Size of the universe and the boundary problem

[Tomdstone]

Every object has an infinity if points

A physical atom is not a mathematical point.

 

[thinkandmull]

You can take the atom and break it, mentally, in half, and again and again, forever. So is the definition of finite “that which has a limit in one direction of its infinity”? Nothing can exist without an infinity of points. Its not imaginable

 

[Tomdstone]

You can take the atom and break it, mentally, in half, and again and again, forever. So is the definition of finite “that which has a limit in one direction of its infinity”? Nothing can exist without an infinity of points. Its not imaginable

Not sure in reality because of quantum theory.
A bounded object may have an infinity of mathematical points, but it does not have infinite extension such as the real line. The real valued interval [0,1] is a bounded interval, but it does have an infinite number of mathematical points. The real line is unbounded.

 

[thinkandmull]

I don’t think any of us would have a problem getting Zeno’s paradox or the Banach-Tarski paradox if we had learned rudimentary calculus as children like Asian kids do

 

[Oreoracle]

Visualization is part of reality. Isn’t it?

What I mean is that science attempts to explain phenomena, but is visualization a necessary ingredient in an explanation? We teach high schoolers to visualize atoms and sound waves just for the sake of making the material more easily digestible, but there’s no reason to suspect that these depictions are accurate. They just mimic the behavior of actual atoms and sound waves, which is all that matters for our purposes.

I don’t think any of us would have a problem getting Zeno’s paradox or the Banach-Tarski paradox if we had learned rudimentary calculus as children like Asian kids do

Zeno’s Paradox, sure. The Banach-Tarski Paradox requires measure theory to grasp at the bare minimum, which is well beyond not only calculus but even undergraduate analysis. Even with a graduate degree I only know how to construct nonmeasurable sets, certainly not how to rearrange such sets to replicate the paradox.