-- How many
roads must a man walk down before he finds a
damn good pub?
Let us define n to be the number of roads a man must travel before he
finds the pub defined above. We may thus define n+1 to be the first
road which a man need not travel in order to reach a good pub. Now the
traversal of road n+1 is not a necessary condition, but rather a
sufficient one; thus it is sufficient for n+2 as well. Thus the
statement is true for x roads where x is >= n. Therefore, by induction,
it is true for any finite number x greater than n. We may conclude that
the statement is true for sufficiently large x, or alternatively that as
x approaches infinity, the number of roads that have been travelled
become sufficient to have found a good pub.
