Comment author:Caledonian2
09 April 2008 10:10:41PM
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Would you argue that odd numbers are as probable as even numbers in the set of natural numbers, because the order of the category of infinities that they belong to is the same?

How about squares (1, 2, 4, 9, 16, ...) versus non-square numbers? Prime numbers versus composite numbers?

As far as I understand, the sets of odd numbers, squares, and primes are all countable.

As such, a one-to-one correspondence can be established between them and the counting numbers. Therefore, considered across infinity, there are just as many primes as there are odd numbers.

There are as many examples of ABABABAB as there are examples of AB[random sequence of English letters six symbols long] in the full Library. There are as many examples of ABABABAB as there are examples of AB[random sequence of English letters ten-thousand symbols long] in the full Library.

I acknowledge that this is very counterintuitive. But isn't the point of this blog to move beyond mere intuition and look at what rationality has to say?

## Comments (166)

OldAs far as I understand, the sets of odd numbers, squares, and primes are all countable.

As such, a one-to-one correspondence can be established between them and the counting numbers. Therefore, considered across infinity, there are just as many primes as there are odd numbers.

There are as many examples of ABABABAB as there are examples of AB[random sequence of English letters six symbols long] in the full Library. There are as many examples of ABABABAB as there are examples of AB[random sequence of English letters ten-thousand symbols long] in the full Library.

I acknowledge that this is very counterintuitive. But isn't the point of this blog to move beyond mere intuition and look at what rationality has to say?