It does work, actually if we’re using Integers (there are as many integers as Rationals so we don’t need to care about the latter set) we get the good old discrete probability distribution where we either have finite number of possibilities or at most countable infinity of possibilities, e.g set of all Integers.
Real numbers are strictly larger set than integers, so in continuous distribution we have in a sense more possibilities than countably infinite discrete distribution.
Good point. Does this work over all infinite sets, though? Integers? Rationals?
It does work, actually if we’re using Integers (there are as many integers as Rationals so we don’t need to care about the latter set) we get the good old discrete probability distribution where we either have finite number of possibilities or at most countable infinity of possibilities, e.g set of all Integers.
Real numbers are strictly larger set than integers, so in continuous distribution we have in a sense more possibilities than countably infinite discrete distribution.