🧵 Untitled Thread
Anonymous at Sat, 2 Nov 2024 12:06:59 UTC No. 16459562
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… does that mean that there are infinite infinities? And an infinite number of those infinities? And an infinite number of those infinities? And…(infinitely times. And that infinitely times. And…) continues forever. And that continues forever. And that continues forever. And that continues forever. And…(…)…
Anonymous at Sat, 2 Nov 2024 14:23:02 UTC No. 16459652
>>16459562
>Fractions
The rational numbers are dense in themselves but nonetheles are countable
The real numbers are uncountable
https://en.m.wikipedia.org/wiki/Can
https://iep.utm.edu/zenos-paradoxes
Anonymous at Sat, 2 Nov 2024 14:45:39 UTC No. 16459679
>>16459562
How many times will this copypasta be allowed, and can you name a larger infinity?
Anonymous at Sat, 2 Nov 2024 15:09:02 UTC No. 16459696
>>16459652
>the rational numbers are dense in themselves
All sets are dense in themselves, Anon.
But the rationals are also dense in the reals.
Anonymous at Sat, 2 Nov 2024 16:29:48 UTC No. 16459752
>>16459562
Yes, if it ever stopped it wouldn't be infinite
Anonymous at Sat, 2 Nov 2024 22:50:15 UTC No. 16460162
>>16459652
> The real numbers are uncountable
maybe learn to count lol
Anonymous at Mon, 4 Nov 2024 14:12:41 UTC No. 16462110
>>16459652
>The real numbers are uncountable
/sci/ is retarded
Anonymous at Mon, 4 Nov 2024 14:15:33 UTC No. 16462113
>Speaking of which delinquency
Anonymous at Tue, 5 Nov 2024 19:01:52 UTC No. 16463938
>>16459562
There are infinite number of thinkable infinities. So what purpose does that have to our finite grasp of reality may ask. The answer is there is none.
Anonymous at Thu, 7 Nov 2024 18:57:13 UTC No. 16466259
Anonymous at Thu, 7 Nov 2024 19:39:22 UTC No. 16466316
Anonymous at Thu, 7 Nov 2024 20:43:00 UTC No. 16466395
take an infinite set, like the natural numbers. you can define a bigger one by taking all the permutations of its elements. call this bigger set the 'power set'. do that again and, well, now you have a set of all power sets. there's a power set for that too you know? your brain will always underestimate infinity e.g. there are things that are bigger than any type of cardinality, majestic as unicorns, that will just slip away from comprehension and mock you for as much as you have fucks to give
Anonymous at Thu, 7 Nov 2024 20:54:24 UTC No. 16466406
>>16462110
They don't map onto natural numbers.
Boom. Owari da.
Anonymous at Thu, 7 Nov 2024 20:56:07 UTC No. 16466408
>>16466395
What number is in the power set of all naturals that is not contained in the naturals?
Anonymous at Fri, 8 Nov 2024 00:09:41 UTC No. 16466604
>>16466408
No number (except the empty set) belongs to the power set of the natural numbers. At most, the singleton of each number belongs to the power but [math]n\neq\{n\}[/math]
Anonymous at Fri, 8 Nov 2024 02:11:49 UTC No. 16466687
>>16466408
the power set of the natural numbers has the same cardinality of the real numbers. therefore, any number that is not natural: 1/2, sqrt(2), pi, etc.. can be put to correspondence with an element in that power set