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because we choose to represent floating point exceptions with the special values Infinity Are you using projective or affine infinity?

I have absolutely no idea. Which one should we be using? How do we find out which one we are using? If (-1)/0 is -Infinity you are using affine, if it's Infinity you are using projective. IEEE754 allows you to have both (selectable in some fashion). One is not better than the other; they are both useful. The affine completion of the number axis makes the use of -0 more comprehensible (1/(-Infinity) == -0, 1/(-0) == -Infinity).

-- Lennart