Thinking about infinity

[robvalue]

...As to how a finite object can be made up of infinitely many parts, that is covered all the time (at least abstractly) in mathematics by such processes as summing an infinite geometric series, or performing integration to calculate the area under a curve...

So, should we consider an infinite geometric series (and/or its sum), or integration as real "only in the abstract" or "a step removed from reality"?

Well, it's logically possible that it could map accurately to reality. So we know it is possible abstractly, but it remains only a logical possibility for reality.

We have made a model of a real object, and our results may or may not accurately map back to reality. This is where evidence and testing comes in. Our resident QM experts may well have a decent opinion regarding this. I am not qualified to say. But ultimately, reality holds the truth and we're just trying to get close to it.

This discussion is about the extreme limits of reality, and as such our models are going to be increasingly difficult to test. Normally we don't require such an extreme level of accuracy.