/sci/ - Science & Math

>>12461651
/x/ is that way

>>12461651
He's a professional mathematician and a professor. Take your meds.

He's too educated and has too much academic standing to be a crank.
He's certainly eccentric, which is fine -- eccentrics can ultimately be right.

>>12461723
>eccentrics can ultimately be right.
>implying it's not already obvious to you that he's right about everything

>>12461659
Completely irrelevant. Tooker has a PhD and knows more math than 99% of this board.

>>12461732
>We need to be more rigorous in math
>Ahh yes, X is true because it's obvious.

Op here

I'm not saying i think he's wrong, I just think he should have a larger following and papers so that his results are accepted in a more gracious manner since he's about to rock the foundations of the math developed in the last three centuries. One should be careful to make esoteric sounding comparisons while being watched by the seetheing eyes of academia since they could use that to try and shove him under the bus out of spite or pride.

>>12461651
>Does this fall in the realm of brainlets using meaningless diagrams and squiggly lines without mathematical basis to justify their retarded "theories" of gravity?
Yes, absolutely.

>>12461723
>He's too educated and has too much academic standing to be a crank.
Many cranks are educated, anon. As for academic standing, he has none.

>He's certainly eccentric, which is fine -- eccentrics can ultimately be right.
They can be. But usually they are not.

>>12461762
Take your meds, schizo. Wildberger is completely right about everything. Your inability to grasp the concepts involved doesn't make him wrong.

>>12461775
>Still not a single proof put forth supporting Wildberger's claims
Yeah, okay bud.

>>12461775
>Your inability to grasp the concepts involved doesn't make him wrong.
His inability to grasp the concepts involved makes him wrong.

>>12461785
>>12461786
MEDS. NOW.

>>12461732
>implying it's not already obvious to you that he's right about everything
Yes, that's right. I know enough to realize he goes against the grain, but I don't know enough about the history of real foundations or about potential counterarguments to dissect his claims.

>>12461762
>Many cranks are educated, anon. As for academic standing, he has none.
I meant that he's a professor at UNSW, one of our top universities over here, and that he's taught at Stanford.

>>12461804
He doesn't really make claims in the first place. All his arguments boil down to "infinite sequences reeeee", and fail to produce any substance that one might dissect. This is the real reason why this man is ignored by all serious mathematicians.

>>12461819
This is, unfortunately, reasonably common for cranks that only develop their insanity after they hold a tenured position. Such people tend to stick around for a long time after they have lost all community standing. Sometimes that is the case because they can still manage useful work separately from their insanity; sometimes it is because they can be hard to get rid of. But in any case, it is not an unheard of situation, sadly.

>>12461839
Wildberger is not a crank, dumbass.

>>12461847
I don't know about his other accomplishments, but his work that is commonly discussed on /sci/ is most definitely crankery. It could be that he has actual virtue elsewhere, and only has everyone fooled that he is a crank entire by writing such convincing crankery. I cannot judge that, though I can guess. I can definitely confirm that his work is indistinguishable from that of a crank, though.

>>12461866
>his work that is commonly discussed on /sci/ is most definitely crankery
How so?

>>12461839
Fair enough.

>>12461750
tooker does not have a phd, he got kicked out of his masters program

>>12461839
>>12461866
How is he a crank? Do you even know what his positions are? You are just accusing him without providing any evidence for your claim.

Getting too many garbage Google results on this Tooker fellow. Where can I get the crank 411 on him?

>>12461870
See every /sci/ thread on this topic ever for details. Also see >>12461823. I'm not going to do yet another independent review here when all the other ones out there do a perfectly serviceable job.

>>12461888
Every /sci/ thread on this topic ever proves he's completely right about his claims and explains to ignorant people like you how you're completely misunderstanding his positions. It's so annoying when people like you who don't have a clue about logic, foundations, probably have never even seen anyone define and prove the arithmetic of real numbers, pretend to know about a topic and call established academics cranks. But this is, of course, the quality of people you would expect on 4chan. Fortunately not everyone here is like you.

>>12461659
lol, so was Ted K.

