I just got Pinter's book, "A Book of Abstract Algebra", for the modern algebra course that I'm taking. It's a very nice book, I'm enjoying reading through it so far. What's especially interesting is the connections to computer science and controls, mostly because I switched to math and physics out of electrical engineering. Anyway, in its introduction chapter on groups, it makes the following statement: (Emphasis mine). Out of curiosity, I am wondering if there exists a proof of this statement, that is, that any and every single piece of information in the universe, of arbitrary complexity and abstraction, could be encoded as a string of binary digits, assuming one could access that information and had a storage device large enough. Intuitively, I would say that it's obvious, a piece of information can be stored in every digit and in theory we can always increase the information capacity by adding digits, but I'm wondering if a rigorous proof exists. (Note: I put this in the abstract algebra section because it came up in an abstract algebra textbook, I will understand if the mods feel it is more appropriate in the computer science section).