 Bounded nondecreasing rational sequences are uncountable

Map a binary sequence $({ϵ}_j)$ to the rational partial sums $s_n={\sum }_{j=1}^n{ϵ}_j{3}^{-j}$. 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