I always disliked this question. It's explicitly an exercise in futility. The real answer to the question is to point out that the question is broken. It's pit

I always disliked this question. It's explicitly an exercise in futility. The real answer to the question is to point out that the question is broken. It's pitting the prescriptive against the descriptive, then acting surprised they aren't the same thing. The question "how big" only works with the set of "quantifiable". It's just a type error. Yet it's unsatisfying to say infinity isn't quantifiable, because when we do, we aren't being descriptive. Infinity is by definition unquantifiable, which is a prescriptive statement. Prescriptive answers just aren't any fun. We aren't learning anything from them, because we knew before we asked. When we talk about "bigger and smaller" infinity, we are just using infinity as an abstraction in the very same way we use variables. It's just as straightforward as going from "x+1>x" to "+1>". We all know that "plus one is more". The first statement is using nouns, and the second is using functions. It's just a type difference, nothing more. The thing we are spending so much time blathering in awe about is just the relative difficulty in describing abstraction. Abstraction is amazing, impressive, useful, often surprising or elegant. It is not however, mythical. There's this thing we do where what we are talking about doesn't have any substance. It's called nonsense. That's it. There is no "deeper meaning" behind the explicit absence of meaning. It can be entertaining to talk in circles, but we know they aren't getting us anywhere new.