Question Number 9530 by geovane10math last updated on 12/Dec/16
$$\mathrm{Why}\:\:{i}\:\ngtr\:\mathrm{0}\:\mathrm{and}\:{i}\:\nless\:\mathrm{0}\:???? \\ $$
Commented by geovane10math last updated on 14/Dec/16
$${why} \\ $$
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.](https://www.tinkutara.com/question/Q9557.png)
$$\left.\mathrm{i}\right){If}\:{i}>\mathrm{0} \\ $$$${i}\centerdot{i}>\mathrm{0}\centerdot{i} \\ $$$$−\mathrm{1}>\mathrm{0}…\left[{contradiction}\right] \\ $$$$\left.\mathrm{ii}\right){If}\:{i}<\mathrm{0} \\ $$$${i}\centerdot{i}>\mathrm{0}\centerdot{i} \\ $$$$\:\:\left({multiply}\:{both}\:{sides}\:{by}\:−{ve}\:{numbers}\right) \\ $$$$−\mathrm{1}>\mathrm{0}…\left[{contradiction}\right] \\ $$$$\left.{f}\left.{rom}\:\mathrm{i}\right)\:{and}\:\mathrm{ii}\right),\:{i}\ngtr\mathrm{0}\:{and}\:{i}\nless\mathrm{0}. \\ $$
Commented by geovane10math last updated on 15/Dec/16
$${thanks} \\ $$
Answered by FilupSmith last updated on 15/Dec/16
$${i}\in\mathbb{C},\:\:\mathrm{0}\in\mathbb{R} \\ $$$$\mathbb{R}\subseteq\mathbb{C}\Rightarrow\mathbb{C}\nsubseteq\mathbb{R} \\ $$$$\therefore{i}\nleqslant\mathrm{0}\wedge{i}\ngeqslant\mathrm{0} \\ $$$$\because{i}\notin\mathbb{R} \\ $$