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Counting: From Finite to Infinite and Beyond

Some infinites are bigger than other infinites.

- Georg Cantor

If a machine is expected to be infallible, it cannot also be intelligent.

- Alan Turing

Every student learns about counting at some point in their grade schools. In this chapter, we will treat the subject of counting in a formal way where every claim is mathematically proved. First, we will consider the subject of counting a finite number of objects. After that, we will start dealing with infinite objects and end the chapter with connections to computation.