This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 3

2007 VJIMC, Problem 1
Tags: dense , set theory
Construct a set $A\subset[0,1]\times[0,1]$ such that $A$ is dense in $[0,1]\times[0,1]$ and every vertical and every horizontal line intersects $A$ in at most one point.

1963 Putnam, B2
Tags: dense
Let $S$ be the set of all numbers of the form $2^m 3^n$, where $m$ and $n$ are integers. Is $S$ dense in the set of positive real numbers?

2003 IMC, 3
Tags: dense , topology , real analysis
Let $A$ be a closed subset of $\mathbb{R}^{n}$ and let $B$ be the set of all those points $b \in \mathbb{R}^{n}$ for which there exists exactly one point $a_{0}\in A $ such that $|a_{0}-b|= \inf_{a\in A}|a-b|$. Prove that $B$ is dense in $\mathbb{R}^{n}$; that is, the closure of $B$ is $\mathbb{R}^{n}$