The following question is from one of my homework:
Show that the field $\mathbb{Q}(X)$, the field of rational functions over $\mathbb{Q}$ in one indeterminate $X$, admits the structure of an ordered field having the Archimedean property. What can you say about $\mathbb{Q}(X, Y) ?$
My interpretation of the question is that it asks to define an valid ordering on $\mathbb{Q}(X)$ which has the Archimedean property. I am unable to find such an ordering. I could find some orderings on $\mathbb{Q}(X)$ (for example, to define $f>g$ if $f-g$ has both the numerator and denominator having positive leading coefficients) but all of those failed to satisfy the Archimedean property. Any help is appreciated. Thanks in advance.