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## Homework Statement

Express the following using existential and universal quantifiers restricted to the sets of Real numbers and natural numbers

## Homework Equations

## The Attempt at a Solution

I believe the existance of rational numbers can be stated as:

##(\forall n \in \Re)(\exists p,q \in \mathbb{N}) \ni [(p \mid q)=x]##

So to say that there are irrational numbers is the negation of this being:

##\neg (\forall x \in \Re)(\exists p,q \in \mathbb{N}) \ni [(p \mid q)=x]##

Which becomes

##(\exists x\in \Re)\ni(\forall p, q \in \mathbb{N})[(p\nmid q )\ne x]##

Is my rationality correct

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