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Question Number 71551 by mhmd last updated on 17/Oct/19

whats the mean R^(++)  ?and R^(−−) ?

$${whats}\:{the}\:{mean}\:{R}^{++} \:?{and}\:{R}^{−−} ? \\ $$

Answered by MJS last updated on 17/Oct/19

I only know R^+ ={x∈R∣x>0} and  R^− ={x∈R∣x<0}  and  R×R=R^2 ={ ((x),(y) )∣x∈R∧y∈R}  so maybe  R^(++) =R^+ ×R^+ ={ ((x),(y) )∈R^2 ∣x>0∧y>0}  and similar for R^(−+) , R^(−−) , R^(+−)

$$\mathrm{I}\:\mathrm{only}\:\mathrm{know}\:\mathbb{R}^{+} =\left\{{x}\in\mathbb{R}\mid{x}>\mathrm{0}\right\}\:\mathrm{and} \\ $$$$\mathbb{R}^{−} =\left\{{x}\in\mathbb{R}\mid{x}<\mathrm{0}\right\} \\ $$$$\mathrm{and} \\ $$$$\mathbb{R}×\mathbb{R}=\mathbb{R}^{\mathrm{2}} =\left\{\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\mid{x}\in\mathbb{R}\wedge{y}\in\mathbb{R}\right\} \\ $$$$\mathrm{so}\:\mathrm{maybe} \\ $$$$\mathbb{R}^{++} =\mathbb{R}^{+} ×\mathbb{R}^{+} =\left\{\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\in\mathbb{R}^{\mathrm{2}} \mid{x}>\mathrm{0}\wedge{y}>\mathrm{0}\right\} \\ $$$$\mathrm{and}\:\mathrm{similar}\:\mathrm{for}\:\mathbb{R}^{−+} ,\:\mathbb{R}^{−−} ,\:\mathbb{R}^{+−} \\ $$

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