# All Questions

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### How prove this inequality $|n\sqrt{2009}-m|>\dfrac{1}{kn}$

if $k>\sqrt{2009}+\sqrt{2010}$,show that for any positive integer numbers $m,n$, have $$|n\sqrt{2009}-m|>\dfrac{1}{kn}$$ My try: $$\Longleftrightarrow(n\sqrt{2009}-m)^2k^2n^2>1$$ ...
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### Arrangements of 1, 2, 2, 4, 6, 6, 6 greater than 3,000,000

How many numbers greater than 3,000,000 can be formed by arrangements of 1, 2, 2, 4, 6, 6, 6? Any approach on how to solve this?
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### Is $\text{fix}_\Omega(G_\alpha)$ a block of imprimitivity when $G$ is infinite?

Let $G$ be an infinite transitive permutation group acting on a set $\Omega$. Is $\text{fix}_\Omega(G_\alpha)$ a block of imprimitivity for $G$ in $\Omega$? $G_\alpha$ is the set of elements of ...
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I'm currently doing an exercise where this should be shown: Let $S$ be a set and $p$ a prime number and $m\in N$ such that $p$ does not divide $m$. Suppose $|S| = ... 4answers 4k views ###$\lim x \sin (1/x)$, when$x \to 0$Here's my solution: $$\lim x\sin (1/x) = \lim\, x \dfrac{\sin (1/x)}{x(1/x)} = \lim\, x/x = 1$$ when$x \to 0$However on the internet I read that the solution of this equation is 0. How can this be? ... 3answers 166 views ### A problem about the quadratic form$x^TAx=0$.$A$is an$m\times m$real matrix in$\mathbb{R}^{m\times m}$. If$x^TAx=0\ \forall\ x\in\mathbb{R}^m$, can we conclude that$A=0_{m\times m}$? Why? Note:$x^T$is the transpose of$x$.$0_{m\times ...
What is the highest power of 3 available in $58! - 38!$ ( ! stands for factorial) I can take $38!$ out as common to get $38! ( \frac{58!}{38!} - 1).$ I know how to find out the power of 3 in $38!$ ...