Sorry if this question has been asked, but a couldn't find one using the method I need.
I want to prove that every natural number greater than 1 is divisible by some prime number using the WOP. I have done this by taking S to be the set of natural numbers greater than 1 which aren't divisible by a prime. But my notes now say to do it by taking S to be the set of all factors of n which are greater than 1.
Any help would be appreciated. Thanks.