>>12461895
If you honestly think that, then I doubt I can convince you otherwise, for the reasons are always explained in those threads and have not changed. If you go and study those foundations you cite, perhaps that might change someday.

>>12461904
The only reason you gave is "all he says is infinite sequences reeee", which obviously means you don't know a thing about what his actual positions are or why he's taken them. You probably also think he's one of the only mathematicians with such a position, not being aware of people like Weyl, Kronecker, Nelson, Vopenka, Poincare etc.
I'm not even sure why I bother with people like you. You already demonstrated you don't actually care about reasons or foundations and only rely on your first (faulty) impressions to baselessly accuse people who are honestly trying to improve the state of modern mathematics.

>>12461918
>which obviously means you don't know a thing about what his actual positions are or why he's taken them.
No, it means I care a lot more about the arguments he actually makes out loud than I care about the carefully unstated philosophy that may or may not underlie those ideas.

>You probably also think he's one of the only mathematicians with such a position, not being aware of people like Weyl, Kronecker, Nelson, Vopenka, Poincare etc.
I am well aware of various forms of finitism. I understand and respect the ideas and arguments behind those philosophies.

Wildburger never makes these arguments in any of his (popular) publications, though. His (stated) justifications for his positions all derive from claims like "this definition doesn't work" (which means fuck all and everyone knows it) without further justification, or "this is not acceptable" (because reasons?), or just good old "problematic". And THAT is crankery. I know that there are mathematically meaningful positions similar to his, but he sure doesn't refer to any of those, and I am not at all convinced he understands the difference.

What is more damning is that he has a tendency of hugely misrepresenting the common understanding of mathematics in his (popular) work, creating a strawman that represents the part of standard mathematical foundations as something way more vague than it really is. "The term 'sequence' is not defined"? Really? I can find more examples if I have enough brain bleach to go through a few of his works, but I think you get the idea. For parts of mathematics he doesn't like, he presents the mathematics as a vague confused mess, even when he knows perfectly well (I would hope) that any mathematician at all could clarify his nonsense -- he doesn't present what most mathematicians think to then criticize it, he presents a deliberately incoherent strawman version of it to sell his dislike. And that is a level of crankery that no level of underlying philosophy can fix.

>>12461918
>>12461965
If you two arent too busy sucking each other's cocks, could you put into words what you think is right and wrong about his approach to for example analysis?

Meta numbers are just this faggot trying to rename the reals.

>>12461965
>His (stated) justifications for his positions all derive from claims like "this definition doesn't work" (which means fuck all and everyone knows it) without further justification, or "this is not acceptable" (because reasons?), or just good old "problematic". And THAT is crankery
Give actual examples of him doing this in a context where he does this to the main thing he's talking about (I'm aware of him tangentially mentioning that something doesn't work and that he talks about why in another video, but when he's discussing the main topic of the video he doesn't just do this). It seems like you're just being dishonest.

>>12461994
What a dumbass.
He calls them "meta numbers" because they're not actually numbers and behave nothing like numbers. You can't add them, subtract them or compare them, even in principle. The word "meta" is to distinguish it from other entities in math which actually are numbers and have proper theories for them.
Also he (rightfully) rejects any notions of incomputable and indescribable reals, which you probably believe are "real numbers", so even this basic fact demonstrates that it's not just a renaming of the set and that you're a complete idiot.

>>12461965
>"The term 'sequence' is not defined"? Really?
In his videos he talks about how the word sequence in mathematics is commonly used by people already expecting to know what it means (this is true for example in high school or early undergrad courses), and when they attempt to "define" the word sequence they use the word "set", which is an undefined notion.
In this regard, he is completely right.
>he presents the mathematics as a vague confused mess
Which it is.
>knows perfectly well (I would hope) that any mathematician at all could clarify his nonsense
Then why don't they?
>he doesn't present what most mathematicians think to then criticize it
He does exactly that. He goes over the definitions of a Cauchy sequence or a Dedekind cut and calmly explains why modern mathematicians find them appealing and why they don't actually work.
>he presents a deliberately incoherent strawman version of it to sell his dislike
Like you?

