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 No.27213

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 fractions, does that 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…(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…(…)…

How do you define the natural numbers without infinity?

 No.27218

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>>27213
The accepted answer to those questions is yes, it's a whole subfield of study in contemporary math.
https://en.wikipedia.org/wiki/The_Higher_Infinite
There are more meaningful types of "infinities" than is possible to immediately conceptualize, probably more than a human can conceptualize at all

As for natural numbers, it's just induction right? For each there's always one bigger by one, no need to invoke infinity. For a finitist, this will just mean that any number you think of, you can think of one +1 bigger than that. No need to concern yourself with infinity here I think, if you don't want to.

 No.27301

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