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Today's maths PSA: Events of probability 0 are not necessarily impossible.

@michal @ColinTheMathmo Pick a real number between 0 and 1, the probability that it is rational is 0.

(I think this is a standard example, but would be interested in knowing more “concrete” examples.)

@leonardopacheco @ColinTheMathmo Curious, is it really 0 or "infinitesimally small"?

@leonardopacheco Another standard example is an infinite sequence of tosses with a fair coin. It's logically possible for the coin to come up heads on every toss, but the probability of the event zero. Not sure if that's more concrete, though.

@11011110 @ColinTheMathmo There's also the situation that almost all random choices from the [0,1] interval are literally undescribable.

Hm, now I wonder what the situation would be if we restricted ourselves to rational numbers. That seems like a weird distribution on the entire set of natural numbers!

@11011110 @ColinTheMathmo Oh, no, of course, they mean the power set, that's why it's also a subset.

Okay! But that's also weird! Using \(\wp\) for power set!

@ColinTheMathmo Is this Colin's Paradox?

What happens when a zero probability meets an infinite trial space?

Michal@michal@kottman.xyz@ColinTheMathmo Is there an example where this applies? Or is it just a question of semantica, e.g. "X is possible in general, but in the given circumstances the probability is 0"?