= Countability of disjoint positive-length intervals
A family of pairwise disjoint real intervals of positive length is <countable>. Each interval contains a <rational number> in its interior by the <density of the rational numbers>. Fix an enumeration of the <rational numbers> and select the first member lying inside each interval. Disjointness makes this selection an <injection> into a <countable set>. The argument also applies to disjoint nonempty open subsets of the real line.
Back to article page
