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Question Number 207832 by Davidtim last updated on 28/May/24

$$ProvethatSgn\left(0\right)=0$$

Commented by Davidtim last updated on 28/May/24

$$helpme$$

Answered by Frix last updated on 28/May/24

$$\mathrm{\forall }c\in \mathbb{C}:\mathrm{sign}c:=\frac{c}{\mid c\mid }\Rightarrow \mathrm{sign}0\mathrm{is}\mathrm{not}\mathrm{defined}$$$$\mathrm{The}\mathrm{sign}\mathrm{is}\mathrm{the}\mathrm{direction}\mathrm{of}\mathrm{a}\mathrm{vector}\mathrm{in}\mathrm{the}$$$$\mathrm{Complex}\mathrm{Plane}.$$$$\mathrm{sign}(a+b\mathrm{i})=\frac{a+b\mathrm{i}}{\mid a+b\mathrm{i}\mid };\mathrm{sign}\left(r{\mathrm{e}}^{\mathrm{i}\theta }\right)={\mathrm{e}}^{\mathrm{i}\theta }$$$$\mathrm{The}\mathrm{vector}\left(\begin{array}{c}0\\ 0\end{array}\right)\mathrm{has}\mathrm{no}\mathrm{direction}.$$

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