Symbolically, sure, but then you’re not dealing with infinities you’re just representing them.
It’s a meme it’s playing fast and loose with things but the general gist is that mathematics, to this day, doesn’t really care about Gödel/Church/Turing, incompleteness, the halting problem, whatever angle you want to look at it from. Formalists lost the war and they simply went on doing maths as if nothing had happened, as if a system could be simultaneously complete and consistent. There’s people out there preaching to the unenlightened masses but it’s an uphill battle.