# Theorem: All Odd Numbers Are Prime

Theorem: All odd numbers are prime

Proof: Here is a set-theoretical proof of this assertion :

1) it is well known that there is an infinite number of odd primes

2) Test each and every prime in any order

3) If you encounter a number you can prove being prime (which can be done in a finite amount of time, assuming it is), put it into set # 1

4) If you encounter a number you cannot prove being prime, put it into set # 2

5) now read all odd numbers, beginning with set #1. You won't be able to get to the numbers of set #2 in a finite amount of time, so you will encounter only prime numbers.

Since no non-prime odd number will be found, the assertions "there exists a non-prime odd" cant't be proved.

End of the proof.

... Wait a minut. What if, in step #5, we read the first item in 1 second time, then the second in 1/2 second time, and so on ? Oops ...

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