Is G-d Infinite?
Seems like a silly question: G-d is the Absolute Infinite. No?
Actually, it’s not clear Hashem is infinite, as that would be a positive attribute of G-d.
Aristotle did not believe in the possibility of an actual infinity, a completed set of infinite size. To him, “parallel lines meet at infinity” and “parallel lines never meet” are the same thing. And “[a]s an example of a potentially infinite series in respect to increase, one number can always be added after another in the series that starts 1,2,3,… but the process of adding more and more numbers cannot be exhausted or completed.”
For that matter, that’s what infinity is etymologically; it’s a statement of not being (“in-“) finite, not of being something. The Rambam’s negative theology fits that. Hashem’s Omnipotence doesn’t mean that He has Infinite Power, but that power isn’t even a relevant concept. Hashem is Omnipresent not because He has infinite volume, but because “where is G-d” is a meaningless question. Like asking “Where is ‘1+1=2’?” In a sense it’s nowhere, being an idea not an object. In another sense, it’s true everywhere. The question is simply meaningless. Similarly, Hashem’s Omnipotence — the Rambam explains (Guide 1:58) that it is not that Hashem has infinite power, but that He can get anything done without invoking the concept of power. And Omniscience, and so on…
Hashem is Absolutely One, which is quite finite, actually. It’s His effects that are infinite. Hashem is the Ein Sof (literally: Without End, not that far from in+finite, actually) not because His attributes are infinite, but because they do not begin, neither can they end.
Leopold Kronecker (19th cent) was the first mathematician of note to treat infinity as though it were a number, leaving to Georg Cantor to produce a whole theory of transfinite numbers (yes, numbers, in the plural). So, given we live after their day, we might assume the assertion is valid, although I still wouldn’t take it as a certainty, as I don’t think we can make it consistent with Absolute Unity. And while Hashem’s Indivisiblity and Uniqueness are both mandatory beliefs, notice that His Infinity is not.