That's not "infinite." It's a strictly finite construct that can be forced to repeat itself an arbitrary number of times. The only interesting question is the

That's not "infinite." It's a strictly finite construct that can be forced to repeat itself an arbitrary number of times. The only interesting question is the size of the repeating block. (Presumably quite small.) This is sort of analogous to the Library of Babel -- a fictional construct which contains every possible combination of Latin characters that fit in a 400-page book. The library has something like 26^1312000 books, but then inevitably must repeat. Its contents are either not infinite, or each volume it contains repeats itself infinitely many times. Ramsey Theory describes this stuff, and it's a useful thing to know, as it wards against sloppy use of "infinite" and "finite."