Peter Taylor
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 57m 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? Apr24 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, ...? Apr21 comment 5 point estimation This thread contains information on how to make your question legible. Apr21 comment What is the number of points with integer coordinates in in a rectangle? Part 1 seems to be ambiguous about whether they're points on the line or points in $\mathbb{R}^2$. Apr18 comment Approximation for the Summation of Sequence of Powers of Sines Functions. It might be easier to see if you merge the inequalities and write $0 < z_m < z_{m-1} < \ldots < z_2 < z_1< \frac{\pi}2$ Apr18 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?? Apr17 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. Apr17 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? Apr17 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 Apr15 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? Apr2 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. Mar31 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. Mar30 comment Division of a number @DanBrumleve (and whoever upvoted that comment), this has nothing to do with the scope of worldbuilding as defined in their on topic page. The appropriate site for this question is gamedev, although there it would be a duplicate of How to determine the amount of experience needed for leveling up. Mar29 comment $\sin(\pi - a) = \sin (a)$. How/why? What's your definition of $\sin$? Is it in terms of triangles or complex exponentials? Mar25 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. Mar24 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. Mar24 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. Mar24 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. Mar18 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. Mar18 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?