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