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Comment by rbanffy | Hacker News Reader

But, if the set is infinite, won’t the odds of any individual number to be selected be effectively zero?

It is, and if you choose the number uniformly at random, it's not just "effectively" zero, it is precisely zero.

GP's point, as I understand it, is that it is not actually possible to choose a number from [0, 1] uniformly at random in "real life".

I think you could argue that, e.g. in the dartboard thought experiment, the probability of choosing individual points doesn't really matter: only probabilities of measurable subsets with positive measure matter.

I guess, but, the set is not even countably infinite. "Selecting at random" is something that happens in the real, non-infinite world, not in the mathematically rigorous would where infinities can exist. So, no, probability-zero events do not happen in either.

Not necessarily - you might just come up with a number you know is in the set, say pi/4. I know it's in the set because it satisfies the conditions that define it. Still, the odds of that particular number being picked up are zero.

If you picked that, you did not pick uniformly from the unit interval. You picked from something else, which was much smaller.

so how does the random function selecting the number select the number before the last number in the infinite set?

It wouldn't "select" as if it were an infinite deck of cards, but rather generate a number we know is on the infinite set. It can very well take an infinite amount of time to come up with the digits though...

> rather generate a number

How?

A series of random bits?

What last number?

exactly

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