Actual Infinity in Reality?

[GrandizerII]

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Oh, please.

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Infinite number of elements. Infinite being descriptive term for the endless number of elements in the set. Look at the whole set/collection of numbers/elements, and that there is your infinity. It's not somewhere near "the magical ends".


If you were talking about actual infinity, then why are you struggling with the premise? Actual infinity exists, meaning all elements exist in it without bounds/ends. Complete doesn't mean having ends in this context. It means all elements are present.

You can correct me if I am wrong here.   You are saying that there is an infinity where all elements are present, (there can be no more)  and yet the definition of infinity means that it is without inherent limitation there is always more.  You are saying that there is no more and more at the same time, in the same way.  You can make a rule about a set, where the rule creates an open set where anything more is included.  But you do not have all at any point in the process a list of all.  You have a rule which includes all that may be.  Even in your imagination, you cannot have an infinite number of things (barely a fraction really).  At best you have a shorthand, which includes all that may be.

It doesn't matter how many times you assert that actual infinities exist, you haven't really done anything to show that they do, and saying all but not all, over and over; I don't believe helps your case.

Bolded mine. I told you you're confusing actual infinity with potential infinity. In actual infinity, there cannot be anymore. As all the elements are there. All the hotel rooms are occupied. All time moments exist already and always.

You are making an argument of intuition against infinity. That's not the same as making a logical argument against it.

And if all I'm saying in this thread that actual infinity seems logically possible, unless demonstrated otherwise, then if you contest this, it is up to you to "disprove" actual infinity.

EDIT: Considering that there are sets that are infinite in only one direction, I do have to be more careful with generalizing things. But usually, for the real world context, I'm referring to an infinite set in both ways.