Question Number 75940 by Rio Michael last updated on 21/Dec/19
$${Given}\:{that}\:{a}\in\mathbb{Z}\:{and}\:{k}\in\mathbb{Z}\:{and}\:\left[{a}+{x}\right]\:=\:{a}\:+\left[{x}\right]\:=\:{k} \\ $$$$\left.{a}\right)\:{show}\:{that}\:\:{k}−{a}\leqslant\:{x}\leqslant\:{k}−{a}\:+\mathrm{1} \\ $$$$\left.{b}\left.\right)\:{Deduce}\:{from}\:\left({a}\right)\right)\:{that}\:\left[{x}+{a}\right]\:=\:\left[{x}\right]\:+{a} \\ $$