Breathed infinity, then, is a segment of this continuous line. It is all the time that passes from the beginning of an inhale to the end of an exhale. For simplicity, we can assume the breath takes one second, starting at \(t=0\) and ending at \(t=1\). For mathematical reasons, let's drop the two endpoints and only consider the points of time in between \(t=0\) and \(t=1\).

If we think of this subset of eternal infinity as a subset of the real line \(\mathbb{R}\), then we write it as \((0,1)\). This notation \((0,1)\) means all the real numbers in between zero and one (but not including zero or one). So we are going to equate breathed infinity with the set \((0,1)\).

**The claim that eternal infinity is the same size as breathed infinity, then, is the claim that \(|\mathbb{R}| = |(0,1)|.\)**