Fimpellizieri

 45 $55$ gangsters shoot the nearest gangster to them, where all the distances between them are different. Prove that at least one gangster will survive. 33 Using the Left-Inverse to “Solve” an Impossible System of Equations 30 Integral of a function's derivative does not equal the original function? 19 Total distance traveled when visiting all rational numbers 17 Number of total possibilities for an equation

### Reputation (17,621)

 +10 If $f_n \to f$ uniformly from $[a,b] \to \Bbb R$, every $f_n$ is continuous and each $f_n$ has a zero, then $f$ has a zero. +10 Can there exist any continuous function on R that maps a rational number to an irrational number and an irrational number to a rational number? +55 A set $\Omega$ is bounded if there exists $M > 0$ such that $|z| < M$ whenever $z \in \Omega$. The set $\Omega$ is contained in some large disc. +15 How to find $(a_{1}a_{2})^n+(a_{1}a_{3})^n+(a_{2}a_{3})^n+\cdots$, which came from $\prod\limits_{k=1}^{\infty}(1-a_{k}x)$?

### Questions (9)

 5 Least number of rounds to find all hidden pairs 5 For all $x\in\mathbb{N}^*$ there is some $y\in\mathbb{N}^*$ such that $xy$ contains only $0$s and $1$s. 5 Evaluate the sum $\sum_{i=0}^{n} (-1)^{n-i} \binom{n}{i} f(i)$ 2 Combinatorial identity on partitions 2 Maximizing Stirling numbers of the second kind

### Tags (343)

 199 real-analysis × 113 97 probability × 57 177 linear-algebra × 92 82 limits × 47 173 calculus × 100 76 integration × 27 153 combinatorics × 62 62 puzzle × 7 119 sequences-and-series × 53 50 algebra-precalculus × 27

### Accounts (10)

 Mathematics 17,621 rep 11836 Puzzling 2,307 rep 1819 Seasoned Advice 198 rep 5 Stack Overflow 105 rep 3 MathOverflow 101 rep 1