Oops, brain fart. No, 1 is not equal to 4 even in Grothendieck's world. Scheme theory only gets you so far... A correct example of what I had in mind is x^2 +

Oops, brain fart. No, 1 is not equal to 4 even in Grothendieck's world. Scheme theory only gets you so far... A correct example of what I had in mind is x^2 + y^2 = 1 and (x - 2)^2 + y^2 = 1. That said, algebraic geometry takes care of this "bad example" also. This is done exactly as alcolade explained: consider "points at infinity" in projective space.