Quote Originally Posted by Plato View Post
Read the following sentence, please.
If $q$ is a positive integer that is not a square, then $\sqrt{q}$ is irrational.
The square-root of every non-square positive integer is irrational.
In classical logic that is known as a universal positive: All P is Q.
As such it is more inclusive than the existential positive: some P is Q, $\sqrt{2}$ is irrational.
I'm really sorry I don't see the difference clearly in the two proofs. Doesn't the proof I gave prove that the square root of a non square integer is irrational also like the second proof?