So I have this statement that says:
For every two real numbers $x$ and $y$ with $x < y$, there is a real number with the property $P$ between $x$ and $y$.
Let $P(x)$ be the statement that says that a real number $x$ has some property $P$.
I have to write this using connectives and quantifiers and construct a negation for this proposition.
I've started by using the statements:
$(∀x \in R)(∀y \in R)(x < y)(x < P(x) < y)$
Something along the lines of this although I know this is incorrect.