# nik

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 74 How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? 21 If $f$ is continuous at $a$, is it continuous in some open interval around $a$? 18 If $\sum\limits_{n = 1}^\infty {{a_n}}$ converges, then $\sum\limits_{n = 1}^\infty {\left( {\frac{1}{{1 + {a_n}}}} \right)}$ is a convergent series? 14 Does $\lim \frac {a_n}{b_n}=1$ imply $\lim \frac {f(a_n)}{f(b_n)}=1$? 13 Are all good mathematicians fluent in computational aspects of mathematics

# 5,738 Reputation

 +25 The number of elements of intersection of $aH ∩ Ha^2$ +30 How to test interval inclusion $x\in [a,b)$ with a single comparison? +55 Is the boundary of an open subset of $\mathbb{R}^n$ always a topological manifold? +10 Is there an analytic function satisfying $\,\,f\big(\!\frac 1 n\!\big)=\frac 1 {\sqrt{n}},\,$ for every $\,n\in\mathbb N$?

# 11 Questions

 12 If $S^1 \hookrightarrow X$ induces an injection of $H_1$, then $X$ retracts onto $S^1$ 9 When is there a ring structure on an abelian group $(A,+)$? 9 Proving $\{P(a)\}$ (where $a$ is transcendental) is dense 5 Tangent bundle of a quotient by a proper action 5 Why is the recognition principle important?

# 113 Tags

 79 calculus × 13 43 limits × 5 74 arithmetic 38 group-theory × 15 50 real-analysis × 12 35 sequences-and-series × 4 49 abstract-algebra × 17 30 linear-algebra × 15 49 general-topology × 17 26 examples-counterexamples × 3

# 14 Accounts

 Mathematics 5,738 rep 1235 TeX - LaTeX 334 rep 17 Stack Overflow 101 rep 1 Server Fault 101 rep 1 Super User 101 rep 2