If you stop anywhere in an infinite series, it’s regress remains actually infinite, and you can continue to a number greater than an actual infinite, which is a contradiction because the very notion of an infinite series is dependent on the idea that it’s parts **altogether** comprise an actually infinite number. This is to say that each part of the series is **intrinsic** to it being an actual infinite. In other-words you should be able to take one part away from the series and it should cease to be infinite, but it doesn’t. Therefore what makes the series infinite cannot be due to **how many parts** it is comprised of ( *the very thing that defines it as an actually infinite number in the first place* ); which is incoherent, making the idea of an actually infinite series meaningless.

Have you studied Set Theory?

No, but you are free to show how set theory contradicts my argument.

Some of your assertions in your argument are just nonsense, such as

as the term ‘an actual infinite number’ does not mean anything.

The mathematical concepts of infinity as well as different degrees of infinity are hard and Set Theory is worth studying since it encompass literally centuries of thought by very smart people about infinities and other related ideas.

I’m off to a ham radio thing, so will be off line for a while, looking forward to your reply

Anything that is comprised of actual parts is comprised of an actual number of something. It is a quantity. There is an irreducible point between one actual state and another, in fact it is that which defines one state from another. So it is clear to a person, *that is willing to reason things through rather than jump to the conclusion that they know better*, that an actual number of something exists in the real world. The question is does an actually infinite number exist. **And yes, and actually infinite number is meaningless, and an infinite regress is exactly that.**

This is a Red herring, a clue or piece of information which is or is intended to be misleading or distracting.

That’s the thing. Cantors sets are mathematical concepts alone, and in any case are not proof that an actual infinite can be comprised of a finite quantity of irreducible numbers. In fact the concept of infinite sets doesn’t apply to my definition of a regress, even if it so happened to apply to something else. So it’s bizarre that you would bring it up as a counter argument, unless of course you are willing to back up your assumptions.

My advise would be to show the relevance of set theory, and if there is any, show me how it defeats my argument. Anything less than that is either a straw-man or an assertion **or an attempt to imply ignorance without providing an argument.**

I get an impression that this is a misunderstanding…

Thus I’ll try to present an argument that is supposed to be mostly equivalent to the one in original post, but worded differently.

Let’s make a temporary assumption that we had a hotel that has an infinite number of rooms that is full. Then, if a new guest arrives, it is possible to make place for him after every guest is moved from room i to room i+1. But that’s absurd. Therefore, we cannot have a “real”, “actual”, “physical” hotel with an infinite number of rooms.

It should be easy to recognise that this argument is mostly “Hilbert’s Hotel”.

Yeah, well I’ll concede that it is possible that I don’t understand what the op is trying to say here.

But there are obviously infinite serieses that converge to a finite number, such as the summation of:

1/(2^n)

Where n is the set of integers greater than or equal to zero. That, of course, sums up to the finite number 2.

But in this case we are not talking about integers.

Okay, true. I’m not sure what difference that makes though. It is still an infinite series

It’s incoherent to you because you are treating infinity as if it were a real number. It is not. There is no point on the real number line that can be identified with infinity. That is your mistake.

You aren’t going to be able to make any progress in understanding this until you divest yourself of the idea that infinity is somehow number, or that it is some type of “place holder”. Otherwise, you’ll just be spinning your wheels and getting nowhere.

Here is an article explaining it. There are PLENTY of other ones that you can find, and any introductory textbook of number theory or set theory will have a thorough explanation.

https://scienceblogs.com/goodmath/2008/10/13/infinity-is-not-a-number

If it is not a number of something then an infinite regress of events or states is impossible, because an infinite number is dependent on every single number it is comprised of in-order to be actually infinite; otherwise it’s meaningless.

No. And you are completely wasting your time and will never arrive at an understanding unless you divest yourself of that idea. Until then, the only possible output of your reasoning is mathematical nonsense, meaningless to anyone, including yourself.

If you truly want to understand this, you are going to have to put in the work and learn the math. My advice is to hit the books.

Good luck!

You are not understanding what i am saying. A real infinite regress of states is an infinite regress of irreducible numbers. If an actual infinite is not comprised of truly distinct numbers then an infinite regress has no meaning at all and is therefore a false concept.

I understand what you are TRYING to say, but it is still mathematical and philosophical nonsense based on your completely erroneous understanding of the concept of infinity.

In other words: Garbage in, garbage out.

Like I said, you are completely wasting your time with this until you have a proper understanding of the concept. There is no other way for you to make progress.

Spend your time productively learning the math.

You can accuse me of what ever you want but you have no argument.

Here it is again.

If you disagree with anything written here then you have to give a counter rebuttal that highlights the error in this specific argument. Otherwise you have no business telling me anything. I am not arguing that there is such a thing as an actually infinite number, i am saying this is precisely what is being argued when one speaks of an infinite regress of prior states.

It’s not a matter of me disagreeing with you. It’s that EVERY SINGLE mathematician on the planet does.

There is no counter rebuttal because there is nothing to rebut, except a bunch of mathematical nonsense.

If you want to play the game, you’ve got to learn the rules (the math). Otherwise you’ll end up in the corner playing by yourself, as you are now.

You can’t just make assertions. It is not even clear to me that you understand what i am saying because your responses don’t make sense.

And thus far all you have given is assertions so who knows.

If you don’t want to be a part of the discussion leave.

What the heck, I’ll give it a try…

What is the sum of all the odd integers?

What is the sum of all the even integers?

What is the sum of all the integers that are multiples of 10?

These concepts work in pure mathematics. But i am applying numbers to distinct ontological states. To speak of an integer strictly in terms of it representing a distinct state compared to other states is arbitrary and meaningless.

Oh, well have fun with that…