Take a sorted list. This list has 1,099,511,627,776 elements in it. (That's over a trillion!) A sequencial search would have to make at most 1,099,511,627,776 comparisons to find any given element. Searching through the list sorted in a binary tree would require 40 comparisons or less to find any given element. That's 27,487,790,694.4 times less the number of comparisons required. Surely you see the usefulness of binary trees. Binary trees are our friends indeed.