m. c. de marco: To invent new life and new civilizations...

Division by Zero

I was telling someone about this story and decided to google it, without any hope of finding it online. But apparently it was reprinted by Fantastic Metropolis a few years ago and is still up there: “Division by Zero” by Ted Chiang.

There is a well-known “proof” that demonstrates that one equals two. It begins with some definitions: “Let a = 1; let b = 1.” It ends with the conclusion “a = 2a,” that is, one equals two. Hidden inconspicuously in the middle is a division by zero, and at that point the proof has stepped off the brink, making all rules null and void. Permitting division by zero allows one to prove not only that one and two are equal, but that any two numbers at all—real or imaginary, rational or irrational—are equal.