So i'm trying to prove that the map(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(x,y,z) = \frac{(x,y)}{1-z}[/tex]

from the unit sphere S^2 to R^2 is injective by the usual means:

[tex]f(x_1,y_1,z_1)=f(x_2,y_2,z_2) \Rightarrow (x_1,y_1,z_1)=(x_2,y_2,z_2)[/tex]

But i can't seem to show it....

I end up with the result that

[tex]\frac{x_1}{x_2}=\frac{y_1}{y_2},\frac{x_1}{x_2}=\frac{1-z_1}{1-z_2}[/tex],

but i'm uncertain as to what this means for points on a circle......help please?

(i have actually already found the inverse map, but i just found it a little frustrating that i couldn't prove injectiveness just straightforwardly like this..)

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# Stereographic projection

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