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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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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
30
Given $y_n=(1+\frac{1}{n})^{n+1}$ show that $\lbrace y_n \rbrace$ is a decreasing sequence
Feb 17, 2013
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
24
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
Mar 11, 2015
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
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
23
Open sets in product topology
Nov 18, 2013
22
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
Mar 14, 2013
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
20
product of two uniformly continuous functions is uniformly continuous
Mar 29, 2013
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What is the difference between LyX and LaTeX?
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Is it possible to earn a PhD in mathematics with emphasis in teaching?
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