- #1

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[tex]\mathrm{d}s^2=\mathrm{d}x_i\mathrm{d}x^i[/tex]

for the distance? I mean in a very abstract fashion. All I know is that there is some coordinate mesh. Why don't I take other powers for the distance for example?

Or if that bilinear equation is only a special case, then why is our space obeying it?