Hagen von Eitzen
Reputation
372/400 score
 Apr10 answered Show that $G$ is a group if the cancellation law holds when identity element is not sure to be in $G$ Apr10 comment Generate Random Numbers between (0-99) with possible calculation availabilty between them. As soon as an even number and a multiple of $5$ occur, you are on the safe side. This fails only with a probability about $(4/5)^{12}$. Only then do you need to check for sums. With $12\choose 4$ potential sums essentially (for this rough estimated) uniformly distributed $\pmod{10}$, the chance of this failing is only about $0.9^{12\choose 4}$. Apr9 comment How to prove that gcd(k! mod m, m) > 1, for every k > $\alpha$ Is $n$ and $m$ the same? Apr9 comment Flipping a coin 1000 times. Yes. If a coin is experimentally verified to "always" show head, it is not too bad to assume that it always shows head. At least this is correct, if we assume that the a priori distribution of $p$ is uniform. Apr9 answered Proving Integer Modulo is Well-Defined Apr9 comment Homotopy on the unit circle Do you know what the winding-number is? Apr9 answered An MCQ question on continuity. Apr9 answered Flipping a coin 1000 times. Apr9 comment How to show that $(C^0((a,b)), d_\infty)$ is not a metric space @sj134 Apply the definition of $\sup$ and check. Apr9 answered Showing that the symmetry group of a circle is non-abelian Apr9 answered Show $e^z e^w = e^{z+w} \ \forall \ z,w \in \mathbb C$ by differentiation of $f(t):=e^{w+tz}e^{-tz}, \ t \in \mathbb R$. Apr9 comment Let $f(x) := x^2 \sin \frac 1 x, f(0)=0$. Show $f$ is differentiable on $\mathbb R$. I suggest to rather use $|\sin\alpha|\le 1$ Apr9 comment Let $a \in \mathbb R$. Use $\lim_{t\rightarrow 0} \frac {\log(1+at)} t = a$ to show $\lim_{t\rightarrow \infty} (1+\frac a t)^t = e^a$ Let $f(x)=\log(1+ax)$ and $x_0=0$. Apr9 comment Integer valued polynomial through some known points Hm, that would translate (in the language of the first proposition) to an additional requirement of the form $q|P(qk)$ for all $qk>n$. This seems to be tricky if $q\not|y_n$ ... Apr8 comment Protocol to split a common item between 2 people Even with the pizza the players may attribute different value to it: If you know that I don't like anchovies (and you like them), you might cut the pizza into a large piece with many anchovies and a small one with no anchovies. How big can you make the difference between the pieces? It depends on how littel I like anchovies, and how good you can estimate that I don't, and how much you can be sure that I won't pick the anchovies just to teach you a lessnon not to split unfair ... Apr8 comment is there an efficient algorithm for comparing collections of points? @celtschk It might be easier to computer the matrix with entries $\langle q_i,q_j\rangle$ (and similar for $p$s) and find invariants, for example the eigenvalues multiset. Do examples exist where the eigenvalues are the same and yet the points can not be rotated into another? Apr8 revised Integer valued polynomial through some known points added 6 characters in body Apr8 answered Integer valued polynomial through some known points Apr8 answered Expressing a Polynomial as a sum of cube roots of integers Apr8 comment Is an anomaly in base-n arithmetic discoverable in base-m arithmetic? Look thoroughly at $7888609052210118054117285652827862296732064351090230047702789306640624$. Is the start "$7888\ldots$" an anomaly? I don't think so. At least it is not related to the remarkable base 5 pattern.