FUZxxl
Reputation
2,324
Next privilege 2,500 Rep.
Create tag synonyms
 Sep 21 comment Easy proof, that $\rm e\notin \mathbb Q$ @francis-jamet We showed that the limit exists just as Srivatsan described. Sep 21 comment Easy proof, that $\rm e\notin \mathbb Q$ @SrivatsanNarayanan Thank you! By the way, is it clear, which proof I refer to? Sep 21 comment Easy proof, that $\rm e\notin \mathbb Q$ @anon Fixed the first one. The second proof is not difficult, but takes too much time. That's all. Sep 21 comment Easy proof, that $\rm e\notin \mathbb Q$ @Yuval That is actually how we did this. The problem is, that the students in my class don't like proofs containing too many “It is easy to see that...”s. The proof using this strategie filled one A4 page in the script and took 20 minutes for me to explain. (Although it is quite easy if you think about it). Sep 13 comment Database for mathematical syntax @3Sphere Such a reference is quite useful if you see a formula in the Internet or in a paper where the author sees no reason to include a syntax definition. So even a lookup with many definitions is great, as one can often tell the right one from the context. Sep 5 comment Solving $8=x(2(1-\sqrt{5}))+(1-x)(2(1+\sqrt{5}))$ There is a simple way: Just use Wolfram Alpha Aug 29 comment Reducing the time to calculate Collatz sequences @Thijs Good point. Thank you! Aug 29 comment Reducing the time to calculate Collatz sequences @Qiachu But then, I would need to save all that information. Assume, that I want to test all $n$ in the intervall $[1,1\,000\,000\,000]$ - I would need about 1 GiB just for caching! But otherwise, a good idea. Aug 8 comment How many real roots are there to $2^x=x^2$? @Arturo Err, that would make it clearer, but the time for editing is up. Aug 8 comment How many real roots are there to $2^x=x^2$? @Arturo This was meant because the answerer stated, that $x = 2, x = 4$ are the only solutions. Aug 8 comment How many real roots are there to $2^x=x^2$? Why is $x\approx-0.76666469596212309311$ a solution? Jun 15 comment All functions $\frac{1}{f\left(y^2f(x)\right)} = \big(f(x)\big)^2\left(\frac{1}{f\left(x^2-y^2\right)} + \frac{2x^2}{f(y)}\right)$ @J. J. Ah, thanks. I didn't read the ${}^+$ in $\mathbb R^+$. Jun 15 comment All functions $\frac{1}{f\left(y^2f(x)\right)} = \big(f(x)\big)^2\left(\frac{1}{f\left(x^2-y^2\right)} + \frac{2x^2}{f(y)}\right)$ I just spotted a possible mistake: $1/f(0)=f(0)$ does not implies $f(0)=1$. It only implies, that $f(0)\in\{-1,1\}$. Jun 14 comment Is such a cryptographic system possible? That's a great article! Jun 14 comment How to solve this recurrence using generating functions? @muffel IIRC it's written by Graham, Patashnik and Knuth. Jun 13 comment How to solve this recurrence using generating functions? @muffel Concrete Mathematics is an awesom book when it comes to sums and generating functions. Just if you're curios. Jun 13 comment How to solve this recurrence using generating functions? @muffel For b) and c) recall that $\sum_{i=0}^ni^2=n(n+1)(2n+1)/6$. Jun 13 comment Expected value for a random variable Oh, yes. You're right. May 28 comment Convert any number to positive. How? In textbooks, the first one is often written $\lvert x\rvert$. May 24 comment A question on logic - where intuition can fail @amWhy: Thanks for finding such a good title.