You can construct anything from zero-dimensional points if you have enough of them

>You can construct anything from zero-dimensional points if you have enough of them.

No wonder nobody takes "high level" math seriously.

Take two zero dimentional point.

You now need one bit of information to describe which point you're talking about.

Simple as that

every set is just a collection of points
that's not the point of banach tarski you dumbass

>I don't know how to dispute this so I'll just claim it's irrelevant.
Wow n1

>tfw you can't understand high level math
I don't know it

true, but the point is that you can partition the ball into only a finite number of subsets, and then you can rearrange those subsets *by isometries* - not just an arbitrary totally random shuffling.

>a line of infinitesimal length contains points that are injective and surjective to the points of arbitrarily size and dimension

hmm, math... dare i say it.. could it be that it... really makes me think

*arbitrarily large

not infinite dimension :^)

And they think Aspieburger is a crank for rejecting things like this.

I never understood the full proof of this but if I remember it uses non-measurable sets and some odd transformations.

but you can for everything up to infinite dimension.
why not for the limit also?

instead, he thinks a finite number of points can make up the continuum of space

Points can't make up anything you dork. They have no volume.

I'm not a mathematician but from what I understand, he thinks that things have to be well defined first. He thinks that infinity is like a process, a line that you can extend forever but never a box containing all the numbers.

it really tingles my tendies when i look at something that should be inherently topological but instead is some joint set-group-theoretical circlejerkery

i'd like to see you equidecompose that ball after i put a topology on it asshole

>brainlet topologist implying he could even define an infinite topological space

youre a sunday driver. were the mechanics

>implying the points aren't in superposition

well that's totally reasonable is it not?

Define zero-dimension point..