Question 332840
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2\ +\ 1\ =\ -1]


Sign of the sum is the sign of the lesser of the addends.


In general,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \text{sgn}(x\ +\ y)\ =\ \left\{\large{\text{sgn}(x)\text{ if }|x|\ >\ |y|\cr\text{sgn}(y)\text{ if }|x|\ <\ |y|\cr\text{sgn}(0)\text{ if }|x|\ =\ |y|,\text{ and }x\ \neq\ y\cr\text{sgn}(x)\text{ if }|x|\ =\ |y|,\text{ and }x\ =\ y}\right]


Where

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \text{sgn}(x)\ =\ \left\{\large{\ \ 1\text{ if }x\ >\ |0|\cr\ \ 0\text{ if }x\ =\ 0\cr-1\text{ if }x\ <\ 0\right]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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