All of logic and math is a convincence tool. There are no, circles, quantities. Reality just is. We created these tools because they're a convinent way to cope with complexity of reality. There are no "objects" in a sense that chair is just atoms arranged chair-like. And atoms are just smaller particles arranged atom-like and yet physics operate in these objects treating them as something that exist.
So, now we have created these mental tools called mathematics that are heavily constrained. Then we create models that are approximately map 1:1 to some patterns that exist in reality (IE patterns that are roughly local so that we can call them objects). Due to the fact that our mental tools have heavy constrains and that we iteratively adjust these models to fit reality at focal points, we can approximately predict reality, because we already mapped the constrains into the model. But we shouldn't mistake model for the reality. Map is not territory.
Yep. Humans (and other animals) have an inbuilt ability to count small numbers of objects, so whole numbers seem more natural to us, but it's just a bias.
So, now we have created these mental tools called mathematics that are heavily constrained. Then we create models that are approximately map 1:1 to some patterns that exist in reality (IE patterns that are roughly local so that we can call them objects). Due to the fact that our mental tools have heavy constrains and that we iteratively adjust these models to fit reality at focal points, we can approximately predict reality, because we already mapped the constrains into the model. But we shouldn't mistake model for the reality. Map is not territory.