In article <email@example.com>, I wrote: > (probability of a complete match) * (length of a complete match). > >The probability of a complete match is zero, and the length of a complete >match is infinite. There isn't a good way of defining 0 * infinity, >so the expected value is undefined.
Sorry, I should have thought this problem through more carefully before posting.
Suppose that in comparing Herc's sequence with the other sequence, I find that for every *finite* prefix, there is someone who shares that finite prefix with Herc, but there is nobody whose sequence matches Herc's *completely*. Then we need to decide what the "length of the longest matching prefix" should be defined to be in this case. If we define it to be infinite, then the expected value comes out to be infinite.
But of course, this doesn't mean that Herc's sequence matches someone else's sequence exactly with probability 1. That probability is still 0. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences