Actual Infinity in Reality?

[polymath257]

Third, the idea that all events that will ever happen are equally real simultaneously is NOT the same as infinite set theory in mathematics. The first is an actual infinite and the second is a potential infinite. To be clear, mathematicians are talking about potential infinities when the talk about sets. This is because one side is bounded and only the open side is potentially infinite. These two terms have very different definitions and cannot be used interchangeably or use one to prove the other.

This is just false. Mathematicians are talking about actual infinities. They even talk about different sizes of actual infinities (for example the difference between countably and uncountably infinite sets).

There is no requirement of having an 'open end' in the description of a set:

N={x: x is a natural number}

is a perfectly well defined, infinite set. No 'open side' and no 'bounded side'. The description in terms of a list,

N={1,2,3,4,...}

is more a convenience for those who cannot read mathematics than anything else.

What you seem to think is that the second is some sort of process. It isn't. It *does* appeal to your understanding to know what things are in the set and what are not. But the list itself is just a notational convention and nothing else. In the same way, we can define an uncountbaly infinite set

R={x: x is a real number}

or

[0,1]={x: x is a real number and 0<=x<=1}.

Both of these are uncountably infinite sets.

There is no such thing as a 'potentially infinite set' in math. Sets are either finite or infinite. In the latter case, they are actually infinite. They can be countably infinite or uncountably infinite. For the uncountbaly infinite sets, there are infinitely many different possible cardinalities (although very few are used in practice)

Look in *any* math book and you will find NO distinction made between potential and actual infinity. The reason? Those notions have been replaced. They are no longer used because they are confused and ill defined.

So, I will make a challenge. Look in *any* advanced level math book produced in the last half century. Find *any* reference that discusses *at all* the notion of 'potential infinity'. I challenge you to find a single source *in math* for your claims from the last 50 years (I'll even go 75 years).