Sampling Without Replacement Should Be Called Sampling

Sampling without replacement should be called sampling. And sampling with replacement should be called sampling with replacement.

In what situation, where I’m interested in estimating the count of black marbles in an urn, would I take out a marble and then put it back in the urn?

The convention that we always sample with replacement illustrates the tension between simple theory and practical use. And that even in mathematical fields, results are often driven by collective reasoning.