For the sake of simplicity, assume your breath takes one second. Ignore \(t=0\) and \(t=1\), but take every instant between \(0\) and \(1\). This set, thought of as a subset of the real line, is written \((0,1)\).

So we will assume \(\mathscr{B}\) is the same size as \((0,1)\).

And in the first module, we showed that digital infinity is the same size as \(\mathbb{N}\).

**Thus we will justify the claim that breathed infinity is larger than digital infinity, by proving the mathematical statement \(|(0,1)| > |\mathbb{N}|\).**