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A countable set has elements (or members) that can be listed, like the numbers 1, 2, 3, and so on. You must be able to associate each element with a natural number. The interval of all the real numbers between 0 and 1, is not countable. But the interval of all rational numbers between 0 and 1 is countable. We could list the first element as 0, the second element as 1, the third element as 1/2, the fourth as 1/4, the fifth as 3/4, the sixth as 1/3, the seventh as 2/3, and so on. This set is also infinite because there is no finite bound on the number of elements. The term "population" has many meanings. A "countable infinite population" probably refers to a statistical population. This is a particular kind of set considered by statistics.

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