Bounded nondecreasing rational sequences are uncountable
= Bounded nondecreasing rational sequences are uncountable
Map a <binary sequence> $(\epsilon_j)$ to the rational partial sums $s_n=\sum_{j=1}^n\epsilon_j3^{-j}$. They are nondecreasing and bounded above by $1/2$. A first different digit makes the corresponding partial sums different at that index, so the map is injective. <Cantor's diagonal argument> then makes this family uncountable despite every individual term being rational.
// Target: special-relativity.bigb