>>12461995
I'm afraid I don't have any specific examples handy. As not-a-fan, I don't keep track of which of his stuff goes in which publications, as you might expect. But if you have a particular video you consider a showcase of his actual ideas and criticisms, rather than a strawman, link it and I can pick it apart in detail.

>>12462010
>You can't add them, subtract them or compare them, even in principle.

By your definition this should be impossible.
pi+pi=2*pi
pi-pi=0

I assume he claims e is a meta number also, then this should also be unknowable

pi>e

>irrational numbers dont exist
>but metanumebrs do, and all numbers you call irrational are akchtually metanumbers
fucking stupid

>>12462024
What you're doing is looking at expressions and applying algorithms for arithmetic that don't generalize to real numbers.
By "you can't add or subtract them" I meant in general there's no way to do it. This is exactly why you're stumped when someone asks you to calculate pi+e.
>then this should also be unknowable pi>e
This doesn't follow. Again, by a metanumber he doesn't mean that the entities are not meaningful or you can't do some arithmetic-like things with them, all he means is that you can't fit them in a general framework of numbers, or at least he doesn't know of a way to do it in a logically sound way. Is this clear to you?

>>12462036
>>but metanumebrs do, and all numbers you call irrational are akchtually metanumbers
Already explained how this is wrong and how this is not at all his position in this post
>>12462010

>>12462022
>But if you have a particular video you consider a showcase of his actual ideas and criticisms, rather than a strawman, link it and I can pick it apart in detail
Sure, try
https://www.youtube.com/watch?v=3cI7sFr707s
Also it's not often you hear someone accuse of of committing a strawman fallacy when favorably explaining the positions of someone they actually like lol.

>>12462040
you can fit them in a general framework of "theory of numbers and meta numbers". numbers are algorithmic in nature while meta numbers require more abstract reasoning. for example there's no finite algorithm for performing meta addition, but that's okay since we're not pretending it has anything to do with addition of numbers.

>>12462020
the meaning of "sequence" is intuitively clear. you don't need to invoke a specific implementation (set theory) to describe/define it.

>>12462056
The fact that many mathematicians (myself included) were genuinely surprised to learn in an analysis class that there "exist" sequences which cannot be described proves that the notion of a general sequence is not at all intuitively clear.

>>12462048
>theory of numbers and meta numbers
Can you explain this theory to me? What do you mean by a general meta number?
The whole point of Wildberger claiming pi is a meta number is that he's no idea how to fit it into a general framework of numbers, which you claim to be able to do. Please enlighten us. What is a general metanumber?

>>12462062
>What is a general metanumber?
a point on the number line which is not a number

>>12462064
But I thought all points on the number line were numbers?

>>12462066
no, only some of them

>>12462045
>Sure, try
It's a long one, gonna be a while.

>>12462071
Take your time. The material can be quite challenging for you, so don't be afraid to pause and think for a while from time to time.

Wildberger is poor's man Doron Zeilberger

>>12462077
Both are based. Why shit on one and praise another?

>>12461965
Based

>>12462040
>pi+e
[eqn]e+\pi \;=\; \sum_{n=0}^\infty \, \left[\frac{1}{n!}+4 \cdot \frac{(-1)^n}{2n+1}\right].\![/eqn]

>>12462092
Ok you've just rephrased the problem to another problem. You have to calculate the sum.

>>12462101
The sum exists and is unique

>>12462101
>You have to calculate the sum.
what do you mean by this?

>>12462104
That's fine and good that you think that, anon. But the question was what is it, not whether or not it exists.
>>12462111
I mean that I want you to go and add those terms together and tell me the answer. Or if that's too complicated for you, I'll ask an infinitely simpler question: is the result you get (after adding up all this unending sequence of terms) rational or not?

>what is 2+3
>The answer exists and is unique!
>Good job Nicolas. Here, have a star.

>>12462116
>I mean that I want you to go and add those terms together and tell me the answer
I can't add infinitely many terms together

>>12462124
Did you expect me to do it for you instead?

>>12462126
no? you're making very little sense now

>>12462127
Why did you provide it as an answer then? You didn't calculate the sum and you didn't expect me to calculate the sum, so who was expected to actually add those terms together?

>>12462128
you didn't explain what do you mean by calculate. we can't add infinitely many terms together as you suggested.

