I have read (and re-read) the wikipedia article on Exchangeability https://en.wikipedia.org/wiki/Exchangeable_random_variables . The disconnect for me is that : after having sampled without replacement the distribution of the remaining items differs from the original distribution. I am specifically referring to a small enough population that the sample size may have a meaningful effect on the distribution of the unsampled items in the population.
So let's say we are at the tenth item of a given sample - that distribution also differs from the distribution (and expected succeeding items) of a separate sample from the same population.
So I'm missing the basic intuition of what the
Exchangeability means here. A concise explanation specifically explaining why the "without replacement" actually works (vs "with" replacement that instead would actually make sense to me) would be helpful.