My first reaction ... well, I checked to see if anyone else had said this, and I don't think they have, so here goes:

But that the task is completable--that it is finite--that has to be true, or else there is no point or purpose to learning anything.

O RLY? How tall are you? No, don't round it off: tell me precisely. Or choose any other measurement in the real world.* And the answer is unattainable, because the precision required is infinite.

* (Even if there are some real-world measurements with integer values, there are at least as many whose values are irrational and probably transcendent.)

That's one way in which complete knowledge of the universe is unattainable. I'm at work, so I'll stop here, at least for now.