It really isn't ... the semantics of infinity are completely different than the semantics of 'really, really, big.' An infinite data store would, by definition

It really isn't ... the semantics of infinity are completely different than the semantics of 'really, really, big.' An infinite data store would, by definition, contain my DNA, correct (and incorrect) predictions about the universe (down to the molecule) for all time, the true value of Pi, and every piece of knowledge that has ever or will ever exist. An actual infinite is just a ludicrous concept.