Can somebody explain his problem to me?

there's no nice arithmetical theory for the reals

>>8729917
Have you seen the construction of the real numbers?

>>8729917

he fell for the "start with the greeks" meme, hard

>>8729933
I have a copy of Rudin's principles of analysis and in chapter 1 their construction is shown.

>>8729940

Dedekind cuts are a fallacy

>>8729951
why?

>>8729961

t. Brainlet

study wildberger more.

>>8729917
Ever seen those memes that say
HAS SCIENCE GONE TOO FAR?

Well, replace science with math and that's basically it.

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>>8729940

Rudin gets literally BTFO not 10 minutes into Wildberger's MF 116.

>>8730003
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

>>8730988
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!"

>>8730988
>>8730993
ignore the other poster he's just trying to meme.

>>8729917
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.

>>8731015
also also = are also*

>>8731015
So what's the largest number?

>>8731015
this doesnt work. you cant use a thought experiment to prove your point. mathematics is detached from reality.

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>>8731015
this assumes numbers are a real physical thing

>>8731034
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...

>>8731038
Just as real as a thought

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

>>8731031
Let's call it L, the number of all things

>>8731054
when you have L dicks in your ass and i put mine in, too - how many dicks do you have in your ass?

>>8731054
what is a "thing"

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>>8731054
>Let's call it L
>Making up numbers

>>8731072
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'

>>8731074
The smallest possible amount of information

>>8731077
Whats your point?

>>8731102
>writes L+1 down like it exists
>says L+1 isn't a thing because it can't be thought of

>>8731105
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"

>>8731119
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"

>>8731140
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.

>>8731190
but the L doesn't exist.
numbers don't exist.

>>8731280
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.

>>8731311
fuck is this bait? i can't tell how many layers of irony we're on right now desu

>>8731334
less than L layers I would assume :^)

>>8731334
I ain't even baiting. There are different ways to look at things and this is on of them.

https://www.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"

>>8729965
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

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>>8729917

>>8729951
Do you have proofs to back up your conjecture?

>>8731015
According to standard physics, the universe is infinite, homogenous, and isotopic. This implies there is infinite matter in the universe.

>>8731054
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.

>>8731311
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.

>>8730993
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.

>>8731746
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.

>>8731015
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]

>>8731907
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.

>>8731882
nicely put, I prefer this kind of attack on the continuum, rather than this ultra-finitist stuff which seems rather dogmatic

>>8732188
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.

>>8731015
>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.

>>8731015
Is this really it? Wtf, I didn't know a mathematician could be this gay