The only difference of note, I think, is that you can't enumerate the elements. Instead of being able to say "for each element, ..." you'd have to say "for all

The only difference of note, I think, is that you can't enumerate the elements. Instead of being able to say "for each element, ..." you'd have to say "for all elements, ...", like the example of vector length defined as an integral over the full number range.