>>12462130
I expected you to add the two numbers e and pi together and give me the answer.

>>12462137
e + pi is the answer. what else do you want?

>>12462139
You just repeated the question. I want the answer. Or if that's too hard for you at least tell me if the answer is rational.

>>12462144
answer is e + pi. we don't know if it's rational.

>>12462152
Let x= pi and y = 2 - pi.
Can you calculate x+y for me?

>>12462160
sure. x + y = e + pi

>>12462162
If this is a joke I don't get it.

>>12462165
why would it be a joke?

>>12462173
I thought it could be a joke because it's obviously wrong. x+y = pi + (2- pi) = 2, no?

>>12462176
I misread. x + y = 2

>>12462119
>What's [math]\frac{1}{3}+\frac{1}{3}+\frac{1}{3}[/math]
>Oh no, the answer is [math]0.\bar{9}[/math], but this number does not exist!
Existence in the context of mathematics is not an ontological problem. Is a true or false statement within the set of usual formal rules

>>12462137
>>12462144
>is e+[math]\pi[/math] irrational
It still is an open problem: https://mathworld.wolfram.com/e.html..
>add the two numbers e and pi together and give me the answer
You can have the answer to any precision you want. What does it mean to have an answer of arbitrary precision? Means exactly this sum: >>12462092, when you haven't stated an error margin initially. The actual infinite sum is never performed, as pic related explain. Why? First, because the actual infinite sequence of digits of pi or e is not known, unlike the infinite sequence [math]0.\bar{9}[/math] that is fully known. Second, because pi and e are useful because of their properties, not because their exact digit expansion, that is know exists and is unique, again because of >>12462092. If you have solved any physics and engineering problem you should know that you don't really need many digits of pi.

>>12462045
>>12461995
>Sure, try https://www.youtube.com/watch?v=3cI7sFr707s
Okay, I have watched most of it (I skipped some of more long-winded stuff). I think it's a good representative sample, which illustrates my point accurately.

Wildberger points out the following characteristics of Cauchy-based real numbers (I skipped some secondary ones):
>1. The meaning of the term "infinite sequence of rationals".
You can see an infinite sequence as a choice function or as an algorithm. Yes, that's correct. The standard view is the choice function, not the algorithm.
>1.1. There are no examples.
Correct. The reals are uncountable and the things you can describe finitely are countable, so whatever you can describe is going to be a small subset of the full space.
>1.2. Any operations with such sequences must involve an infinite amount of time and memory, i.e. they are completely impossible.
Indeed. The reals are uncountable, and you can't do arithmetic on uncountable things.
>2. The Cauchy requirement is ambiguous.
No it isn't. Yes, checking the Cauchy would take an infinite amount of work, which is *inconvenient*, but that doesn't make it ambiguous. It's perfectly unambiguous.
>3. The meaning of "equivalence class" is ambiguous.
No it isn't, same as point 2. Yes, checking whether two sequences are equivalent would take an infinite amount of work. No, that does not make the notion ambiguous.
>5. Show us the arithmatic!
You cannot do arithmetic with uncountable things.

[continued 1/2]

>>12462204
[continued 2/2]
Some of his points here (2, 3) are total bullshit. Points 1 and 5 are correct. So why are they relevant?

Well, Wildberger rejects this definition of the real numbers because because:
>1: This approach is very much in some kind of fairy tale land.
>2: you are actually requiring an infinite amount of work. That is in my view not a proper definition.
>3: [Large set is large.] You are being taught this stuff which doesn't work, which is almost patently ridiculous.
>5:
No arguments given here at all.
>6: Real number arithmetic is just so simple to do isn't it. [...] reason to be highly skeptical of the real numbers. It doesn't work.

Wildberger describes the mathematical background in >>12462204, some of which is valid, and some of which is not. The parts that are not total bullshit are generally accepted as such by most mathematicians, and not seen as in any way wrong. The real numbers are not conceived of by most mathematicians as something you can do arithmetic on, they are seen as something you can do algebra on, and which you can finitely approximate of you want to do arithmetic.

