What is the correct negation of the statement
P: There are infinitely many integers such that is irrational.
Is it correct to say There exist no integers such that is irrational.
or
Is it correct to say There is a finite set of integers such that is irrational.
I disagree. Nether of those is the negation.
It is: .
That is, there is at most a finite set of integers each of which has an irrational square root.
Or: “the set of integers having irrational square roots is finite."
The statement “There is a finite set of integers each having a irrational square root” is always true.