Actual Infinity in Reality?

[SteveII]

What you have then is a limit of mathematics to account for the difference. It would mean the two are mathematically equivalent. This does not mean that the two are logically equivalent. 

When we are talking about spanning infinite series of things (as in Zeno's paradoxes) we are decidedly NOT talking about mathematics. 

And don't tell me next that mathematics and logic are the same thing. https://en.wikipedia.org/wiki/Logic#Types

Do you see mathematical logic listed there by any chance? In fact, Aristotelian logic (syllogistic logic) is clearly described as having little more than historic value and being obsolete.

Logic is a subset of mathematics. You see, mathematics is the study of formal systems and logic consists of a few such systems. Propositional logic, predicate logic, even modal logic are *formal* systems and so are a part of math.

This is probably where you should have taken the intro to philosophy class before all your math classes. It skews reality for students to think they are the center of the world.

Mathematics is its own discipline. Math employs a type of logic: mathematical logic. There is a whole host of things that have to do with philosophy and logic that have nothing to do with math. (see the link I posted that discusses 9 different types of logic --a BRANCH of philospohy)

The two expressions have no meaning outside of mathematics. So the mathematical equivalence is all there is. The issue doens't even arise in propositional logic since propositional logic isn't strong enough to even talk about whole numbers, let along real numbers.

What in the world do you think the tens of thousands of pages written on Zeno's paradoxes alone have been discussing? If you can discuss infinity dividing a distance, you are not talking about mathematics. 

You have a way over-inflated view of mathematics. It is not the end all. Only mathematicians who don't know anything about philosophy/metaphysics think that. 

And, yes, if we are talking about an infinite series of things, we are most certainly talking about mathematics.

Certainly not. The idea of an infinite series of things is not itself a mathematical concept. Grandizer likes to champion an infinite series of causes. Philosophers for millennium have discussed infinite regresses (and how to avoid them). The concept also comes up in religion, computer science, physics, engineering, and a bunch of other disciplines. 

Again, mathematics is no where near the center of the universe.