As an infinite set atheist, I think it's important to distinguish people who say "infinite" when they want to talk about the limit of unbounded finite behaviors

As an infinite set atheist, I think it's important to distinguish people who say "infinite" when they want to talk about the limit of unbounded finite behaviors ("a Turing machine has an infinitely long tape") and people who say "infinite" when they want to talk about big collections ("the cardinality of the collection of real points between 0 and 1"). A smarter language would have different words for these.