The statistic of deaths / mile is irrelevant. Of course more drunk walkers die per mile walked than drunk drivers die per mile driven, because it takes them > 10 times as long to get anywhere. I think it's more likely that accident rates are based more on time traveled than on distance traveled.
Is there a positive integer that does not have an accurate semantic definition in english of less than 100 characters? (i.e. "The first number", "The first prime", "The third perfect square", etc.)
Proof that there is no such number:
Suppose there were. Construct a list of all the numbers that don't have an accurate english semantic definition in less than 100 characters. The first of these can be accurately defined as "The first number that does not have an accurate english semantic definition in less than 100 characters", a contradiction. :-P
I know it's a joke, but the inductive step fails for n = 2. Each of the two groups of 1 horses being the same colour does not imply that all the horses are the same colour.