I have $P(x,y) \iff xy=1$; the universe of discourse for $x$ is the set of positive integers, and the universe of discourse for $y$ is the set of real numbers. $$ \forall x \exists y P(x,y) $$
I'm confused about reading the above statement. I'm quoting above statement from a book that says the statement read as "For every positive integer $x$ there is a real number $y$" such that $xy=1$. so the statement is true...I want to know what value, that makes this statement true, of $y$. is there only one value of $y$ for all values of $x$? or I need to change the value of $y$ every time when i change $x$.
Please If someone could explain it would be appreciated. thank you.