THE ABSOLUTE MADMAN DID IT AGAIN

I said exactly what you greentexted.
Any problem with that?
Actually, I could even add:
>This is also a very un-grounded introduction of examples mostly taken from the most "common" examples of groups, rings, etc. encountered in early studies of mathematics.
I said this because as far as I'm concerned, as far as I've been taught or as I've read maths, there are two ways to introduce notions:
>Way number 1: a proper introduction should state one or several problems, or a class of problems, and then should present the tools / ideas / notions used to solve them. That is what a "grounded" introduction would look like.
>Way number 2: another introduction would be a constructive class, starting from what the student knows - and this is generally, purposedly, assessed to be very little, in order to construct the theory properly, with correct notations and definitions. Starting with definitions, then showing properties or theorems, and passing by examples, and so on. Like a proper construction of a theory in mathematics.

This video does not fall into either of these two categories. Therefore, it is not a proper introduction. (and again I don't blame the guy: he did many other, much better, videos).

He is pretty consistent. You just didn't watch other videos. Also, you are ignorant as fuck

Well, your irrational and biased response is proving two things. The first being: you're very emotionally attached to this video and/or this thread. The second being: you're not ready to discuss rationally. Nothing judgmental.

I suggest you say when you're ready to discuss again. About Wildberger's shitty videos, Bourbaki's history of maths or Poncelet's theorem. Anytime, m8. I like arguing rationally, I like being proven I'm wrong (and not being shouted at that I am), as well as I like sometimes being right.

Kind regards.

Does anyone take him seriously tho?

That said, continue being an ignorant clown. Only watchng his other videos might have helped but you wouldn't do this. It's easire for you to fall for memes

Well as I said earlier, he is fun and he looks like a nice guy, but nothing really solid is being said in this video.
His videos on Projective Geometry are by fare much better. He is at the blackboard, and he proves theorems and all, and not just telling stories about how to "see" things in maths.

>(((set theory))) and (((analysis)))
You are a brainlet if you use echos on Veeky Forums.

is he a magician

He has aged significantly since he started this series.

>what you mean in other words is: "time passes by"
Do you have other lovely tautologies to bring to the community, user?

Its a highlught/preview video

>(((set theory)))
en.wikipedia.org/wiki/Georg_Cantor#Cantor.27s_ancestry

>not {{{set theory}}}

It's actually (((algebra))), {{{set theory}}}, [[[linear algebra]]] and .

What are the {{{ brackets. I know the ((( ones.

...

So it's just set brackets? I thought it would have to do with white supremacists or something. You know, flip the script

Set Theory was a (((Masonic))) ploy to misdirect math research, and backdoor it at the same time. Riemann had to be killed because he came to close to forming the real theory. All the great mathematicians who died young were done in my Jesuit/Masonic hitmen.

you're blowing a casual observation out of proportion. everyone knows time doesn't really progress, because past, present and future all exist simultaneously. this is the nature of infinity that Wildcheeseboober doesn't understand.

he's probably stressed because you assholes keep tormenting him. you remember why georg cantor ended up in a sanatorium, don't you?

>sanatorium

Is where someone with TB ended up, has the same root word as sanitary if I remember rightly.

It's pretty good user. Thanks.

First he came for the Analysts
And I did not speak out—
Because I was not an Analyst

Then he came for the Number Theorists
And I did not speak out—
Because I was not a Number Theorist

Then he came for the Algebrists
And I did not speak out—
Because I was not an Algebrist.

Then he came for my field of study—
And there was no one left to speak for me.

He has to be stopped, Veeky Forums.

a mathemagician

No one will stop him. He will purify mathematics. He will take set theorists to the gas chambers until a pure ultra-finitist race remains.

He can't keep getting away with it.

Wildberger is not allowed to debunk set theory with his feefees. "I don't like infinity" is not a reason to get rid of set theory.

How? How do we stop him when he's right?

>"I don't like infinity

But that is a really shallow version of his argument.

He doesn't like infinity because it makes many statements in mathematics non-computable, creating a useless divide between pure mathematics and computational mathematics.

For example, irrational numbers as defined by cauchy sequences. Give two cauchy sequences to a computer and ask it to compute if they are the same number well. Well, two cauchy sequences can be different at infinitely many points, but still converge to the same thing? How could the computer find out if the cauchy sequences are equal? It would essentially have to make many assumptions.

Like, imagine if I gave you these terms:
1.4,1.42,1.413,1.4143,...

you would say that it converges to root 2, but what if I tell you that the 99999999999999999999999999999999999th term is actually 5 and then every term after that is 5?

A computer would have to assume that the first terms are representative of the entire sequence, and that is not always the case.

On the other hand, rational numbers can be expressed so simply and are very easy to work with. Therefore, if we defined all of analysis with rational numbers then we would connect pure analysis with computational analysis and probably have a better system.

My calculator from the 1970s can only add and subtract integers. Oh well I guess we have to throw out most of algebra and the rationals because there should be no divide between pure math and what my calculator can compute right?

No because you can represent rationals with a single pair of integers. A finite amount of integers. Very friendly for computers and humans.

>consistent ultra finitist
>introduces limits as n tends to infinity

How do I do that on my calculator? I can't! You see rationals are a FRAUD.

You are retarded my friend.

And so is Wildburger.

QED

multiply 3/5 times 2/6

First compute 3*2 in your calculator
then 5*6

and then you get your answer m8. You just gotta get clever. I know that without the axiom of infinity you can't even compute 1+1 in your small brain but try to think outside the box.

