The number you pick is guaranteed smaller with each iteration, and once you get the smallest one you're done.

Yes, but you keep adding numbers to the set, and it's a continuous real distribution, so infinite isn't *that* unreasonable.

I never said I was right, or even that I'd bet on it, that was just my first reaction. I'm sure the hordes of actual mathematicians will pounce on me with their mockery masked by logic any minute now. =o]