Actual Infinity in Reality?

[GrandizerII]

Think of it this way, Steve.

What's finity + finity?

What's finity - finity?

Get my drift?

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When you ask if there are 'more', there are, again, two senses for this.

There is the sense of subsets. When you remove elements, the result is a subset of the original. When you add elements, the original is a subset of the result. We usually say that subsets have 'fewer' elements than the supersets.

In all your cases, the subset relation correctly describes the notion of 'more' that you are seeking.

When when talking about cardinality (infinite in your case, is the countably infinite cardinality), subtraction is not well defined. That means that different situations can lead to different answers. There is a similarity with division by 0: 0*3=0, so 0/0=3. But 0*5=0, so 0/0=5. That isn't a contradiction. it is simply that you used division inappropriately. In the case of infinite sets above, you used subtraction inappropriately.

So, yes, this *is* just counter-intuitive: subtraction is not well-defined. That's all.

Here are three different quotes to consider:

In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity [LINKED TO BELOW] is included) of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given, actual, completed objects. This is contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and each individual result is finite and is achieved in a finite number of steps. https://en.wikipedia.org/wiki/Actual_infinity

In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908.[1] https://en.wikipedia.org/wiki/Axiom_of_infinity

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects  with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.[1][2][3] https://en.wikipedia.org/wiki/Abstraction_(mathematics)

All emphasis added.

Therefore the the abstraction of actual infinity (from the first quote) is based on an axiom that there exists at lease one infinite set. Appropriately, an axiom in mathematics is defined as: a statement or proposition on which an abstractly defined structure is based. In case we are still unclear, the third quote defines an Abstraction. I highlighted the key theme all the way through this. Abstract. 

You have NOT made an argument (in this or the previous thread) where you show how this abstract concept in mathematics applies to the real world. It should be simple to propose some thought experiments or examples for us all to consider. I understand your point that the concept in mathematics exists--now you need to provide some evidence that it applies to real objects. Re-iterating infinite set theory from mathematics will not further this discussion.

No, stop it, Steve. You've been told this multiple times now. If there is no logical contradiction with infinity in the mathematical world, then unless you demonstrate otherwise, it seems logically possible for actual infinity in the physical world to be a thing (just not necessarily in a finite local universe like this).

Give us an example of a real world constraint preventing this from happening (with evidence of course).