>you would say that it converges to root 2, but what if I tell you that the 99999999999999999999999999999999999th term is actually 5 and then every term after that is 5?
>A computer would have to assume that the first terms are representative of the entire sequence, and that is not always the case.

Then I wouldn't say it is root 2

We have to assume that, too, until/unless you decide to give more information.

Nothing wrong with that. It is a definition, after all. He could have called it pancakes or whatever.

In the end, it is a very nice solution. Again, very computable as it relies only on rational numbers and natural numbers so call it a finitist interpretation of infinity.

I fundamentally disagree with this reasoning. I think it's a good thing that there's people like Wildberger challenging these notions as we always need our ideas to be challenged but I just fundamentally disagree with him. To me, that just means that math is beyond computers, which it ought to be.

>rational numbers can be expressed so simply and are very easy to work with. Therefore, if we defined all of analysis with rational numbers

My main problem with this is then what do you say about x^2 - 2 = 0? It's demonstrably not rational and then you can't solve it. The rationals aren't complete, you can't solve every equation in them, and we're refusing to talk about unterminating decimals just because you can't do "arithmetic" with them.

>multiply 3/5 times 2/6
Sorry this "/" symbol does not mean anything. Try again.

Being beyond computers means that you're either doing something wrong, or representing it incompletely. If a computer can't do something, that's because you don't know enough to make it do it right.

Only math that can be done on my fingers and toes is real. Stop trying to trick students into thinking there are numbers greater than 20, you hack fraud!

Lol, sorry that without your brainlet crutches like "infinity" and "choice" you can't even do basic arithmetic.

Like I said, I fundamentally disagree with this philosophy.

Putting preference on some arbitrary form of representation is simply nonsense and has nothing to do with math.

>My main problem with this is then what do you say about x^2 - 2 = 0? It's demonstrably not rational and then you can't solve it. The rationals aren't complete

There is no rational solution... but there are the extended rationals.

youtube.com/watch?v=YMQkLojL2ek

Here Papa Wild talks about how to do analysis with them.

It relies on checking infinitely many inequalities for infinitely many values of n so his definition of limit is as invalid as he claims the definition of reals is

Couple of years ago our computers were able to handle numbers only half as big as they can today, does that mean we should update maths every time some development in computers happens? I mean, it seems nice to have our maths independent from some fancy abacus.

But why not use well defined and already established reals instead of this bullshit defined by a crank waving his hands?

he is funny because everything he does was already done during 1900-1930. And it's much more well written in bourbaki set theory book. Hell we even proved you can do math without variables (see combinatoric logics and whatever).

I'd like to /thread but there are too many funny post :

true he's quite funny because he occults A LOT of math history you're talking about.
yeah, kind of a statistician to sum it up. finitist isn't so bad fundamentally, but let's not delude ourself in thinking that finitist theories are as powerfull as "classic" ones (in the logical sense of the term).
this actually explains Gallois' death a lot better and his "rush" to write down everything.
true, and you can actually do some maths without it.
wrong. I know it's not well known, but non computatibility != infinity. You can delve into machine theories and recursive analysis. J-L Krivine who's one of the big shot in machine theory also wrote an excellent book on set theory which you can read and write down your own fundamental approach to math from it. Secondly, "convergence" is a notion which has a meaning only in light onf infinity, so that point of view is already dangerous. Your wolfram and whatnot use computer algebra and real numbers actually, a well studied field in mathematics and theoretical computer science. You should read some on it.

ow kek... a definition in mathematics doesn't work like this. It's like a label. when you say N goes to infinity, you mean : for all N. Same with root of 2 which you define as : x in IR+ s.t. x^2 = 0
which you have proven already it existed and was unique!
true, the sole reason to actually use reals is their completeness and relative computability. Moreover, saying that reals aren't representable and whatnot is clearly a sign of not knowing much about theoretical computer science (which is used in any CAS) and I'm not talking about ugly ass floating point representation.

hahaha ow, wow... let's get serious. A computer is a machine, a model of computation to be exact. Stop saying that it's guidding you. This kind of mindset leads to stupid people not even knowing the power and limitation of what they have between their hands, talking about muh AI and whatnot and actually thinking they can truly do interesting things outside of their overuse of R/matlab toolboxes.

choice is fucken awesome though.

true to a certain extent. but that's actually quite a general philosophy.

don't even try... he is redoing a basic course of recursive analyss wew. It wouldn't surprise me if he starts talking about recursivity, and state overpowered incompleteness theorem because he has only a finite scope of things and then goes on using it as justification.

This has to be one of the most autistic threads I've seen this year.

"As he aged, Cantor suffered from more and more recurrences of mental illness, which some have directly linked to his constant contemplation of such complex, abstract and paradoxical concepts. In the last decades of his life,...He spent long periods in the Halle sanatorium recovering from attacks of manic depression and paranoia, and it was there, alone in his room, that he finally died in 1918, his great project still unfinished."

A Sanatorium was just a long-term facility for patients. The root word sanitas merely relates to ‘health. While most typically associated with the confinement of TB patients, remember that in Cantor's time the pathology of mental illness was not fully understood and often treated in much the same way as other chronic diseases-by isolation from society. In Cantor's time, you still had great MDs like Virchow believing that germs were not the principal cause of disease, but instead the organs themselves malfunctioning and thus creating a habitat where certain germs flourished. He even criticized hand-washing despite working out the pathology of Trichinella spiralis infection.

fuck off you whacky autist