A note on the natural density of product sets
Copyright policy )A note on the natural density of product sets
Given two sets of natural numbers $\mathcal{A}$ and $\mathcal{B}$ of natural density $1$ we prove that their product set $\mathcal{A}\cdot \mathcal{B}:=\{ab:a\in\mathcal{A},\,b\in\mathcal{B}\}$ also has natural density $1$. On the other hand, for any $\varepsilon>0$, we show there are sets $\mathcal{A}$ of density $>1-\varepsilon$ for which the product set $\mathcal{A}\cdot\mathcal{A}$ has density $
6 pages
- University of Genoa Italy
- University of Montreal Canada
- Polytechnic University of Turin Italy
density, Mathematics - Number Theory, Density, gaps, topology, FOS: Mathematics, product sets, Mathematics - Combinatorics, 11B05 (primary), Number Theory (math.NT), Combinatorics (math.CO)
density, Mathematics - Number Theory, Density, gaps, topology, FOS: Mathematics, product sets, Mathematics - Combinatorics, 11B05 (primary), Number Theory (math.NT), Combinatorics (math.CO)
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