I'm having trouble with proving this question on my assignment:
For all real numbers $x$, there exists a real number $y$ so that $x + y^2$ is rational.
I'm not sure exactly how to prove or disprove this. I proved earlier that for all real numbers $x$, there exists some $y$ such that $x+y$ is rational by cases and i'm assuming this is similar but I'm having trouble starting.