Actual Infinity in Reality?

[RoadRunner79]

A point represents a location between 0 and 1. Wasn't that obvious?

And yes, there is an infinite number of such points.

And yes, we *do* reach the end. The *logic* that I presented shows that. Your *claim* is based on a faulty *assumption* that you cannot a complete an infinity. And no, that is NOT a fact. Remember, to be infinite *only* means that it cannot be put into correspondence with some counting number. it does NOT mean 'has no bound'. it does NOT mean 'goes on forever'. it does NOT mean 'has no end'. The example of the sequence we have been considering shows the differences.

Of course 'infinity' means every one of those things you say it does not mean! The very first sentence in the Wikipedia article:

Infinity (symbol: ∞) is a concept describing something without any bound or larger than any natural number. 

Need more?

in·fi·nite
ˈinfənət/
adjective
adjective: infinite

1. 1.
   limitless or endless in space, extent, or size; impossible to measure or calculate.
   synonyms:
   boundless, unbounded, unlimited, limitless, never-ending, interminable; More
   • very great in amount or degree.
     "he bathed the wound with infinite care"
     
   • MATHEMATICS
     greater than any assignable quantity or countable number.
     
   • MATHEMATICS
     (of a series) able to be continued indefinitely.
     

Where are you getting your definition?

I think it's the same place as words such as "end", "contradiction", "assume", "never", "last" and the like.

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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.

So what is it about the order that makes a thing infinite?  Why is it, that you cannot list the elements, but you seem to think that you can go through them all sequentially?  Are not both a process?  When cutting in half in the dichotomy paradox, would that then demonstrate that the process; not the number of points is infinite?