Actual Infinity in Reality?

[polymath257]

1) Both are infinite. Yes, having an 'end' is a matter of how things are ordered, NOT a matter of the quantity.

The interval from 0 to 1 has an infinite number of real numbers, but has an end at both ends.

2. ???? What does time look like under a microscope? Silly question.

So what order equates them the description of being infinite?  And infinity is used often (I would say normally) in regards to quantity.  Which would seemingly be the case in your "points" / "Locations".  Or are you saying now that there is not an endless number of points (that they can be completed)?

Yes, of course I am saying they can be completed. That is what it means to be an actual infinity, after all.

The problem is that you have two very different notions of having an 'end'. One uses a list of the elements. The other is based on the order properties. if you want to list the elements of an infinite set one by one, you won't ever end that process. But that isn't required in the Zeno paradoxes. ALL that is required there is that every position has a time associated with it. THAT'S ALL.


So, if you use 'infinity' to describe quantity, then 'not having an end' is NOT the description you can use. That doesn't describe a quantity: it describes a process.