Simple Question: Totally Boundedness of [0,1] intersect R-Q

I read in that Dover "Counterexamples in Topology" (great book btw)
that the irrational numbers between 0 and 1 are not a compact space.
Now it says, and I already knew, that totally bounded and complete
implies compact.

It says that the irrational numbers between 0 and 1 are complete. I
haven't worked it but I believe it. So that means that it is not
totally bounded. If I recall my definitions correct, for any e>0, [0,1]
intersect R-Q can be covered by finitely many epsilon-balls. This is
what I don't understand. I can't possibly see how this isn't totally
bounded. Isn't (0,1) totally bounded??

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