21,683 reputation
31557
bio website
location
age
visits member for 2 years, 11 months
seen 3 hours ago

17h
revised Whether two quotients of $\mathbb{Z}^2$ are isomorphic.
deleted 2 characters in body
17h
comment Whether two quotients of $\mathbb{Z}^2$ are isomorphic.
@user26857 you mean, isomorphic to ${\mathbb Z}\oplus 7{\mathbb Z}$. The subgroups are certainly not identical to $\lbrace (x,7y)|x,y\in{\mathbb Z}\rbrace$. I corrected the SNF part, thanks.
23h
answered Whether two quotients of $\mathbb{Z}^2$ are isomorphic.
1d
comment Block diagonalizing two matrices simultaneously
Perhaps your question will make a lot of sense to physicists, but I think you did not take enough time to translate it into something understandable by mathematicians. What do you mean by "block diagonalize" ? Perhaps you could point to a wikipedia link explaining what the "connectivity" is.
2d
comment Can the inequality $a^3 + b^3 + c^3 \ge a^2b + ac^3 + b^2c$ be derived from arithmetic-geometric means?
Is $ac^3$ a typo for $ac^2$ ?
Aug
19
revised Tightenning Interval Mapping
added 151 characters in body
Aug
19
answered Tightenning Interval Mapping
Aug
18
comment convergence in probability induced by a metric
@mathmath8128 The function $f(t)=\frac{t}{1+t}=1-\frac{1}{1+t}$ is increasing on $(0,\infty)$, so that $|X_n-X|\geq \varepsilon$ yields $f(|X_n-X|) \geq f(\varepsilon)$
Aug
18
comment Prove $\left(\sum_{1 \le i <j \le n} |x_i-x_j|\right)^2 \ge (n-1)\sum_{1\le i<j \le n} (x_i-x_j)^2.$
@math110 you use $x_k=x_1+\sum_{j=2}^k y_j$ : you replace $x_2$ by $x_1+y_2$, you replace $x_3$ by $x_1+y_2+y_3$ etc.
Aug
17
awarded  Nice Question
Aug
16
comment Every endomorphims is a linear combination of how many idempotents in infinite dimensions?
At the very end of the proof of(II), shouldn't it be ${\rm ker}(\pi_1)+{\rm ker}(\pi_2)$ rather than ${\rm ker}(\pi_2)+{\rm ker}(\pi_3)$ ?
Aug
16
awarded  real-analysis
Aug
15
answered If a polynomial has only real zeros then $a_{0}+a_{1}+\cdots+a_{n}\le\frac{(n+1)^n}{\binom{n}{s}(n-s)^{n-s}(s+1)^s}\cdot\max_{k}a_{k}$
Aug
15
comment A “repeated roots allowed” version of the continuity of roots
The reordering issue is easy : the functions $\min$ and $\max$ are continuous ${\mathbb R}^2 \to {\mathbb R}$, because $\min(x,y)=\frac{x+y-|x-y|}{2}$ and $\max(x,y)=\frac{x+y+|x-y|}{2}$
Aug
15
comment How to find the minimum value of $\sum_{1\le i<j\le 6}[a_{i}+a_{j}]$
Thank you for taking the time to write such an elaborate answer.
Aug
15
asked A “repeated roots allowed” version of the continuity of roots
Aug
15
answered Determining if a recursively defined sequence converges and finding its limit
Aug
14
comment Prove that the length of segment on tangent is constant for $y=\frac a2\ln{\frac{a+\sqrt{a^2-x^2}}{a-\sqrt{a^2-x^2}}}-\sqrt{a^2-x^2}$
You’re right, I was mistaken
Aug
14
answered How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
Aug
14
comment What is the set with characteristic function $\chi_A(x) + \chi_B(x)-\chi_A(x)\chi_B(x)$?
You are correct, the "answer given" is false.