Question Number 71551 by mhmd last updated on 17/Oct/19
$${whats}\:{the}\:{mean}\:{R}^{++} \:?{and}\:{R}^{−−} ? \\ $$
Answered by MJS last updated on 17/Oct/19
$$\mathrm{I}\:\mathrm{only}\:\mathrm{know}\:\mathbb{R}^{+} =\left\{{x}\in\mathbb{R}\mid{x}>\mathrm{0}\right\}\:\mathrm{and} \\ $$$$\mathbb{R}^{−} =\left\{{x}\in\mathbb{R}\mid{x}<\mathrm{0}\right\} \\ $$$$\mathrm{and} \\ $$$$\mathbb{R}×\mathbb{R}=\mathbb{R}^{\mathrm{2}} =\left\{\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\mid{x}\in\mathbb{R}\wedge{y}\in\mathbb{R}\right\} \\ $$$$\mathrm{so}\:\mathrm{maybe} \\ $$$$\mathbb{R}^{++} =\mathbb{R}^{+} ×\mathbb{R}^{+} =\left\{\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\in\mathbb{R}^{\mathrm{2}} \mid{x}>\mathrm{0}\wedge{y}>\mathrm{0}\right\} \\ $$$$\mathrm{and}\:\mathrm{similar}\:\mathrm{for}\:\mathbb{R}^{−+} ,\:\mathbb{R}^{−−} ,\:\mathbb{R}^{+−} \\ $$