(1.9 hours to learn)
A set is countably infinite if it can be put into one-to-one correspondence with the natural numbers. Countably infinite sets include the natural numbers, the rationals, and the algebraic numbers -- surprisingly, these are all "the same size" in the set-theoretic sense. By contrast, the set of real numbers is uncountably infinite. The more general notion of cardinality lets us distinguish different "sizes" of infinity.
-this concept has no prerequisites-
- What does it mean for two sets to have the same cardinality, and why is this an equivalence relation?
- Define countability.
- Be able to prove that sets are countable.
- Prove that the set of real numbers is not countable.
Core resources (read/watch one of the following)
-No Additional Notes-
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