Abstract
A set is said to be countable if its members can be enumerated—first member, second member, third member, and so on—and each member eventually appears in the enumeration. Notice that we do not assume that the enumeration ever comes to an end. If it does not, the set is called countably infinite.
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Notes
- 1.
In this book we use an ordinary minus sign to denote set difference. This is convenient later to show the parallel between set difference and number difference in measure theory. In any case, it will always be clear what kind of objects we are taking the difference of.
- 2.
We use the notation \(\langle a,b,c,\ldots \rangle\) for the infinite sequence in conformity with the notations ⟨a, b⟩ and ⟨a, b, c⟩ for ordered pairs and triples.
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Stillwell, J. (2013). Infinite Sets. In: The Real Numbers. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-01577-4_3
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