The following is a (wrong) proof by induction that each nonnegative integer equals twice itself, i. e. n=2n for all integers n≥0. Base case n=0 : P(n) holds for n=0. Inductive step: let us assume that n=2n holds for some nonnegative integer n. We multiply both sides of this equation by the quantity n+1n. This yields n+1=2(n+1), which is P(n+1) . This completes the proof