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Published in:
2011 | OriginalPaper | Chapter
Countable and Uncountable Sets
Authors : Ulrich Daepp, Pamela Gorkin
Published in: Reading, Writing, and Proving
Publisher: Springer New York
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Having mastered finite sets, we now turn to understanding the infinite. We know that ℕ is infinite, and we know that ℚ is infinite (see Problem 22.8). Are they equivalent? In some sense, we can count ℕ and it may feel as though we cannot count ℚ—that is, as though we cannot list a first element, second element, third element, and so on. However, we shall see that ℚ and ℕ are, in fact, equivalent.