Peter Taylor
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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 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. Mar 5 comment Examples of non-hamiltonian decomposable graphs Any non-hamiltonian graph, for a start. Or any graph whose number of edges isn't an integer multiple of its number of vertices. Can you narrow down a bit more what you're looking for? PS Mathworld's page on Hamilton decomposition may have what you want. Mar 5 comment Probability of get 3 cards out of 4 One million tries seems somewhat overkill given that there are only 270725 ways of choosing 4 cards from a 52-card deck: it would probably be easy and just as fast to adapt your program to calculate the exact value you seek. But I'm not clear what it is you're calculating. What do you mean by "off-suited and off-ranked"?