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 Nov 24 answered Prove existence Nov 23 comment Alternative definition of Gamma function. Show that $\lim_{n \to \infty} \frac{n! \; n^m}{m \times (m+1) \times \dots \times (m+n)} = (m-1)!$ excuse me I am having trouble reading... can you use $$...$$ in order to make some of these equations a little bigger? Nov 23 asked Alternative definition of Gamma function. Show that $\lim_{n \to \infty} \frac{n! \; n^m}{m \times (m+1) \times \dots \times (m+n)} = (m-1)!$ Nov 22 answered curvature in $\mathbb{R}^2$, osculating circle Nov 22 accepted Do the adeles $\mathbb{A}$ have the same cardinality as the real numbers $\mathbb{R}$? Nov 22 asked Do the adeles $\mathbb{A}$ have the same cardinality as the real numbers $\mathbb{R}$? Nov 16 comment How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$? I am also pointing out a typo in your response... you say $\sum i^{\color{red}{-}1/2}$ you should take out the minus sign. Nov 16 comment How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$? my question was originally about $\sum \frac{1}{\sqrt{n}}$ but I simplified it to $\sum \sqrt{n}$ after I drew the wrong charts :-P for me the surprise is how accurate I can get my answer without using any calculus at all. there are many result of this kind where I could try to use the same principle. Thank you. Nov 16 comment Prove that $\{w \mid \text{ w has even length and the first half of w has more 0s than the second half of w} \}$ is not regular? consider also cs.stackexchange.com for questions about automata theory but there may be people who can answer here Nov 16 accepted How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$? Nov 16 comment How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$? Indeed, if we add up the area of the $\color{#20E070}{\text{green}}$ rectangle and the $\color{#E0E070}{\text{yellow}}$ triangle, we do get a trapezium, whose area is $A = \frac{1}{2} \times b \times (h_1 + h_2)$. Nov 16 comment Is a linear factor more likely than a quadratic factor? I don't know the details, but using Turan's Sieve they show polynomnials in $\mathbb{Z}[x]$ are irreducible with probability $1$. So generically just pick numbers at random, that polynomial should be irreducible. Nov 16 revised How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$? edited title Nov 16 asked How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$? Nov 14 answered Tensor products and morphisms Nov 14 comment upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$ The modern theory is this type of simultaneous approximation, $\sqrt{m} \approx n + \sqrt{2}$ is related to dynamical systems like planets orbiting around the Sun. If you want, see Etienne Ghys on pétits diviseurs or small divisors. This is not important right now. Nov 14 revised upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$ added 768 characters in body Nov 14 revised upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$ added 768 characters in body Nov 14 revised upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$ added 768 characters in body Nov 14 revised upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$ added 768 characters in body