DannyTR

Need to be clear about language at this point: https://en.wikipedia.org/wiki/Actual_infinity - The points on a number line is only a potential infinity not an actual infinity. - As you look finer, you see more points so it tends to infinity but never actually reaches actual infinity. As in a limit. Never reaches infinity. - Physically, it’s impossible for matter to exist with size 1/oo, so you would run out of resolution before you reached actually infinite points - But an infinite set has already reached actual infinity which is impossible. You cannot construct an actually infinite set so by extension you cannot have an actually infinite number of points on a line segment.

The universe is part of the material world so I’d argue the universe cannot be Actually Infinite. Give me an example of the actually infinite from nature. There are none. IE: This is empirical evidence that the Actually Infinite does not exist.

It is only defined using an axiom saying it exists, they don’t prove it exists. https://en.m.wikipedia.org/wiki/Axiom_of_infinity That axiom is Wrong. It’s easy to prove there is no largest number and actual infinity does not exist in the material world... so the axiom is wrong.

I’d argue that if actual infinity can’t exist mathematically or in the material world, it cannot exist in cosmology, IE time and space and the universe are finite.

https://en.wikipedia.org/wiki/Measure_problem_(cosmology) Two beaded cows as likely as one headed cows? A paradox surely. Paradoxes are indicative of an underlying logic error. In the case of the measure problem, it is probability that fails us. Why? Because we are plugging in the Actually Infinite as a real number. The Actually Infinite is an illogical concept that does not exist mathematically or in the material world. Infinity is defined in maths in two major ways: - Calculus. The limit concept. Tending to but never reaching Actual Infinity - Set theory. Actual completed infinite sets are allowed, IE Actual Infinity. How is Actual Infinity defines in set theory? It’s just an axiom that says something equivalent to ‘actual infinite sets exists’. So Actual Infinity is undefined in mathematics. Further more, it’s easy to prove that Actual Infinity is not a number: - There is no number X such that X > all other numbers - Because X+1 > X - Therefore Actual Infinity is not a number. So so a simple solution to the measure problem seems to be dropping the infinite universe...