# Suppose $c\epsilon\Bbb Q$ and $y,z\in\Bbb R$. Show that if $c > y +z$ then there are rationals $a > y$ and $b > z$ such that $c > a + b$.

Suppose $c$ belongs to $\Bbb Q$ and $y,z$ are any real numbers. Show that if $c > y +z$ then there are rational numbers $a > y$ and $b > z$ such that $c > a + b$.

I'm really lost on how to prove this. Any help would be much appreciated!

HINT: Pick any rational $a\in(y,c-z)$. (Why must there be one?) Then $c>a+z$. (Why?) Now use a similar idea to show that there a rational $b>z$ such that $c>a+b$.