Actual Infinity in Reality?

[polymath257]

LOL. Sure there are. BTW, you are failing to prove that actual infinities exist. You bring up some potential infinities candidates or that potential infinities are used in some equations--but that is not the same, is it.

And, so, if no one can prove that actual infinities exist, that makes their existence "impossible"??

Perhaps the concept of 'logically independent' is relevant here.

Two systems, equally consistent internally: one with infinities and one without. Neither has internal contradictions. So the question is which is a better model of reality?

But that isn't a question that can be determined without observing reality, now is it?

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Yes, I am quite aware of the properties of infinite sets. And yes, the odd counting numbers form a countable set. So do the integers, the collection of fractions, the collection of numbers that are solutions of polynomial equations with integer coefficients, and many other sets.

Part of the issue is, as far as I can see, that there is more than one concept of 'larger' when dealing with sets. Cardinality (being in one-to-one correspondence) is often not the most relevant idea of size. Being a subset is another that can be more useful, verious concepts of density or probability are others.