Can somebody explain his problem to me?

just watched that video, before 13 minutes he doesnt even do anything but present dedekind cuts, so how could Rudin get BTFO by presenting his ideas? After that, he tries to "disprove" set theory by starting out with the axiom that no infinite sets exist, he is pretty much just prooving that from his set of axioms(if he even produced those) they don't work, woah who would've thought

forgot to add: his criticism of rudins book on analysis is pretty much that he didn't explain set theory in a book that is not about set theory but one that builds on it. He should rather talk about ZMF instead of this strawman "oh it's not in this book? Then it must be written down nowhere!"

ignore the other poster he's just trying to meme.

Imagine the smallest thing in the universe.

Now Imagine you want to give a number to all of those smallest things in the universe.

If we assume infinity exist then this means there are more numbers than there are things, and this is obv false .

In other words - a number is a thought and a thought is just a constellation of physical matter.

If physical matter is finite then thoughts also also finite and therefore numbers are too.

also also = are also*

So what's the largest number?

this doesnt work. you cant use a thought experiment to prove your point. mathematics is detached from reality.

this assumes numbers are a real physical thing

But thats exactly the problem, mathematicians think they are somehow god like people who doesnt live in this reality.

>>B-but we have a soul and then theres god and there are monsters and angles too...

>>T-Thougs are floating in another physical realm not cot connected to ours and if we die the thought will stay existent and then it flys in a robot brain on another star called heaven...

Just as real as a thought

What IS a number if its not thought or not written down? Non existant.

Let's call it L, the number of all things

when you have L dicks in your ass and i put mine in, too - how many dicks do you have in your ass?

what is a "thing"

>Let's call it L
>Making up numbers

Its not possible because L + 1 would be "outside the number range"

Lets say all possible numbers are L and all impossible numbers are part of L'

Just like x/y where x and y eof N and x=1 and y=3 will land into Q L+1 will land into L'

The smallest possible amount of information

Whats your point?

>writes L+1 down like it exists
>says L+1 isn't a thing because it can't be thought of

Imagine a bucket full of balls, the balls represent all particles in the universe

Now I take a bunch of them and arrange them in a shape of an L and I say "this L represents the amount of balls in the bucket"

Now there comes you little retard and you take another ball out of the bucket and place them beside my L and you say "hure durr now there are more balls in the bucket, namely L + 1"

And I say "Listen you little shit, there is only a finite amount of balls, there cant be more in the bucket taking one out and adding them to my L doesnt change that. You cant create more balls that way, you are just a retard"

I take a bunch of balls and arrange them in the shape of an "L+1" and say "this L+1 represents the amount of balls in the bucket plus one"

That +1 ball would simply not exist. Adding 1 wouldnt create another ball. L +1 is an imaginary number - like a Unicorn which is an inmaginary Animal.

but the L doesn't exist.
numbers don't exist.

Numbers are thoughts and thoughts are an arragement of matter, therefore numbers are an arragement of matter. The smallest possible arrangement of matter is, assuming the universe is discrete (which is what physicists believe) no arrangement at all. So the smallest representation of a number is a bijection from N to all the "balls" the universe is made of.

fuck is this bait? i can't tell how many layers of irony we're on right now desu

less than L layers I would assume :^)

I ain't even baiting. There are different ways to look at things and this is on of them.

youtube.com/watch?v=QSZsTeO-C1o

>"hurr durr I cannot find le value therefore it doesn't exist"
>"therefore le fundamental theorem of algebra is wrong"

not this guy but what Wildberger claims to be false about Dedekind cuts is a perfectly valid statement in regular set theory, may it be a bit counter-intuitive when thinking about it in the first place, leaving the impression that such a result can't be accepted

...

Do you have proofs to back up your conjecture?

According to standard physics, the universe is infinite, homogenous, and isotopic. This implies there is infinite matter in the universe.

Wow it's almost like we have this ability to think about things that don't exist or are hypothetical, and extend logical principles to those things. Amazing.

Numbers are not thoughts. Thoughts represent concepts like numbers. Just like the symbol 9 is not a number but represents the number 9. So your argument is actually that only a finite amount of numbers can be represented, not that only a finite amount "exist". But infinity is clearly represented and conceptually used in a variety of rigorous ways. This temper tantrum over representation and it's confusion with existence is utterly pointless and nonmathematical. It's merely contrarian masturbation.

He's just pointing out that most textbooks avoid the problem by relying on a lack of formalism.

There are textbooks that go through the explicit construction like Landau's Foundations of Analysis but those books only give a few explicit constructions of a few "easy" irrationals. They don't explicitly give a general method for constructing a real out of Dedekind cuts because such a thing is impossible due to the fact that such constructions require the use of finite sentences but the space of all finite sentences is countable.

Numbers are sets defined in the classical logic equipped with the axioms of set theory. The "concepts" and "thoughts" you are talking about are little more than metaphors and analogies, tools you use to try to build intuition about mathematics. They are not mathematics itself however.

But what about combinations and permutations of those "smallest things"? There'd obviously more than the original number of things, but it's still physically meaningful.

[eqn]\rm {\color{red}A}^{\displaystyle \color{yellow}u^{\displaystyle \color{green}t \color{cyan}i}} {}^{\displaystyle \color{blue}s} \color{magenta}m[/eqn]

There exists a number for every smallest thing, this means we can say that a smallest thing is a number itself. Read it again, I dont mean we can biject N to the smallest things I mean the smallest things are N itself. They are the smallest physical representation of N. Everything == N. You can rearrange and permute things but if you want to give them a Number then you must give them another "smallest thing". Like take the smallest thing that represents number 34 and map it to the things representing number {1,2,3} this doesnt create a new smallest thing.

nicely put, I prefer this kind of attack on the continuum, rather than this ultra-finitist stuff which seems rather dogmatic

I don't know why you have a preference in your philosophy for a number to represent the smallest "thing" rather than represent "possible thing" you can still argue your point, because the power set of a set of finite things is still finite. That is, given L smallest things, 2^L is the number of possible things (every combination of those small things) but that is still finite.

>In other words - a number is a thought and a thought is just a constellation of physical matter.
no! numbers are abstract concepts that can be applied to everyday life. the "amount' of numbers is not restricted by reality because there is no amount.

Is this really it? Wtf, I didn't know a mathematician could be this gay