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Jun
1
comment Fundamental theorem of calculus and complex integration
Ok, then yes. I was much disturbed by one of your sentence (the one in italic in my first comment). It's not that irrelevant to the question. Sorry anyway :o)
Jun
1
comment Fundamental theorem of calculus and complex integration
"The fact that the unit circle contains 0, on which neither cosec(z) nor cot(z) is defined is irrelevant. The only thing that matters is that the statements above hold true on the path itself." No, this is wrong.
Jun
1
comment Why spherical coordinates is not a covering?
@Martigan It's the idea, but it won't work as is, because for example with $\varphi \in (\pi/2, \pi/2+\pi)$, you don't get a bijection : it's neither injective nor surjective.
Jun
1
comment Why spherical coordinates is not a covering?
"Length" $2\pi$ on the $\theta$ side, but $\pi$ on the $\varphi$ side.
Jun
1
comment Probability of 10 coin flips?
@Tyler And even if it's not needed to consider the whole sample, it does not harm either, so your answer is right.
Jun
1
comment Why spherical coordinates is not a covering?
I'm not sure if it's what causes trouble to you, but a covering map needs not be bijective, it has only to be surjective. Maybe have a look at covering space on Wikipedia.
May
30
comment Website with possible closed forms of numbers
Or maybe Plouffe's inverter, now offline and replaced by isc.carma.newcastle.edu.au
May
27
comment Find the correct betting combination
@AlexeyBurdin is it really 3,5,7,17,22 ? I mean, if you bet t/3 on the first, you will only have 2t/3 left if it wins. With a total bet of t, it's a loss. Or you mean you also recover your bet, but I thought it was the meaning of the first "Rs.1" in what you get.
May
27
comment Find the correct betting combination
I guess $Rs$ means rupees (you may remove the money symbol, as it's useless, and is unclear in many countries). Is the gain proportional to the bet? I mean, if I bet $n$ rupees on team $5$ and I win, will I win $21n$ rupees?
May
27
comment What is the probability that 5 randomly chosen cards in a deck add up to 40 or greater?
Thanks! I'm glad we finally get the same answer. :)
May
27
comment What is the probability that 5 randomly chosen cards in a deck add up to 40 or greater?
I don't find the same answer, but I have a doubt :) Do you take the number of possibilities of combinations into account? I mean for the (1,1,1,2) case for instance, there are $5 \choose 2$ ways to place the pair. You don't seem to take the order into account at all (hence the 2598960), but I'm not sure it's correct, since the different "patterns" ((1,1,1,1,1), (1,1,1,2)...) don't have the same number of possibilities.
May
27
comment If $\det A=1$ and the matrices $A^{2015}$ and $A^{2017}$ are integer, is $A$ an integer matrix?
Even simpler: $A^2$ is an integer matrix, so $A^{2016}=(A^2)^{1013}$ is also an integer matrix. No need for recursion, though it also works of course. Now check determinant, and apply the same trick as above to get $A^2$, and you'll find $A$.
May
25
comment Hessian-Matrix positive definite $\iff$ $a$ local minimum?
Try $f(x,y)=x^4+y^4$ at $x=y=0$.
May
25
comment Fibonacci-related infinite sum
For the first, this and this give a reference to an article of Edmund Landau which is here pp. 298-300 (in french).
May
25
comment Fibonacci-related infinite sum
Not completely unrelated : mathoverflow.net/questions/51426/…
May
25
comment Inductively prove that any natural number $\ge 12$ can be written as the sum of 4s and 5s
Notice that the set $S$ of numbers $n\geq12$ that cannot be written $n=4a+5b$ is either empty, either has a minimum element $n_0$ (since $S$ is then a nonempty set of nonnegative integers, or a subset of $\Bbb N$, which is well ordered). But then $n_0$ must be $\leq15$, otherwise one of $n_0-4$ or $n_0-5$ would be in $S$, contradiction. Thus you just have to check $12,13,14,15$. Almost the same argument will give you an induction proof.
May
25
comment Sum of zeros of $P(x)$
Statement of the problem (#10) and related discussion on Art of Problem Solving. Since you wrote the same question there, it's nice to tell :)
May
25
comment How does $\cos (2z) = e^{2zi}$?
@snowman sine is odd
May
14
comment Probability of dice with a cumulative successes
Do you mean that according to his skill, the attacker will roll 1, or 2 or .. or 5 dice? And for each outcome that is 9 or 10, he will roll another die? Then, does this apply to the additionnal dice (I mean, if he gets 9 or 10 on the 6th die, he will throw yet another die). Anyway, you have to know the "base" number of dice (between 1 to 5) to compute the probability to win. With only one die for example, the attacker can't win with more than 1 success, obviously.
May
14
comment Computing a certain $2014$-fold product using a particular associative binary operation $\ast$
@FlorinM. You also need the fact that it's commutative.