Here is what I post as an answer sometimes, if I see a question quickly enough for it to make the slightest difference. I have learned to post it CW and not to reply to comments, the people who want help here for these questions want what they want and are unpleasant. Meanwhile, one may claim sep...
It seems there is a way to get the 30 most recent posts by a user, click on profile "activity" and go to RSS FEED. However, from what I can see, when the user deletes the question, it also disappears from this feed. I will see for sure, I have subscribed, not sure how that works. This business a...
It seems there is a way to get the 30 most recent posts by a user, click on profile "activity" and go to RSS FEED. However, from what I can see, when the user deletes the question, it also disappears from this feed. I will see for sure, I have subscribed, not sure how that works. This business a...
It seems there is a way to get the 30 most recent posts by a user, click on profile "activity" and go to RSS FEED. However, from what I can see, when the user deletes the question, it also disappears from this feed. I will see for sure, I have subscribed, not sure how that works. This business a...
It seems there is a way to get the 30 most recent posts by a user, click on profile "activity" and go to RSS FEED. However, from what I can see, when the user deletes the question, it also disappears from this feed. I will see for sure, I have subscribed, not sure how that works. This business a...
A length $t$ in the hyperbolic plane can be constructed if and only if $\sinh t$ is a length that can be constructed in the Euclidean plane. The constructible angles in the hyperbolic plane are exactly the same as those in the Euclidean plane. My Article Place to download Marvin's article cli...
The Hessian matrix (second partial derivatives) of the first quadratic form is $$ H =\left( \begin{array}{cc} 2a & b \\ b & 2c \end{array} \right) $$ The relationship called "equivalence" takes an integer matrix $P \in SL_2 \mathbb Z,$ with new Hessian matrix given by $$ P^t H P. $$ If desire...
A bilinear form is just a type of function. Therefore, addition of bilinear forms is just regular function addition: pointwise addition. If $f, g$ are bilinear forms then $$(f+g)(v, u) = f(v, u) + g(v, u)$$
meanwhile, if they are integers and not equal, $$ |x-y| \geq 1. $$ In any case, $$ x^2 + xy + y^2 \geq \frac{3}{4} \; x^2, $$ $$ x^2 + xy + y^2 \geq \frac{3}{4} \; y^2. $$
Can ANY pythagorean quadruple be generated using 4 integer variables $(m,n,p,q)$? I've read up on Mordell's method, which uses a 3-variable system of generating pythagorean quadruples, and it is widely documented that this doesn't generate them all. However there is also another method which int...
I am trying to integrate this function: $$\int {\frac{1}{x\sqrt{x+1}}\mathrm{d}x}.$$ When I googled it I saw methods that used both "$u$" and "$s$" substitution. I sort of understood what was going on but got stuck after substituting in $s$. I could not simplify any further. My professor used ...
I found a lot of ways to prove that $\sum\limits_{n=1}^\infty \frac 1 {n^2}$ converges. I wondered if you could also prove it using the the fraction criteria ($\lim\limits_{n\to \infty} |\frac {a_n+1} {a_n}|<1)$ and that $\frac 1 {n^2} < \frac 1 {(n-1)\cdot n}$ Which results in: $\lim\limits...
I found a lot of ways to prove that $\sum\limits_{n=1}^\infty \frac 1 {n^2}$ converges. I wondered if you could also prove it using the the fraction criteria ($\lim\limits_{n\to \infty} |\frac {a_n+1} {a_n}|<1)$ and that $\frac 1 {n^2} < \frac 1 {(n-1)\cdot n}$ Which results in: $\lim\limits...
A partition of an integer $n$ is a way of writing $n$ as a sum of integers. The partition function $p(n)$ counts the number of distinct partitions of $n$. In 1918, Hardy and Ramanujan proved the amazing result $$p(n) \sim \frac {1} {4n\sqrt3} \exp\left({\pi \sqrt {\frac{2n}{3}}}\right)$$ This ...
I have troubles with the following exercise, especially because you don't know anything about the sequence $a_n$: $b_n$ and $a_n$ are both real sequences and $b_n \to 1$ Prove: $\lim \sup (a_n*b_n)=\lim \sup (a_n)$, and $\lim \sup (a_n^{b_n}))=\lim \sup (a_n)$
I have added some links to posts on this meta to the tag-info for cross-posting. Namely Asking the same question on MSE and MO and Moderator Supported (Official) Guidelines for "Legitimate" CrossPosting? Since I do not want to include there some misleading information, I would be grateful if so...
I have added some links to posts on this meta to the tag-info for cross-posting. Namely Asking the same question on MSE and MO and Moderator Supported (Official) Guidelines for "Legitimate" CrossPosting? Since I do not want to include there some misleading information, I would be grateful if so...
It seems there is a way to get the 30 most recent posts by a user, click on profile "activity" and go to RSS FEED. However, from what I can see, when the user deletes the question, it also disappears from this feed. I will see for sure, I have subscribed, not sure how that works. This business a...
It seems there is a way to get the 30 most recent posts by a user, click on profile "activity" and go to RSS FEED. However, from what I can see, when the user deletes the question, it also disappears from this feed. I will see for sure, I have subscribed, not sure how that works. This business a...
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