Actual Infinity in Reality?

[SteveII]

I don't think the B Theory of time solves the underlying problem of having a series of cause/effect relationships. It seems to me that even if all points of time are equally real, they are still ordered by a structure we call cause/effect--a tangible series of objects we can use in thought experiments. [NOTE: I say this to start because there are some here who deny even this].

Perhaps a variation of Hilbert's Hotel:

We can conceive of a possible world (much like the one you are proposing) with a beginningless series of discrete successive events of equal duration leading up to the present (real or perceived present). 

[ ...en, ... e5, e4, e3, e2, e1, e0]

We can conceive of another possible world with exactly the same events in the same order, but in between each of those events, another event occurs.

[ ...en, En, ... e5, E5, e4, E4, e3, E3, e2, E2, e1,E1, e0]

In this series, an infinite number of additional events have been added to an already infinite series of events. Are there more events? No. Infinity + infinity = infinity. We can also do the subtraction example from Hilbert, and imagine all the events prior to e3 could have been left out of the chain. 

[e3, e2, e1, e0]

In this series, we have subtracted an infinite number of events from an infinite number of events. Infinity - Infinity = 4.  Alternately, every other event could have been left out:

[ ...en, ... e4, e2, e0]

In this series, we have left out an infinite number of events from an infinite number of events. Infinity - Infinity = Infinity. 

This is not just "counter-intuitive". Actual infinities of real objects leads to absurdities (metaphysical impossibilities). Therefore an actual infinite is not logically possible. 

[Example language from a paper from Wes Morrison - http://spot.colorado.edu/~morristo/EndlessFuture.pdf]

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.