But as for *why he considers the points he made to be a problem*, he only gives the arguments I listed above. Which I think we can fairly summarize as "it doesn't work reeeee", mixed in with ridicule, and no actual arguments.

>>12462178
Do you recognize a little bit of a double standard here? Both problems are asking you to sum supposedly "irrational" numbers but you readily know the answer to one while your answer just repeats the question to the first. You don't know if it's rational. This is because you didn't actually do the calculation in the supposed real number arithmetic for the second one. You appealed to completely finite algorithms of expression manipulation, none of which are possible in general.
A (perhaps more) interesting example is the following.
You can algorithmically define a sequence of rational numbers a_n which goes to 1 if Collatz conjecture is true and to -1 if Collatz conjecture is false. According to standard mathematics, the Cauchy sequence (a_n) defines a unique real number. Let's denote it by x.
Now I ask you to perform two operations
3+x and 3-x.
Now you know one of the answers is 4 and the other is 2, but you don't know which is which! Don't you find this a little bit problematic? What kind of arithmetic is this?

>>12462208
>Do you recognize a little bit of a double standard here?
no, why? we have a standard way of representing natural numbers, so when we know that a number is natural (such as x+y), it's convenient to use this representation.
>Both problems are asking you to sum supposedly "irrational" numbers but you readily know the answer to one while your answer just repeats the question to the first.
no, 2 is simply a more convenient representation of pi+(2-pi) while e+pi is, as far as I know, the best representation of e+pi. (here e and pi refer to the two infinite series)
>You don't know if it's rational.
yeah, it's an open problem
>This is because you didn't actually do the calculation in the supposed real number arithmetic for the second one
what do you mean by calculations?
>You appealed to completely finite algorithms of expression manipulation, none of which are possible in general.
I'm not appealing to no finite algorithms.

>Don't you find this a little bit problematic?
no
>What kind of arithmetic is this?
the one where operations can't be performed using finite algorithms

>>12462204
>Yes, checking the Cauchy would take an infinite amount of work, which is *inconvenient*, but that doesn't make it ambiguous
He explicitly points out the ambiguity by asking whether we also ask for an epsilon given N when we're given the sequence.
This explains what is ambiguous about the algorithmic approach. As for the choice approach, as he explains, the ambiguity comes from asking to do something that we can't actually do: verifying that the sequence is Cauchy is impossible in general because doing an infinite amount of work is impossible. This means that interpreting what is actually meant by definition is not an easy task: there is an ambiguity involved.
The same is with your point 3.
>No arguments given here at all.
You literally listed a number of arguments while proclaiming he gave no arguments. You might not like the arguments, you might disagree with them, like Wildberger disagrees with arguments given by modern mathematicians, but that doesn't change the fact that they're arguments.
>something you can do arithmetic on, they are seen as something you can do algebra on
What do you even mean by that? What's the difference?
>and which you can finitely approximate of you want to do arithmetic.
Are you saying you can finitely approximate real numbers. Then please approximate up to 1/2 error the answers to the problem given in
>>12462208

>But as for *why he considers the points he made to be a problem*, he only gives the arguments I listed above
He gives many more arguments in his video series and the arguments he gave here are perfectly valid. I've yet to see you refute them.

>>12462237
>what do you mean by calculations?
The calculations of adding two real numbers as they actually are in a general way, not manipulating their convenient representations as you see fit.
>I'm not appealing to no finite algorithms.
Then how did you calculate the sum? Did you perform an infinite amount of work?
>the one where operations can't be performed using finite algorithms
Ok, I forgot to mention that you're also allowed to use infinite algorithms if you want, or whatever method you want, not necessarily an algorithm. I can see where the issue lies, you thought you were restricted by using finite algorithms. So please, go ahead, use any method you like, not necessarily finite, nor an algorithm, to calculate
e+pi and tell me whether or not the answer is a rational number. Surely you believe the arithmetic with real numbers is possible, so I'll be waiting for your answer.

>>12462253
I don't understand what you mean by calculate e+pi. maybe you can show me, can you calculate 3+2*10 please?

>>12462256
>can you calculate 3+2*10 please
Yes, sure. 3+2*10 = 3+ 20 = 23. Now do a similar thing with your "real numbers", which you believe makes so much sense.

