# tohecz

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bio website kmlinux.fjfi.cvut.cz/… location Prague, Czech Republic age 27 member for 1 year, 9 months seen Jun 27 at 8:08 profile views 105

Math PhD student at Czech Technical University in Prague and at LIAFA in Paris.

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 Jun13 comment Proof of irrationality of a series +1 very nice, simple, straighforward yet not trivial argument :) Jun5 comment Prove $\sqrt6$ is irrational sorry, corrected. And well, I say that I use stronger weapons, which can be used in a large framework, I know that simpler solutions exist. Jun3 comment Evaluate a limit (probably involving L'Hôpital rule) you should use exp in the appropriate places I believe, now you mix e as a number and e(x) as a function. Mar31 comment How do I integrate $\frac{1}{x^6+1}$ @MorganWilde Because you have to, the space of polynomials modulo a quadratic polynomial is generated by $1,x$ and not only by $1$. Mar31 comment How do I integrate $\frac{1}{x^6+1}$ +1 certainly faster than my approach. It's been a while I knew these tricks, now I remember only the general techniques :-/ Mar31 comment How do I integrate $\frac{1}{x^6+1}$ @MorganWilde No worries, I added a small tutorial. Mar31 comment which axiom(s) are behind the Pythagorean Theorem @William if $A_1\wedge A_2\wedge\dots\wedge A_n \Leftrightarrow B$, then $B$ is equivalent to the system of axioms $A_1,\dots,A_n$, so I'm no quite sure what you speak to in the second part. And if $A\wedge B\Rightarrow T$ and $A\wedge C\Rightarrow T$ and $A\wedge B\not\Rightarrow C$ and $A\wedge C\not\Rightarrow T$, then you got two non-equivalent proofs of your theorem $T$. I would never "guess" which axioms are "better" in any other way than possibility to derive ones from the others. (But maybe it's just too late and I overlook some stupidity in my arguments.) Mar31 comment which axiom(s) are behind the Pythagorean Theorem Equivalent = Relying the same set of axioms, usually. Therefore a proof that uses less axioms is "better", and a proof that uses different non-equivalent axioms is simply "different". Mar17 comment Why can't you pick socks using coin flips? +1 for "countable vs. uncountable". Mar2 comment How do I setup the lagrangian for this problem? @Spacey This is analytical. You always need to treat the boundary seperately. Remember that $y(x)=2x$ has to global maximum, still it has a maximum in $[0,1]$, attained at $2$. You can actually construct Lagrangians for each of the boundary point, but the domains of these are single points, so it's a non-sense to do. Mar2 comment How do I setup the lagrangian for this problem? Well, you simply search (by the derivatives method) for maxima inside $(0,2\pi/3)$, let's call it $y_M$. Then the maximum you look for is simply $\max(y_M, y(0), y(2\pi/3))$. Feb26 comment Set of all $a\in\mathbb Z$ that are coprime to $b\in\mathbb Z$ That's probably right, but $b^\perp$ doesn't so much look like a set, so I converge to $(b)^\perp$ :) Thanks anyways! Feb26 comment Set of all $a\in\mathbb Z$ that are coprime to $b\in\mathbb Z$ You're right that introducing a new notation will likely be necessary. I use only $\gcd(a,b)=1$ or not, so I prefer to use the symbol $\perp$. Which made me thinking: Would $(b\mathbb Z)^\perp$ do the job (of course properly defined)? Feb26 comment Infinite Continued Fraction Notation However, it is pretty confusing since $\frac{(2k+1)^2}{6}\neq\frac{(4k+2)^2}{24}$. Feb26 comment What is $\Bbb R^{\times}$? However, $\mathbb{R}^*$ can be used for $\mathbb{R}\cup\{\pm\infty\}$. Some people don't like $\overline{\mathbb{R}}$ for that since for them, closure of $\mathbb{R}$ is just $\mathbb{R}$. Feb14 comment What's the intuition behind Pythagoras' theorem? @Sawarnik Well, it's probably quite difficult to prove it from Euclid's axioms. However, this answer gives a nice insight into the way how PT works, which is probably more important for the OP than exact definitions and proving from axioms. Feb13 comment Find $f\left(A\right)$ for a polynomial function of a square matrix @inquisitor Now it looks correct ;) Feb13 comment Find $f\left(A\right)$ for a polynomial function of a square matrix @inquisitor Ok, then once you know what is determinant, you will learn what is the characteristic polynomial, and then you can understand (but probably not proof ;)) the Hamilton-Cayley Theorem. Before you have that, you can verify by hand that your matrix $A$ satisfies the relation $A^2=7A-10I$. Feb13 comment Find $f\left(A\right)$ for a polynomial function of a square matrix @inquisitor Then you're wrong. Matrix multiplication is not done element-wise. Feb13 comment Find $f\left(A\right)$ for a polynomial function of a square matrix Needed to add, the theorem you use is called Hamilton-Cayley Theorem, and is quite non-trivial ;)