# Show the inequality $x <y$ is definable in the language $\langle \mathbb{R}; +, \times ; 0,1 \rangle$

My initial idea is that I need to find a sentence that expresses 'x is positive' and then I can say: for any $a, b$, $a>b$ iff there is a positive x s.t. $b+x=a$, but can't figure out how, any ideas?

Thanks!

• – user57159 Nov 8 '15 at 15:11
• oh yeah, that is very obvious, I was thinking far too complicated- thanks @RickyDemer – Naomi Nov 8 '15 at 15:15