Actual Infinity in Reality?

[polymath257]

You have been shown several times there are no conflicting answers. Different instances of infinite set are going to yield different results. This is logical, not contradictory.

Same infinite collection - same infinite collection is still 0 (empty collection), and always will be.

It's when you subtract one infinite collection from a different infinite collection that you get other [varying] answers, depending on these collections. It's loosely similar to finite (7) - finity (4) = finity (3) => finity - finity = 3???

And what about 0/0? The answer could be any number, and when we don't know exactly which due to lack of contextual contraints, the answer is that it's indeterminate. Same with infinity - infinity.

For every bit of your answers above, you have assumed the Axiom of Infinity. This axiom was not derived from a logical process. It is simply assumed so particular math problems can be conducted on it. It is not proof of anything or gives guidance to anything in the real world (where the thought experiments are conducted).

So, you have to deal with the items of my list by showing why these six things do not indicate an actual infinity is metaphysically impossible WITHOUT using infinite set theory from mathematics. I have shown that if you use mathematical infinite set theory in your reasoning if an actual infinite can exist, you have begged the question. That is an invalid argument. 

1. You cannot get to infinity by successive addition.
2. You get absurdities when you propose an infinite number of actual objects (Hilbert's Hotel).
3. You get contradictions about how many squares and square roots there must be (Galileo's paradox)
4. Is the vase full or empty in the Ross–Littlewood paradox?
5. Is the lamp on or off in the Thomson's lamp paradox?
6. It seems we cannot traverse even a finite distance in Zeno's paradoxes

1. So what?
2. Give a specific absurdity so we can discuss it in detail.
3. What, precisely, is the contradiction in Galileo's paradox?
4. Since the operations involved are impossible (even if we assume an actual infinity), the question isn't well-posed.
5. Since the operations involved are impossible (even if we assume an actual infinity), the question isn't well-posed.
6. The word 'seems' is the key here. Again, Zeno's paradoxes are not issues if both space and time are infinitely divisible: traversing an infinite set of points in an infinite set of intervals is not an issue. The infinites *resolved* the problem. It was the assumption of finiteness that caused the problem.

Specifically, in both 4. and 5, some activity has to happen at faster than the speed of light (whether flipping a switch, or moving balls). This is a violation of physics. But the issue isn't the actual infinity, but the speeds faster than light.