In this section, we’ve been measuring the distance between bitstrings using the Hamming distance, which is a function ∆ : {0, 1} n × {0, 1} n → Z≥0 , denoting the number of positions in which x and y...

In this section, we’ve been measuring the distance between bitstrings using the Hamming distance, which is a function ∆ : {0, 1} n × {0, 1} n → Z^≥0
, denoting the number of positions in which x and y differ. Prove that ∆ is a metric. (Hint: think about one bit at a time.)