> it isn't clear what that means (if anything) if you think of sets as groups of physical objects. Isn't this similar to the idea that you can count apples or

> it isn't clear what that means (if anything) if you think of sets as groups of physical objects. Isn't this similar to the idea that you can count apples or birds: one, two, three, four, etc, but there's nothing countably physical about infinity, or even arbitrarily large finite numbers. That doesn't impede the usefulness of infinity as an abstraction of counting, in a similar way to the fact that sets are useful as an abstraction of treating groups of things as a thing (and, in fact, we have to treat groups of things as a thing -- most of the physical things we are familiar with have fuzzy boundaries and definitions, because they're all groupings of smaller things).