For x, y ∈ {0, 1} n , define d(x, y) as the smallest i ∈ {0, 1, . . . , n} such that xi+1,...,n = yi+1,...,n. For example, d(01000, 10101) = 5 and d(01000, 10100) = 3 and d(01000, 10000) = 2 and...

For x, y ∈ {0, 1} n , define d(x, y) as the smallest i ∈ {0, 1, . . . , n} such that xi+1,...,n = yi+1,...,n. For example, d(01000, 10101) = 5 and d(01000, 10100) = 3 and d(01000, 10000) = 2 and d(11010, 01010) = 1. (This function measures how far into x and y we must go before the remaining parts match; we could also define d(x, y) as the largest i ∈ {0, 1, . . . , n} such that xi 6= yi , where we treat x0 6= y0.) Is d a metric?