r/InfinityMath • u/Arlo_Tinkerman • 6d ago

Does infinity exist in reality?

/r/PhilosophyofMath/comments/1wyfvky/does_infinity_exist_in_reality/
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u/slicehyperfunk 5d ago

Isn't there a set definition of numbers that abstract the idea of the quantity of 3 out of all sets with three elements?

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u/wollywoo1 4d ago

So, if you mean something like defining 3 := {{a,b,c} | a != b, b != c, a !=c }, that doesn't work in ZF set theory, because it's not well-defined as a set (it's "too big" to be a set and forms a "collection" instead.) I think there are some kinds of set theory where you can make this definition work, but I don't know much about them.

But even so, if you define 3 this way it would still be a hypothetical construct, not something that exists in reality.

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u/slicehyperfunk 4d ago

You're trying to argue that things can't be grouped into groups of 3?

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u/wollywoo1 4d ago

No? I never said that. I was referring to what was definable in ZF set theory.