# tohecz

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bio website kmlinux.fjfi.cvut.cz/… location Prague, Czech Republic age 27 member for 1 year, 11 months seen Aug 25 at 13:27 profile views 110

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

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 Aug23 comment Make $n$ cents with $1$-cent, $2$-cent, and $3$-cent coins Well, citing the question: Is there a way to do this without making use of a generation function? Aug23 comment Make $n$ cents with $1$-cent, $2$-cent, and $3$-cent coins That still uses generating functions though, only simplifies the argument. Aug22 comment Make $n$ cents with $1$-cent, $2$-cent, and $3$-cent coins @Ragnar That gives a generalized Tribonacci sequence, which is much more than $\sim n^3/12$. Aug22 comment Make $n$ cents with $1$-cent, $2$-cent, and $3$-cent coins Well, then the answer can't be correct since even with only 1c and 2c coins, there are $f_n$ (Fibonacci number) solutions; that's exponential, not polynomial. Aug22 comment Make $n$ cents with $1$-cent, $2$-cent, and $3$-cent coins Are $5=1+2+2=2+1+2=2+2+1$ three different solutions? It seems not, but I'm not sure Aug17 comment Is there an interval notation for complex numbers? @Teepeemm It's not interval arithmetics, it's simply set arithmetics with addition and multiplication, and you can do this over any ring, right? Aug17 comment Is there an interval notation for complex numbers? @JimmyK4542 It is common to define $X+Y = \{x+y:x\in X, y\in Y\}$ IMHO. There's no need to introduce an extra symbol for that. Aug17 comment Is there an interval notation for complex numbers? +1 This just shows that defining a complex interval to be a rectangle doesn't sound like a great idea... Aug17 comment Is there an interval notation for complex numbers? @GEdgar Better one: Do not introduce notation unless you are 111% sure you need it and it makes your paper easier to follow. Aug8 comment What is the oldest open problem in geometry? @DavidH Sorry, the margin I mean the comment area is too small to catch all of that :D Aug8 comment What is the oldest open problem in geometry? @littleO This problem is as old as the humankind. First, we thought that the earth is flat. Then we realized that it's not flat, then we forgot this and neglected it, then we found out it's true. Then we thought that the whole space is flat (i.e., $\simeq\mathbb R^3$), only to realize that this is not true either. 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".