miracle173
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 Jan5 comment Find $\lim_{n\to \infty}f_{n}(1)=?$ the functions until n=10: maxima-online.org/… Jan3 comment Three digit number $ABC$ with $ABC = A + B^2 + C^3$ I suppose the equation is wrong, because $ABC$ means $A\times B \times C$. The first trick is to write $$100A+10B+C=A+B^2+C^3$$ Jan3 comment questions about probabilistic primality test Which online Rabin-Miller test do you use? Can you provide the link? Jan3 comment How to show result in terms of $\pi$ in Mathcad? @Rory Daulton: No, it is absolutely on topic to pose a question about Mathcad. If it is a question about Mathcad it does not make sense to change it in a question about anything else. I think the post is about symbolic calculation in Matchcad. Jan2 comment Is $1234567891011121314151617181920212223…$ an integer? I modified the post you referenced becuase it is simply wrong to calll $123\ldots$ a number. Your question title is not posed wll, too. I changed your question tile too, because it contains the invalid assumption that this is a number. Jan2 comment The following is unclear to me:($f$ is the identical function) the inverse of $f: X\to X$ is not continuous(if the second space isnt discrete) The OP contains its (valid) definition of a continous function, so you should write an answer according to this definition and not simply reproduce a standard proof Jan1 comment Show $1+x+(x^2/2!)+ \cdots + (x^n/n!)=0$ has no rational solutions for all $n>1$. you should withdraw the acceptance of this answer. It does not make sense to accept an unvalid answer: The question is now a question with an accepted answer and so nobody who looks for open questions to answer will find it. Jan1 comment Show $1+x+(x^2/2!)+ \cdots + (x^n/n!)=0$ has no rational solutions for all $n>1$. How does the solution that you accepted help you. It stopped there where you already were ($q=\pm 1, p \mid n!$)? Jan1 comment Prime Number Sieve using LCM Function The $b_n$ are actually two independent sequences: $$\\ b_{n}=b_{n-1}+\text{lcm}(2n-1,b_{n-1}), n \ge 2, b_1 =2, \text{former even indexes} \\ b_{n}=b_{n-1}+\text{lcm}(2n-2,b_{n-1}), n \ge 2, b_1=2, \text{former odd indexes}$$ a similar sequence: $$b_n = b_{n-1} + \text{lcm}(n,b_{n-1}), n\ge 2, b_1=1$$ oeis.org/A135504 , oeis.org/A217663 Dec31 comment Counterexample to disprove that $P(A-B) = P(A) - P(B)$? It is always $$P(A-B) \ne P(A) - P(B)$$ because the lhs contains the empty set and the rhs does not. Dec31 comment A generalized derivative I think it should be $\alpha f(x)^{\alpha-1}\cdot f'(x)\left|\right._{x=x_0}$ Dec31 comment How many combinations can a group of n people form? @Kloar: Yopu are absolutely right, I missed this. I will update the answer. Dec31 comment Ratios with Ages @Przemysław Scherwentke: On your homepage I think you want to say that English is not your mother tongue Dec30 comment How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? You should supply your code and try to convince us that it produces all possible solutions. Dec28 comment The game with countable amount of steps if the angel makes the first move, he will loose even for k=1 because the devil will never remove the number from his box that the angel put in his box in the first move. Dec27 comment Convergence and Crash of a derivation (Chomsky) and which work of Chomsky are you citing? Dec27 comment Examples of magmas with all their elements idempotents what did you try? Dec27 comment Filters and Convergence your definition in the comment is blunder, can you correct it. You should add the correct definition to the post Dec24 comment Find the inverse function of $\log_{\sqrt{4-x^2} } \left(x^3+5x^2-x \right)$ The logarithm to base $\sqrt{4-x^2}$ notation can be avoided but I would be surprised if there is an inverse that can be composed of elementary functions $$\begin{array}\\ f(x) &=& \log_{\sqrt{4-x^2} } \left(x^3+5x^2-x \right)\\ &=&\frac{\log(x^3+5x^2-x)}{\log{ \sqrt{4-x^2}}} \\ &=& 2\frac{\log(x)+\log(x-\frac{-5-\sqrt{29}}{2})+\log(x-\frac{-5+\sqrt{29}}{2})}{ \log(2-x)+\log(2+x)} \end{array}$$ Dec23 comment Find the inverse function of $\log_{\sqrt{4-x^2} } \left(x^3+5x^2-x \right)$ What did you try and what is function 3?