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Apr
10
answered Show that $G$ is a group if the cancellation law holds when identity element is not sure to be in $G$
Apr
10
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 $0.9^{12\choose 4}$.
Apr
9
comment How to prove that gcd(k! mod m, m) > 1, for every k > $\alpha$
Is $n$ and $m$ the same?
Apr
9
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.
Apr
9
answered Proving Integer Modulo is Well-Defined
Apr
9
comment Homotopy on the unit circle
Do you know what the winding-number is?
Apr
9
answered An MCQ question on continuity.
Apr
9
answered Flipping a coin 1000 times.
Apr
9
comment How to show that $(C^0((a,b)), d_\infty)$ is not a metric space
@sj134 Apply the definition of $\sup$ and check.
Apr
9
answered Showing that the symmetry group of a circle is non-abelian
Apr
9
answered Show $e^z e^w = e^{z+w} \ \forall \ z,w \in \mathbb C$ by differentiation of $f(t):=e^{w+tz}e^{-tz}, \ t \in \mathbb R$.
Apr
9
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 $|\sin\alpha|\le 1$
Apr
9
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 $x_0=0$.
Apr
9
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 $q\not|y_n$ ...
Apr
8
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 ...
Apr
8
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?
Apr
8
revised Integer valued polynomial through some known points
added 6 characters in body
Apr
8
answered Integer valued polynomial through some known points
Apr
8
answered Expressing a Polynomial as a sum of cube roots of integers
Apr
8
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.