Question Number 155729 by henderson last updated on 03/Oct/21
$$\mathrm{A}=\left\{\left({a},{b}\right)\in\mathrm{IR}^{\mathrm{2}} \:/\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} \leqslant\mathrm{1}\right\} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{A}\:\mathrm{can}'\mathrm{t}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{the}\:\mathrm{cartesian} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{two}\:\mathrm{parts}\:\mathrm{of}\:\mathrm{IR}. \\ $$
Answered by Kamel last updated on 04/Oct/21
$${A}=\left\{\left({a},{b}\right)\in\mathbb{R}^{\mathrm{2}} /\:−\mathrm{1}\leqslant{a}\leqslant\mathrm{1}\:,\:−\sqrt{\mathrm{1}−{a}^{\mathrm{2}} }\leqslant{b}\leqslant\sqrt{\mathrm{1}−{a}^{\mathrm{2}} }\right\} \\ $$