Question Number 1875 by Filup last updated on 20/Oct/15
$$\mathrm{Given}\:\mathrm{that}: \\ $$ $${Z}=\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:...\right\}\:\mathrm{all}\:\mathrm{integers}\:\geqslant\mathrm{0} \\ $$ $${R}=\left\{\mathrm{0},\:\mathrm{0}.\mathrm{01},\:...,\:\mathrm{1},\:\mathrm{1}.\mathrm{01},\:...\right\}\:\mathrm{all}\:\mathrm{reals}\:\geqslant\mathrm{0} \\ $$ $$\:\mathrm{Prove}\:\mathrm{that}\:\mid{R}\mid>\mid{Z}\mid \\ $$