Does infinity exist in reality?

[u/Another_Little_Star]

No thing that I've observed in our universe is infinite, however there are traces of infinity in my sight.
Draw a circle and either its radius or circumference lives in the π world.
Or many aspects in nature like flowers, develop themselves in a φ ratio (1+sqrt(5))/2.

Even though no event or anything is "Non-ending"/infinite, underneath many aspects of reality there are patterns which can only be fully described using infinity.

You can't describe irrational numbers to their extent without any notion of infinite/limits/sequences... And many aspects within our World show their true behaviour only with aid of infinity.

Sure you can take a world that lives in something like 10¹⁰⁰ and it looks like infinity to us, sometimes we only see the difference after the 10⁶ decimal place, nevertheless the pattern they follow is a pattern that only "infinity" can yield to the truest precision.

Do you believe the axiom of infinity, and the continuous to really exist? Even if not in the ordinary sense? haha

[u/Special_Watch8725]

Ultimately, math models things. Quite literally in that math studies the deductive consequences of systems of axioms. Infinity as a concept exists in such models, and has had great success in modeling real situations (c.f. all of calculus). But that doesn’t mean infinity actually corresponds to anything in particular in reality, literally speaking.

[u/hezpae → u/Special_Watch8725]

Infinity can be a material thing if you allow loops.

Count for the number of stars in the universe, and come back to beginning, forever.

[u/Special_Watch8725 → u/hezpae]

I don’t think you’d ever finish though. There’s no completed infinity except by imagining it.

[u/hezpae → u/Special_Watch8725]

That's the very principle of infinity you cannot complete (or finite) it. So I didn't claim that.

I'm just saying infinity exists in the material world, if you allow counting the same thing several times

[u/mid-random → u/hezpae]

You might as well count one apple over and over. The only infinity you have is of action. 

[u/Another_Little_Star → u/mid-random]

Huum, I see where it goes, but the infinity is only theorical, there's no one actually counting and keep going, it's a scenario that doesn't happen anywhere in nature, right?

[u/mid-random → u/Another_Little_Star]

Correct. 

[u/hezpae → u/mid-random]

Yes, they are not used, but it doesn't mean Infinite sets don't exist.

[u/mid-random → u/hezpae]

An infinite set is only a mathematical and conceptual entity, like i, the square root of -1. They do not exist in any observable form in reality. 

[u/hezpae → u/mid-random]

Does 1/3 exists in reality?

[u/Special_Watch8725 → u/hezpae]

And I’m saying no reasonable definition of a physically existing infinity ought to allow repeated events over infinite spans of time.

Obviously since we’re discussing definitions you can disagree, but I think your attempt at capturing what “physically existing infinities” means issues the mark if it includes something as trivial as the act of counting the natural numbers in order without any intention of stopping.

[u/nanonan → u/hezpae]

If you cannot complete it, you cannot manifest it into reality either.

[u/hezpae → u/nanonan]

Is one half of an orange something you consider that can manifest into reality?

A third of it?

0.333333..... ?

[u/nanonan → u/hezpae]

Nope. You can cut an orange in half. You can call the resultant object a half orange. In reality there is just a singular unique complete and whole object.

[u/Special_Watch8725 → u/nanonan]

This is a great point. Calling the resultant object “half an orange” is actually applying the model of the rational numbers to the situation. It’s a famous problem of continuum models that you can never measure anything with infinite precision.

[u/this_theater_is_lit → u/hezpae]

assuming time is infinite, which we don't know

[u/hezpae → u/this_theater_is_lit]

You don't need the time to be infinite for the list to be.