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Question Number 1875 by Filup last updated on 20/Oct/15

Given that:  Z={0, 1, 2, ...} all integers ≥0  R={0, 0.01, ..., 1, 1.01, ...} all reals ≥0   Prove that ∣R∣>∣Z∣

$$\mathrm{Given}\:\mathrm{that}: \\ $$ $${Z}=\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:...\right\}\:\mathrm{all}\:\mathrm{integers}\:\geqslant\mathrm{0} \\ $$ $${R}=\left\{\mathrm{0},\:\mathrm{0}.\mathrm{01},\:...,\:\mathrm{1},\:\mathrm{1}.\mathrm{01},\:...\right\}\:\mathrm{all}\:\mathrm{reals}\:\geqslant\mathrm{0} \\ $$ $$\:\mathrm{Prove}\:\mathrm{that}\:\mid{R}\mid>\mid{Z}\mid \\ $$

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