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**Plato** I disagree. Nether of those is the negation.

It is: $\displaystyle \left( {\exists j \in \mathbb{Z}^ + } \right)\left( {\forall n \in \mathbb{Z}^ + ,n > J \Rightarrow \sqrt n \in \mathbb{\overline Q}} \right)$.

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.