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Oct
6
comment What types of functions do recurrence relations methods apply to?
This seems to be a typical recurrence relation. Concrete Mathematics has a good chapter about it, if you are interested.
Oct
6
comment Why are variables lowercased?
@Olivier oops... I forgot that $\mathbb N$ is not a field. You may use $\mathbb C$ as another example.
Oct
6
comment Why are variables lowercased?
You may also consider fields; they are usually denoted by double-struck capitals, like $\mathbb N$, $\mathbb Q$ and $\mathbb F_2$.
Oct
4
comment How many solutions does an equation system with binary values have?
Thank you. That was a missconception of mine. I thought that the echelon form would allow constructs like above.
Oct
4
comment How many solutions does an equation system with binary values have?
What if a row is not completely zero, just the coefficient $a_{k,k}$ is? In this case, it depends on how you set the free variables, whether the equation in row $k$ becomes $0=0$ or $0=1$... I don't know how to prevent that. If the row is full of zeroes, it is easy. Consider this system: $$\begin{array}{cccc|c}1&1&0&0&1\\0&0&1&0&1\\0&0&1&1&1\\0&0&0&0&0\\\end{array}$$ If you set the rightmost variable to $1$, it has no solutions. How to deal with such a case?
Sep
29
comment Fastest prime generating algorithm
You can't generate all prime numbers nor an infinite subset of all prime numbers in finite time...
Sep
22
comment Proof that $a\equiv 1\,(\textrm{mod }8)$ implies $a$ is a square modulo $2^n$ for all $n$
Ah! I missunderstood. Thank you.
Sep
22
comment Proof that $a\equiv 1\,(\textrm{mod }8)$ implies $a$ is a square modulo $2^n$ for all $n$
$a=17, n=5.\ a\equiv17\mod2^5,$ but 17 is not a square... or didn't I understand your statement?
Sep
22
comment Easy proof, that $\rm e\notin \mathbb Q$
Thanks for the explanation.
Sep
22
comment Easy proof, that $\rm e\notin \mathbb Q$
The last step in the second line is not completely clear to me. Could you please elaborate why this holds?
Sep
21
comment Easy proof, that $\rm e\notin \mathbb Q$
@lhf Thank you for the interesting link.
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.