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

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Anonymous 08-09-25 02:00:18 No.707613

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 infinites. 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…(…)…

Anonymous 08-09-25 02:13:48 No.707619

Broadly correct, but there as many real numbers between 1/8 and 4/8 as between 2/8 and 3/8.

Anonymous 08-09-25 02:37:30 No.707623

Talking about magnitudes of infinities is inherently imcorrect IMO. It is right there in the name. You can still have a qualified infinity, like the infinite positive numbers or infinite negative numbers, but unqualified infinity naturally includes both and everything else.

Anonymous 08-09-25 02:39:35 No.707624

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Infinity is a singularity, an inescapable black hole, so naturally all paths lead there. You are already beyond the event horizon of infinity, there is no escape.

Anonymous 08-09-25 02:41:43 No.707625

Because, naturally, all finite things can only be a subset of infinity, even qualified infinite things are a subset like I said. Unqualified infinity is the set of all sets which any possible thing must be a subset there of.

Anonymous 08-09-25 02:47:35 No.707626

So you can have infinities within infinities within infinities, it matters not. What separates these infinities is they are qualified infinities, but what separates the true infinity is that it is qualityless. A qualified infinity can be infinite, but you still have to define that it is not something else. The infinite set of positive numbers is NOT negative. The true infinity is qualityless so it included any possible thing. Any possible thing is only a subdivision of qualityless infinity.

Anonymous 08-09-25 03:51:29 No.707631

>>707613
'infinity' is an empirically unverifiable concept. there is, quite literally, no such thing. you could never measure it to prove it. we can arbitrarily choose smaller and smaller units of measurement, but the 'infinity' is not present in the world, it is a feature of our categorization of it.

Anonymous 08-09-25 04:04:17 No.707632

>>707631
How many natural numbers are there, then?

Anonymous 08-09-25 06:44:15 No.707651

>>707623
>>707625
"Infinity" is not a set, it does not include anything.

>>707632
ℵ₀.

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