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12h
revised Prove that $\sum_{cyc}\frac{a}{b(3+a-b)}\ge 1$
edited title
12h
comment Is isomorphism not always unique?
...which almost never happens. @jevie
1d
comment Tough equation in my entry exam
For 2., rewrite it as $x^6+x^4+x^2(x+1)^2+2x^2+(x+1)^2+8$.
Jul
18
comment A riddle with a witch and some gnomes
possible duplicate of Rainbow Hats Puzzle
Jul
17
comment A series with only rational terms for $\ln \ln 2$
Your inner sum is conditionally convergent, so simplifying this into a single series is probably not viable. (Though you could couple this approach with some log identities to get around that...)
Jul
15
revised Rainbow Hats Puzzle
deleted 3 characters in body
Jul
14
comment Please give me an example of the algorithm where $\Theta$ will be equal to $e^n$
The physical processes that $e$ is related to tend to be continuous, while the physical processes that are well-described by algorithms tend to be discrete. It's certainly not impossible that you could find some realistic-looking algorithm with the right runtime, but it's not the natural way to go looking for real-world instances of $e$...
Jul
13
reviewed Leave Closed prove validity of following sequent
Jul
12
revised Functions $f$ such that $f(x)+f(-x)=f(x)f(-x)$
edited title
Jul
8
comment A strange (!) behaviour of differentiability
For a simpler example of the same phenomenon, notice that $y=|x|$ is not differentiable at $0$, but $y=|x|^2$ is...
Jul
4
comment Determine whether a series expansion will be a Taylor or Laurent series?
(More trivially, if a Laurent series converges on a disk, it must actually be a Taylor series...)
Jul
4
comment If $K = \frac{2}{1}\times \frac{4}{3}\times \cdots \times \frac{100}{99}.$ Then value of $\lfloor K \rfloor$
It's not hard to make this rigorous. If $p(n)$ is the $n^{\rm th}$ partial Wallis product, the integral proof on Wikipedia immediately gives $\pi \frac{n}{2n+1} \leq p(n) \leq \frac{\pi}{2}$. In this case, $K^2=101p(50)$, so $50\pi \leq K^2 \leq \frac{101}{2} \pi$, which is easily good enough for our purposes.
Jul
1
comment How would you count a base > 36 system?
@Questionmark: There is no standard (except for certain special cases).
Jul
1
comment How would you count a base > 36 system?
amazon.com/On-Beyond-Zebra-Classic-Seuss/dp/0394800842/…
Jul
1
revised How would you count a base > 36 system?
retagging
Jun
30
awarded  Nice Answer
Jun
28
comment Straight in 52cards+2Joker
Are the jokers distinguishable from each other?
Jun
20
reviewed Approve suggested edit on Extracting perspective transformation from a 2D projection
Jun
20
comment How to show $n^2+m^2 = a^2+b^2 = (n-a)^2+(m-b)^2$ has no nonzero integer solutions?
Related: math.stackexchange.com/questions/105330/…. Note that the accepted solution is purely algebraic.
Jun
20
revised How to show $n^2+m^2 = a^2+b^2 = (n-a)^2+(m-b)^2$ has no nonzero integer solutions?
added 46 characters in body