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

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