>>12462259
anon, 23 is literally syntactic sugar for 2 + 3*10. you have just repeated the question.

>>12462264
*3 + 2*10

>>12462264
Do you want the actual natural number that 23 stands for? Which implementation? Here, how about the interpretation of a string of strokes?

23 = |||||||||||||||||||||||

>>12462271
real numbers can't be represented or implemented as strings of strokes so this method of "calculation" doesn't work.

>>12462274
Well then if not strings of strokes, pick whichever other implementation you like. Surely you think e+pi stands for something, so show me what is it.

>>12462283
the infinite series in >>12462092

>>12462286
Oh, I thought it's just an expression that refers to some real number, not the real number itself. Now what does a general rational number look like in your implementation? After figuring this out, answering whether or not pi+e is rational will be a piece of cake! Maybe you could publish. This conversation will have been extremely productive.

>>12462293
>Now what does a general rational number look like in your implementation?
p/q
>After figuring this out, answering whether or not pi+e is rational will be a piece of cake!
not really, it's an open problem

>>12462302
But anon, perhaps you haven't realized that you've already solved the problem! So ingenious of you! You've constructed an implementation of real numbers where e+pi corresponds to the expression
[math]\left[\frac{1}{n!}+4 \cdot \frac{(-1)^n}{2n+1}\right].\![/math]
and all rational numbers correspond to expressions p/q. Since these expressions are different, it follows that e+pi is irrational. How amazing!

>>12462309
different expressions might represent same number

>>12462204
>which is *inconvenient*
I would say it's more than inconvenient. A number system without arithmetic sounds quite ridiculous at face value.

>You cannot do arithmetic with uncountable things.
And you don't see this as a problem because you believe that just because you write an expression that would require an infinite amount of work to compute somehow means that you can manipulate that object e.g. infinite sums or infinite sets.

>>12462206
>The parts that are not total bullshit are generally accepted as such by most mathematicians, and not seen as in any way wrong.
Yes, most mathematicians also believe that writing an expression involving an infinite amount of work means that they've somehow encapsulated it and then can proceed to manipulate it.

>Which I think we can fairly summarize as "it doesn't work reeeee"
No, you clearly missed the point if that's all that you got out of this.

Now, I will preface this by saying I personally believe in the validity of real numbers. However, Wildberger's criticisms are completely reasonable; you just need to put yourself in the shoes of someone who rejects the axiom of infinity. This does not make his math incorrect, it likely just restricts what he can do.
And he does bring up some great philosophical points. When you write an infinite sum, you haven't done the leg work to actually consider it as an object. Sure you can consider approximations up to whatever degree you want and sure it may be that the number is converging to something (in a Cauchy sense), but can you actually say that an infinite sum as a whole is pi?
The answer isn't obviously clear; you probably think it is since you accept real numbers so almost by necessity you are a platonist, but others like Aristotle or Wittgenstein (https://plato.stanford.edu/entries/wittgenstein-mathematics/#InteExteFictSymbSetTheo)) would strongly disagree.
(cont)

>>12462317
But you said these expressions are your chosen implementation of the numbers, just like I did with strings of strokes, where different strings of strokes correspond to different numbers.

>>12462327
Based infinitist. I'm also not prepared to let go of real numbers and will continue to do mathematics with them, yet recognize Wildberger's point of view as very reasonable.
We need more people like you in the world. So few people seem to recognize the subtleties involved in these issues.

>>12462330
>But you said these expressions are your chosen implementation of the numbers
nope I just told you what it *looks* like. it's all implemented as cauchy sequences

>>12462341
No I asked you to give an actual implementation of these real numbers, so I can ask you for example what is 1/2 as a real number and you can point to it and say "here it is!", just like I was able to do with strings of strokes.

>>12462348
1/2 is the class of a_n = 1/2

>>12462360
What is this class? Can you show me like I showed you the number 23?

