A standard example of absurdity is found in dealing with arithmetic. Assume that 0 = 1, and proceed by mathematical induction: 0 = 0 by the axiom of equality. Now (induction hypothesis), if 0 were equal to a certain natural number "n", then 1 would be equal to "n" + 1, (Peano axiom: S"m" = S"n" if and only if "m" = "n"), but since 0 = 1, therefore 0 would also be equal to "n" + 1. By induction, 0 is equal to all numbers, and therefore any two natural numbers become equal.