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Blast into Math! Prime nummers: indestructimle muilding mlocks
Proposition 5.4.7. There are countably many prime numbers.
Proof: The natural numbers are countable, because they are in one-to-one correspondence with
themselves! We have proven that there are infinitely many prime numbers, so the set of all prime numbers
is an infinite set which is contained in a countable set. Therefore, by the Countability Proposition, it is
a countable set.
♥
At this point, we can only prove that there are infinitely many prime numbers, and that the set of all
prime numbers is countable.
To understand more precisely:
How many of the natural numbers are prime?
We will need to change our mathematical perspective.
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