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Question Number 9530 by geovane10math last updated on 12/Dec/16

Why  i ≯ 0 and i ≮ 0 ????

$$\mathrm{Why}\:\:{i}\:\ngtr\:\mathrm{0}\:\mathrm{and}\:{i}\:\nless\:\mathrm{0}\:???? \\ $$

Commented by geovane10math last updated on 14/Dec/16

why

$${why} \\ $$

Answered by nume1114 last updated on 15/Dec/16

i)If i>0  i∙i>0∙i  −1>0...[contradiction]  ii)If i<0  i∙i>0∙i    (multiply both sides by −ve numbers)  −1>0...[contradiction]  from i) and ii), i≯0 and i≮0.

$$\left.\mathrm{i}\right){If}\:{i}>\mathrm{0} \\ $$$${i}\centerdot{i}>\mathrm{0}\centerdot{i} \\ $$$$−\mathrm{1}>\mathrm{0}...\left[{contradiction}\right] \\ $$$$\left.\mathrm{ii}\right){If}\:{i}<\mathrm{0} \\ $$$${i}\centerdot{i}>\mathrm{0}\centerdot{i} \\ $$$$\:\:\left({multiply}\:{both}\:{sides}\:{by}\:−{ve}\:{numbers}\right) \\ $$$$−\mathrm{1}>\mathrm{0}...\left[{contradiction}\right] \\ $$$$\left.{f}\left.{rom}\:\mathrm{i}\right)\:{and}\:\mathrm{ii}\right),\:{i}\ngtr\mathrm{0}\:{and}\:{i}\nless\mathrm{0}. \\ $$

Commented by geovane10math last updated on 15/Dec/16

thanks

$${thanks} \\ $$

Answered by FilupSmith last updated on 15/Dec/16

i∈C,  0∈R  R⊆C⇒C⊈R  ∴i≰0∧i≱0  ∵i∉R

$${i}\in\mathbb{C},\:\:\mathrm{0}\in\mathbb{R} \\ $$$$\mathbb{R}\subseteq\mathbb{C}\Rightarrow\mathbb{C}\nsubseteq\mathbb{R} \\ $$$$\therefore{i}\nleqslant\mathrm{0}\wedge{i}\ngeqslant\mathrm{0} \\ $$$$\because{i}\notin\mathbb{R} \\ $$

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