You're making it sound like infinity does not exist.

Binary sequences are infinite they are not even countable infinite - that's how many there are.

I don't agree that there is not god, but this is not the way to prove his absence.

My primary argument would be - if he created us and as a rule we should pray and ask him for shit, why do no other creatures that he allegedly created - show any acknowledgement of God? Wouldn't at least apes have some sort of a prayer ritual? Would they not construct some sort of basic temples in his name? No, nothing in nature gives a shit about god and I doubt plants / animals dream of going to heaven or are sacred of going to hell.