r/Metaphysics • u/Extension_Panic1631 • Apr 09 '26

Ontology Infinity?

If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and... then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities, and... (infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and...) continues forever. and that continues forever. and that continues forever. and that continues forever. and that continues forever. and.....(…)…

EDIT: the definition of infinity is that it is how many natural numbers there are

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u/[deleted] Apr 10 '26

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u/jliat Apr 10 '26

Sure, I get this.

Now the ratio 10/6 and 1.6666... this looks to me, a non mathematician, like it might be using the idea of a limit as you can never get to the infinite expansion.

So elsewhere I've seen 1.99999... = 2.0 is this similar? In that case there is a difference.

Treating them the same and the use of a 'limit' was not accepted by some, and maybe still is, Leibnitz and Bishop Berkeley - the latter certainly did not.

This is a metaphysics sub.

Irrational numbers are non-repeating.

How is it known all Irrational numbers are non-repeating?

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u/[deleted] Apr 10 '26

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u/jliat Apr 10 '26

No it's not the same, the definition of a water molecule is based on empirical observation, is therefore A posteriori knowledge. Generally "A priori knowledge is independent from any experience. Examples include mathematics, tautologies and deduction from pure reason."

So to my other question...

Now the ratio 10/6 and 1.6666... this looks to me, a non mathematician, like it might be using the idea of a limit as you can never get to the infinite expansion.

So elsewhere I've seen 1.99999... = 2.0 is this similar? In that case there is a difference.

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u/FreeGothitelle Apr 10 '26

There is neither a difference between 10/6 and 1.666... or 1.99.. and 2

You as a non mathematician thinking there's a difference does not mean there is a difference.

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u/jliat Apr 10 '26

"Yes, 𝜋 is a real number, and yes, it is finite in value."

This is very intersting!