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

Question

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?

Or am I going about this the wrong way?

Thanks!

Answer 1

A real number is positive exactly if it is a square and not zero.