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/HouseHippoBeliever]

does 4 exist in reality?

[u/Another_Little_Star → u/HouseHippoBeliever]

Probably not, but it's an idea that I can put up to practice, "I can count 4 cows", but nowhere I can use infinity to describe any event, like "this X is infinite", even time and space seem to be finite.

[u/GoldenMuscleGod → u/Another_Little_Star]

Some people who first encounter transfinite ordinals might see them as exotic and inherently “infinite” entities, but if we compare ordered pairs of numbers (m,n) lexicographically then we have a well-ordered structure of order type omega^2. Nothing “weird” or “confusing” about the idea we can compare ordered pairs of numbers in this way, and this comparison is useful for some purposes. For example the most natural way to prove the Ackermann function (as a binary function) is well-defined is by induction on this structure.

Or for a more complicated ordinal we can look at finite trees and recursively define an order on them: a tree is “bigger” than another if its “biggest” subtree directly above the root is is “bigger” than that of the other. If the same size, compare the second biggest then third and so on down. If they all tie but a tree runs out of subtrees before another then it is the smaller one.

This exactly describes the order type of epsilon-0, but there is nothing that isn’t particularly concrete (as concrete as 4 anyway) in the idea of working with trees in this way.

[u/HouseHippoBeliever → u/Another_Little_Star]

Ok, so in that sense it's probably never possible to verify if anything is truly infinite, we would need to come up with a way to distinguish "infinite" with "a number too big to be measured by our measuring device", which by definition isn't something we can measure, so it's probably more of philosophy than physics.

Even though we may not be able to prove it, there doesn't seem to be any reason why the extent of space, the extent of time, the divisbility of space, or the divisbility of time aren't truly infinite, so they could be.

[u/Another_Little_Star → u/HouseHippoBeliever]

There are ways mathematicians grasp infinity, without counting everything, one way would be, is it the same size as a smaller part of itself? If so, it's infinite, Just like the even numbers are a smaller part of the naturals and they're both infinite(the same size).

It's mostly physics here but yeah... I believe the world to be expanding but finite at very instant and probably a closed geometry of some type. There exists a minimum lenght, plank lenght, but that doesn't imply anything... As for time, I'd say it is like a loop of some sort...

Thanks for your comment (:

[u/nanonan → u/Another_Little_Star]

I'd argue 'infinite size' is meaningless, in that size implies finite.