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ASB
  • Member for 10 years, 3 months
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73 votes
3 answers
3k views

Is $ 0.112123123412345123456\dots $ algebraic or transcendental?

9 votes
2 answers
474 views

Evaluating $ \int_{-\pi /2014}^{\pi /2014}\frac{1}{2014^{x}+1}\left( \frac{\sin ^{2014}x}{\sin ^{2014}x+\cos ^{2014}x}\right) dx $

7 votes
2 answers
2k views

Converse of the theorem "If a real number $c$ is constructible, then $c$ is algebraic of degree a power of 2 over the field $\mathbb{Q}$ of rationals"

6 votes
3 answers
936 views

$ \sum_{n=1}^{\infty}a_{n} $ diverges but $ \sum_{n=1}^{\infty}\frac{a_{n}}{1+a_{n}^{2}} $ sometimes converges and sometime diverges.

5 votes
2 answers
4k views

Proving the Cantor set is closed (without using the fact "the intersection of closed sets is closed")

5 votes
0 answers
248 views

Proving the function $ f $ is continuous on $ [0,1] $

5 votes
3 answers
294 views

How do I explain Complex Analysis to my grandma?

4 votes
4 answers
613 views

How can one proves that $ \lim\limits _{n\rightarrow \infty}\int \limits_{0}^{\infty}\frac{\sin (x^{n})}{x^{n}}dx=1 $?

3 votes
1 answer
171 views

Proving $ \sum_{k=1}^{\infty}\frac{9}{10^{\frac{k(k+1)}{2}}}=0.90900900090... $ is irrational

3 votes
1 answer
209 views

$\sum_{n=1}^{\infty}\underbrace{ \sin\left ( \sin \left ( \dots \sin \left ( \dfrac {\pi}{2} \right ) \dots \right ) \right ) }_{n\text { #} \sin }$ [duplicate]

3 votes
1 answer
109 views

Finding $ \lbrace a_{n}\rbrace $ s.t. $\mathop {\lim }\limits_{n \to \infty }a_{n}=1$ and $\mathop {\lim }\limits_{n \to \infty }a_{n}^{n}=2015$

3 votes
1 answer
190 views

Epimorphism in Category

2 votes
1 answer
181 views

Continuous function between topological spaces

2 votes
0 answers
240 views

Proving the Urysohn's metrization theorem by using the Nagata-Smirnov's metrization theorem

2 votes
2 answers
3k views

Is there any irrational number in decimal with a rational binary expansion?

1 vote
1 answer
51 views

Proving if $ \Gamma_{2}(R)\smallsetminus J(R) $ is a forest then it is either totally disconnected or a star graph

1 vote
1 answer
82 views

If there exists a vertex of $ \Gamma_{2}(R)\setminus J(R) $ which is adjacent to every other vertex then $ R \cong \mathbb{Z}_{2}\times F$

1 vote
2 answers
66 views

Prove that $ f(A) \subseteq B \implies A \subseteq f^{-1}(B) $

0 votes
1 answer
295 views

How to show non unit $x$ is idempotent in $R$ if $xR+aR=R$ for all $a\in R\smallsetminus (J(R)\cup U(R)\cup\{x\})$?

0 votes
2 answers
106 views

How to prove the polynomial $ x^{2011}-x\in \mathbb{Z}_{2011}[x] $ is separable?