# 2015-6 Dense sets

Let $$A$$ be an unbounded subset of the set $$\mathbb R$$ of the real numbers. Let $$T$$ be the set of all real numbers $$t$$ such that $$\{tx-\lfloor tx\rfloor : x\in A\}$$ is dense in $$[0,1]$$. Is $$T$$ dense in $$\mathbb R$$?

GD Star Rating