The problem is to represent (in first order logic) the interval $[0, \infty)$ under the structure $\frak{R}$, whose universe is the real numbers. $\forall$ quantifies the real numbers and $+^{\frak{R}},\cdot^{\frak{R}}$ are their usual meanings (addition, multiplication).
Since this is all nonnegative real numbers, I have this so far:
$\forall v_2 \exists v_1 (v_1 + v_1 = v_1 \land (v_2 = v_1 \lor ?))$
Where $v_2$ is a number in the interval and $v_1$ is $0$. The "?" is where I want to say "$v_2 > 0$", but I'm not sure how to do this with first order logic using all real numbers.
Hint: The non-negative real numbers are the squares.