Mathematics
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Idonknow
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A mathematician is a person who can find analogies between theorems;

A better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories;

And one can imagine that the ultimate mathematician is one who can see analogies between analogies

--S. Banach

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Score Newest
question
41
Prove that there is a real number $a$ such that $\frac{1}{3} \leq \{ a^n \} \leq \frac{2}{3}$ for all $n=1,2,3,...$
May 22, 2015
question
30
Given $y_n=(1+\frac{1}{n})^{n+1}$ show that $\lbrace y_n \rbrace$ is a decreasing sequence
Feb 17, 2013
question
25
Let $p_1, p_2,\dots,p_n$ be polynomials of $k$ variables $x_1,\dots,x_k$ and $p_1^2 + \dots +p_n^2=x_1^2 + \dots + x_k^2$ Prove that $n \geq k$.
May 24, 2015
question
24
If $(a_n)$ is a decreasing sequence of strictly positive numbers and if $\sum{a_n}$ is convergent, show that $\lim{na_n}=0$ [duplicate]
Apr 22, 2013
question
23
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
Mar 11, 2015
question
23
Show that the sequence $\sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}},...$ converges and find its limit. [duplicate]
Feb 28, 2013
question
22
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
Mar 14, 2013
question
21
Open sets in product topology
Nov 18, 2013
question
21
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$ [duplicate]
Apr 15, 2013
question
20
product of two uniformly continuous functions is uniformly continuous
Mar 29, 2013
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40
What is the difference between LyX and LaTeX?
20
Is it possible to earn a PhD in mathematics with emphasis in teaching?
20
Why is the period of rotation the same for two stars orbiting the same centre?
15
Why is Brownian motion useful in finance?
11
Consequences of AES without any one of its operations

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