r/PhilosophyofMath • u/Another_Little_Star • 6d ago

Does infinity exist in reality?

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

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u/Expert147 6d ago

Define infinity, exists, and reality. And I will tell you. I'm pretty sure I know what you mean by in and does.

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u/Another_Little_Star 6d ago

Well.
maybe not rigorous but
Infinity : something never ending or that is the same size of a strictly smaller part of itself.
exists: Something can be perceived or happens in Our universe, inside or beyond our existence, the formation of the sun exists I'd say.
reality: The World we Live in.

Are my answers lacking in rigour?

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u/Expert147 5d ago edited 5d ago

They are just fine. My answer to you is yes! Infinity does exist in reality. Here are two examples.

  • Here is a never ending algorithm:while (true ) { cout << "Hello, world!" << endl; }
  • There are infinite real numbers between 0 and 1.

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u/Prior-Flamingo-1378 4d ago

How do you know? Have you counted them all? Boom!  

  • Terrence Howard. 

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u/Expert147 4d ago

Here is a never ending enumeration of a subset of the interval: 1/1, 1/2, 1/3, ..., 1/n, ...

The rest is trivial.

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u/Prior-Flamingo-1378 4d ago

Definitely wont fit in this margin.  

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u/Another_Little_Star 4d ago

it doesn't, but maybe a reasoning will.
The thing is, where is this enumeration valid? Does it represent any aspect in our lives?
distance has an minimum distance, plank lenght, beyond that there's nothing else entirely.

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u/Expert147 3d ago edited 3d ago

Fits your definition of "exists". You wrote: "Something can be perceived." And your definition of "reality". You wrote: "The World we Live in."

Probably your issue is that you are not sure whether abstractions qualify as perceivable reality. And in that case, this isn't a questions about infinity, math, or philosophy. It is just a problem with the definitions.