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Apr
27
comment Computing efficiently a small base to the power a large number
Are you after exact results or results to some level of relative error?
Apr
24
comment Is an empty parenthesis a valid mathematical expression?
The meaning of mathematical notation is highly dependent on context. Which subfield(s) of mathematics are relevant to the case which interests you? And what is your motivation for the question: trying to interpret someone else's use of them, trying to justify using them yourself, trying to win a random bet, ...?
Apr
18
comment Conditional distribution of two binomials which both depend on a third
You have $C\sim\text{B}(N,c)$ and $N\sim\text{B}(C,\alpha)$. Is that the same $N$ in both cases??
Apr
17
comment Coupon collector variation (with deleterious coupons and tolerance)
It is better than it was, but it would be better still if you outlined what progress you have made with solving the problem.
Apr
17
comment Proving trigonometric identity $\frac{1+\sin x}{1-\sin x}-\frac{1-\sin x}{1+\sin x}=4\sec x \tan x$
Is the part which you don't understand the meaning of $\sec$ or something else?
Apr
17
comment Prove $\lim_\limits{x\to\infty}\dfrac{P_k(x)}{P_{k+1}(x)}=0$
possible duplicate of Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials
Apr
15
comment Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$
Could you explain where the 5 and 30 come from?
Apr
2
comment How can I find the closed form of this recursive relationship: $a_{n}=(a_{n-1})^2+a_{n-1},a_{0}=1$
Knuth's comment in OEIS that "Using the methods of Aho and Sloane, Fibonacci Quarterly 11 (1973), 429-437, it is easy to show that $a_n$ is the integer just a tiny bit below the real number $\theta^{2^n}-\frac12$, where $\theta \approx 1.597910218$ is the exponential of the rapidly convergent series $\ln\frac32+\sum_{n \ge 0} \ln(1+(2a_n+1)^{-2})$" gives you a starting point.
Mar
31
comment Prove that for all naturals $n \ge 6$ there is a set of $n$ positive naturals, $a_1$ to $a_n$ such that $\sum_{i=1}^n \left(\frac{1}{a_i}\right)^2 =1$
$\{2, 2, 2, 2\}$ is not a set. You might want to check that you're solving the right problem.
Mar
29
comment $\sin(\pi - a) = \sin (a)$. How/why?
What's your definition of $\sin$? Is it in terms of triangles or complex exponentials?
Mar
25
comment Math of password cracking
Spaces are \, or \;. Your formula looks correct, so if it overestimates then the obvious question is: why do you think it does 4 billion calculations per second? Edit: wait, I may have it. Does your program exit early when it finds the password? Your calculation is the worst case: if the password is generated uniformly and randomly then on average it will take half that time.
Mar
24
comment Number of ways to set 3 queens to attack each other
I'm not sure whether the problem statement is intended to be that each queen is attacked by at least one queen or by all other queens; and in the latter case, whether you intend to count "all in a straight line" as an exception.
Mar
24
comment $A ⊂ B$ if and only if $A − B = ∅$
The statement is incorrect. Alberto's answer proves the correct statement (with $\subseteq$ instead of $\subset$), but for some reason doesn't point out this important difference.
Mar
24
comment Do all logic problems have one solution?
The NAND operator also includes the case that neither of the operands is true. I think you're confusing it with XOR. But for the first issue, if you know what the problem is with your answer, and you know how to fix the problem, what's the question? And for the second issue, what do you mean? I can see two instances of $P(y)$ in that answer.
Mar
18
comment Growth factor problem
@DavidK, in my experience it is never a good idea to suggest to someone new to the SE network that a question would be a better fit on a different site in the network unless you explicitly mention that it can be migrated by flagging and asking a moderator to do it. Otherwise you end up with cross-posts and much irritation all round. But in this case, it seems to be pure algebraic manipulation, so I think it's a better fit here.
Mar
18
comment Growth factor problem
I've edited in the relevant formulae, but it would be helpful to have more context in terms of what you've tried and how far you get. E.g. is $\frac{d\ln g}{dt} = \frac{\dot{g}}{g}$ a useful hint to get you started, or are you already way beyond that?
Mar
16
comment Mathematical Analysis Question: Cauchy sequences proof
You must surely have tried something. If you show us what you've tried and why it doesn't work, you'll be able to get help which actually helps you.
Mar
15
comment The irreducibility of polynomials for specific cases
In your second paragraph, irreducible should say reducible.
Mar
9
comment Selection from cliques of a graph in polynomial time
Are you given that the cliques are maximal?
Mar
6
comment Examples of non-hamiltonian decomposable graphs
Either I'm misunderstanding your notation or $C_2 \times C_3 = K_6$, which is 5-regular. Note also the statement in the second MathWorld page I linked that every Hamiltonian vertex-transitive graph with no more than 31 vertices has a Hamilton decomposition except the line graphs of the Petersen and Coxeter graphs. The next smallest known non-decomposable vertex-transitive graph has 48 vertices, so if you're looking for examples which can be checked by hand you almost certainly want to look at non-vertex-transitive graphs.