonzero integers $(a,b)$ such that $(a^2+b)(a+b^2)=(a-b)^3$
Hm, then the OP's quadratic id wrong ... I'm afraid. Ah, I see - $a_1+a_2=-\frac{-3b+1}{b+3}\ne-\frac{-3b+1}{b+1}$
Feb
3
answered Find all pairs of nonzero integers $(a,b)$ such that $(a^2+b)(a+b^2)=(a-b)^3$
Feb
3
comment What function can turn $z=x+iy$ into something involving $xy$?
Certainly $\frac12z^2$ "involves" $xy$ as its imaginary part.
Feb
3
comment Is there any algorithm to find Isomorphism function between two graphs?
Trial and error. That is: Verify tehy have the same number of vertices. Sort vertices by degree; the sorted degrees must be equal. Try all permutations of all groups of same-degree vertices and check if this results in a graph isomorphism. - If applicable you may try to make the groups of similar vertices smaller before trying all permutations (which significantly reduces the number of attempts). For example, sort (secondary to the vertex degree) to the sum of neighbour degrees ...
Feb
3
comment Is there any algorithm to find Isomorphism function between two graphs?
This may be a very difficult problem. So difficult indeed that knowledge about graph isomoprhisms has been suggested as a step in zero-knowledge proofs
Feb
3
revised How do you show a set is dense? For example, is the set of all ration numbers $p/q$ with $q ≤ 10$ a dense set?
added 15 characters in body; edited title
Feb
3
comment How do you show a set is dense? For example, is the set of all ration numbers $p/q$ with $q ≤ 10$ a dense set?
You are referring to "$X$ is dense in $Y$", while the OP seems to refer to "$X$ is densely ordered" (though not consistently so). For example $\Bbb Q\setminus [0,1]$ is densely ordered, but not dense in $\Bbb R$.
Feb
3
comment How do you show a set is dense? For example, is the set of all ration numbers $p/q$ with $q ≤ 10$ a dense set?
@user310160 Between the numbers $\frac 01$ and $\frac 1N$ ther can be (at most) $N-1$ numbers with denominator $\le N$. Hence between any two consecutive of this finite set there is none, thus showung that the set is not dense
Feb
3
answered Number theory: Can we reach from $(x_0,y_0)$ to $(x_1,y_1)$ ,with following transitions?