Putnam 1963 B2

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?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.