Prove that the set of functions $f: \mathbb{Q} \rightarrow \{1,2,3\}$ is uncountably infinite.
I'm totally stuck on this one. We have just been shown Georg Cantor's diagonalization argument in class for why $\mathbb{R}$ is uncountably infinite (and I for the most part understand it---assemble an enumeration for the reals, then proceed down the diagonal changing the number in that position to create a number that will not be on the list, since the number will differ from the i-th number in the i-th position), so I'm assuming we're going to have to assemble some sort of similar argument for this.
Anyone able to prod me in the right direction perhaps? This is homework so I'd like to not get an answer (until maybe after the deadline), but maybe a starting point or reference (which I can cite) to get me thinking about it the right way.
Thanks!