  The type $\tau$($\alpha$) of an irrational number $\alpha$ measures the
extent to which rational numbers can closely approximate $\alpha$. More
precisely, $\tau$($\alpha$) is the infimum over those t$\in$R for which
|$\alpha$--h/k|<k^{--t--1} has at most finitely many solutions h,k$\in$Z, k>0.
In this paper, we regard the type as a function
$\tau$:R\Q$\rightarrow$[1,$\infty$] and explore its descriptive properties. We
show that $\tau$ is invariant under the natural action of GL2(Q) on R\Q. We
show that $\tau$ is densely onto, and we compute the descriptive complexity of
the pre-image of the singletons and of certain intervals. Finally, we show that
the function $\tau$ is [1,$\infty$]-upper semi-Baire class 1 complete.
