>Continuum """"hypothesis""""

>some poor uninformed anon fell for the Wildburger meme

You cry about how it's 'obvious' that there are cardinals between those of [math]\mathbb{N}[/math] and [math]\mathbb{R}[/math], while denying that [math]\mathbb{R}[/math] even exists.

>>8590249
No. I claim the Reals do not exist, but if I were to accept their existance, then at least I'd have enough of a brain to realise that there are obviously an uncountable number of cardinalities between any two cardinalities.

>>8590256
>there are obviously an uncountable number of cardinalities between any two cardinalities

Alright anon, I'll bite. Why is it obvious?

>>8590260
What fucking reason can you muster up to defend the "jump" in size from the naturals to the reals? It should be a smooth transition, not a discrete one.

>>8590264
What fucking reason can you muster up to defend a "smooth" transition in size from the naturals to the reals? It should be discrete, not smooth.

>>8590268
It's less counter-intuitive than the other option.

Let P be the union of every subset of the cartesian product of n, n being a natural number, sets.

I'm supposed to believe that for every element in P, there's another element in P with greater cardinality by a discrete quantity and that this culminates with aleph zero, which has greater cardinality than any of these elements, but that magically from here on out we stop being able to have cardinalities increase in discrete, concrete amounts and that we just magically arrive at the cardinality of the reals next, with nothing between them and the naturals?

This is bullshit, you monkey-brained non-finitist.

>>8590230 I know this is a bait but i'm going to bite becaus fuck it:
Your argument is logically incoherent because you're assuming math is an objectively real which is not the case, Math is just a product of a set of rules that we made up, and the reason why we did this is because they turned out to be extremely useful, our choice of axioms is arbitrary, really, we could have defined the number 2 in another way or make up some axiomatic system like Presburger arithmetic but we didn't because they didn't work in the real world, it's like if there is natural selection going on here where the axioms that work gets chosen while the ones that don't get dumped, however there are still some autistic enough people to study the axioms that don't work like wildberger, the thing with wildberger is that he is platonist which is what caused his autism about the real numbers, but still he's stupid because he's assuming that space is not continuous and the universe is finite which are very dangerous assumptions.

>>8590230
Why don't you pick a single point to make, instead of just throwing a bunch of arguments together to see what sticks. Then maybe we can have a discussion.

>>8590281
>>8590264
>should

This is your problem, anon. Infinity is very counterintuitive, as paradoxes like Hilbert's hotel illustrate. Set theory had to be developed to systematically study infinity while avoiding the pratfalls of 'obviousness.'

>>8590264
Because cardinalities ``jump'' from the very beginning. You have sets of size 0, then 1, then 2, etc. Why shouldn't you go from countably infinite to size of the reals in one ``jump''? That's perfectly reasonable to me.

Still waiting for a proper argument against >>8590281

>>8590230
>I thought
That is where you went wrong.
Hypotheses are testable, but
the test does not "verify" anything.
Lrn2hypotheses