Anonymous at Mon, 3 Jun 2024 10:52:43 UTC No. 16207599

>>16207506
>If there are
In our imagination only, don't take it too seriously
>infinite infinities
if you can define a subset within an infinite set in infinite ways, yes, there are infinite subsets within and infinite set.

Anonymous at Mon, 3 Jun 2024 10:54:43 UTC No. 16207602

>>16207506
yes

Anonymous at Mon, 3 Jun 2024 11:10:29 UTC No. 16207616

>>16207599
>if you can define a subset within an infinite set in infinite ways, yes, there are infinite subsets within and infinite set.
me again
how about this: can you even define any point in something continuously infinite? Like, as you zoom in on the number line, no matter how deep into it you go, you will never see "a number", you will always see a continuum, and at no place will you be able to place a stake and call that you first boundary to your set.
How do you define the number 1, for example? Is it the number that is just after the number that is just before the number 1? lol
Or is it the number that precedes the one immediately after it?
Of is it the number between those two?
Literally undefinable

Anonymous at Mon, 3 Jun 2024 13:13:49 UTC No. 16207757

>>16207506
Yes, and you can make a powerful argument for Finitism based off of this: https://www.youtube.com/shorts/W4_OXMCswKU

Anonymous at Mon, 3 Jun 2024 13:16:51 UTC No. 16207764

>>16207757
Oh no not this retard again

Anonymous at Mon, 3 Jun 2024 13:18:18 UTC No. 16207768

>>16207764
I'm back baby, wherever the Lazy Eight rears its logically impossible head I shall be there to slay this foul mathematical hydra

Anonymous at Mon, 3 Jun 2024 14:49:24 UTC No. 16207871

>>16207506
>If there are an infinite number of whole numbers
There is exactly the amount of whole numbers as the chosen base

Anonymous at Mon, 3 Jun 2024 14:58:05 UTC No. 16207875

>>16207506
>does that mean that there are infinite infinities?
Fun fact, the scenario you described (infinitely many natural numbers, MORE infinitely many real numbers) leads to an interesting conclusion: There are only two infinities. There's the cardinality of the naturals and then there's the cardinality of the continuum. Despite both being infinite, the second one is strictly bigger than the other because you can't put the members of the second set in one-to-one correspondence with the members of the first set.

Anonymous at Mon, 3 Jun 2024 15:21:23 UTC No. 16207898

>>16207616
A point has no extension, so a given point is surrounded by all those numbers or tuples within a neighborhood of 0 away from it. The maximum limit of a zoom in to a continuum would not unveil a point, but only those numbers closest to it.
There are some interesting properties here. Consider circles inscribed along the same tangent.
When you zoom in to this region where these circles and tangents meet, the three closest differentiable points which define the circle on these infinitesimal range are infinitely far from one another, similar in appearance to the largest circle with a radius at infinity, it is almost everywhere equivalent to a line.
There are two observations here:
1. There are infinite numbers in the neighborhood of a point.
2. Each circle and the line itself are all exactly the same at this level, rehashing Zeno's conundrum. What determines how to "draw" a circle of some radius through a collection of these 0 neighborhoods.

Anonymous at Mon, 3 Jun 2024 16:20:04 UTC No. 16207956

>>16207506
there are two infinites, the set of all whole numbers and the set of all rational numbers.

Anonymous at Tue, 4 Jun 2024 03:52:09 UTC No. 16209090

>>16207506
>infinite
good try glowie

Anonymous at Tue, 4 Jun 2024 04:53:57 UTC No. 16209193

Perfect
Self replicating
Nanobots
At
Every
Scale
Meaning
The entire universe as you conceive it, is just one nanobots
And a single atom is made of incalculably many nanobots, expanding at an accelerating rate