Actual Infinity in Reality?

[GrandizerII]

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).

Irrelevant. You said it leads to conflicting answers. It doesn't. What you need to do is acknowledge what I said about the maths and address that specifically, if you want to eventually show that it's not metaphysically possible that there be an actual infinity.

And it hasn't been shown to be non-logical (in the conventional sense of the word). Your attempt to disprove it has been an utter failure.

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.

If you can't show that an actual infinity is not logically possible, then you haven't shown that it's not metaphysically possible. Using infinite sets helps to show that you have failed to point out where any logical contradiction regarding actual infinities lies.

1. You cannot get to infinity by successive addition.

Irrelevant. If the elements are all there, then they are there. The set is complete.

2. You get absurdities when you propose an infinite number of actual objects (Hilbert's Hotel).

Stop it, Steve. You've been corrected so many times here it's getting tedious at this point. Veridical paradoxes do not imply actual absurdities. The absurdities you're seeing is all in your mind, due to a failure to understand that assuming infinite sets must lead to different expectations from those that we expect to arise from assuming finite sets, and it has to do with the unbounded end(s) of the infinite set, which your intuition currently isn't well-equipped to deal with.

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?

Read polymath's repeated responses to these. It's getting tiresome of you to keep repeating stuff which has been debunked in this thread over and over again.

6. It seems we cannot traverse even a finite distance in Zeno's paradoxes

There are several potential solutions to this. In addition to what polymath has already argued, another potential solution is that this local universe is quantized in terms of time or space or both (with the infinity in terms of size and divisibility being a property of the wider cosmos).

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Yeah, because all these people participating must be so ignorant compared to you that they don't know what it means, and when to spot it.

I looked it up again.... I don't see a problem with my example or the way that it is being used.   I do see a problem in your assertion, in that the reasoning was not that the properties of the parts are to be applied to the whole as I explained.

Stop acting dense. He doesn't know that the universe, like the physical things in it, is limited. He inferred it from what he sees/intuits about the physical things in the universe.

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BTW, you are missing the whole point of Hilbert's Hotel:

Imagine a hotel with a finite number of rooms. All the rooms are full and a new guest walks in and wants a room. The desk clerk says no rooms are available.

Now imagine a hotel that has an infinite number of rooms. All the rooms are filled up so an infinite number of guests. A new guest walks up and wants a room. All the clerk has to to do is to move the guest in room #1 to room #2 and the guest from #2 to #3 and so on so your new guest can have a room #1. You can do this infinite number of times to a hotel that was already full.

Now imagine instead the clerk moves the guest from #1 to #2 and from #2 to #4 and from #3 to #6 (each being moved to a room number twice the original). All the odd number rooms become vacant. You can add an infinite number of new guests to a hotel that was full and end up with it half empty. 

How many people would be in the hotel if the guest in #1 checked out?

If everyone in odd number rooms checks out, how many checked out? How many are left?

Now what if all the guest above room number 3 check out. How many checked out? How many are left?

So from the above we get:
infinity + infinity = infinity
infinity + infinity = infinity/2
infinity - 1 = infinity
infinity / 2 = infinity
infinity - infinity = 3

Conclusion: the idea of an actual infinite is logically absurd.

Yep, this reponse to Jenny clearly shows that he never did read my responses to the maths. Otherwise, he wouldn't repeat the same old "infinity - infinity = different answer" crap. Steve isn't interested in learning something new if he sees it'll contradict everything he's believed about God.