>>12462366
you can read it in baby rudin if you're genuinely interested

>>12462119
And we can all agree to denote it by 5! wuuu we did it

>>12462327
It isn't at all logically obvious why we should accept infinite objects/doing infinite work as being okay other than the fact that you can represent more numbers/potentially be able to do more things.
At the end of the day, mathematics is a logical endeavor, and the more you assume, the more things you can do (prove). However, considering what we know about our reality and our limits, it isn't at all logically clear we should fully accept an axiom of infinity. That's why the axiom of infinity, while being completely divorced from reality (we can never do an infinite amount of work), is such an alluring proposition.

I personally believe math with an axiom of infinity is just another system with different assumptions where you can do different things. But I wouldn't be so quick to dismiss what Wildberger is doing as nonsensical.
And if nothing else, his unique perspective can potentially give you a different way of viewing things (e.g. rational trigonometry, his extension of rational numbers to a protective infinity, etc.).

>>12462336
>So few people seem to recognize the subtleties involved in these issues.
100% agree. Glad to see I'm not alone :)

>>12462397
*projective infinity

>>12462375
I've already read it, and by the way it doesn't deal with Cauchy sequences but rather does it with Dedekind cuts (which doesn't work either).

>>12462411
then you know what equivalence classes are, right?

>>12462397
>And if nothing else, his unique perspective can potentially give you a different way of viewing things (e.g. rational trigonometry, his extension of rational numbers to a protective infinity, etc.).
I think it's very good that he does this because as he correctly points out, a lot of things that we view as requiring the completed infinite are completely finitistic in nature. Bringing this out to light makes it a lot clearer what actually is going on and also makes the logical soundness of these things much firmer. I can just wish there were more people looking at cool things in mathematics and asking whether they can be justified in a completely finitistic basis, hence making them much more logically stronger in the process.

>>12462416
I know they're supposed to be a "set" satisfying certain conditions. I can't say to know what an equivalence class is because I'm genuinely baffled as to what a set is. Perhaps you'd like to explain?

>>12462440
it's just a collection of cauchy sequences

>>12462101
>You have to calculate the sum.
why?

>>12462466
How many?

>>12462514
Because you want to get the answer and then check whether or not it's rational. Just looking at the sum is not enough to do that, you have to actually calculate it.

>>12462518
The cardinality of the reals

>>12462440
It's a partition of a set, I mean subsets that the union gives you the total but are disjoint

>>12462551
This is because (it'a an easy proof) equivalence clases are equal or disjoint. If you open a first semester algebra book you will find an isomorphism between partitions and equivalences clases induced by equivalence relations

>>12462543
And what is it? Where is it in the ordinal hierarchy?

>>12462551
And what is a set?

>>12462532
>Because you want to get the answer
why?

>>12462636
Because that was the question.

>>12462584
What do you want it to be?

>>12462078
>praise
more like dumb & dumber

>>12462518
Infinity

>>12461839
>every finitist is a crank
Brainlet detected

>>12461839
i love how atheists always turn to obscurantism when they don't understand something

>>12463350
But according to you, there are many "infinities", one for every cardinal number. So the question is: which infinity is it?

>>12462902
I want it to be a well-defined logically sound concept I can understand. Unfortunately nobody has offered such a definition for me.

>>12463500
yeah, that's indeed a good question

>>12463515
That's an infinitard cope. It's not a good question, it's a completely meaningless question. After results by Cohen & Godel you should have realized this, like set theorists such as Feferman.

>>12463579
so?

>>12463585
So this means "the real numbers" don't actually exist, because if they did CH would be a meaningful question.

>>12461651
PRAISE THE HOLY BURGER!

>>12461651
quick rundown of this shit?

>>12463503
>well-defined logically sound
what are you asking for
it's an axiomatically defined object with some operations defined with it and it hasn't been shown to be inconsistent
that's the best we can do thanks to godel. you can't prove its consistency unless it's inconsistent

>>12463871
>that's the best we can do thanks to godel
Wrong. You can have maths that is PROVABLY consistent. The reason that you can't prove consistency of theories about the completed infinity, is because, as Godel showed, questions about the completed infinity are MEANINGLESS. They don't refer to anything, there is no "true set of natural numbers". It's just a fairy tale.
>it's an axiomatically defined object
An axiomatically defined object would be something like a the definition of a (finite) group.
Your "axiomatic definition" is not actually a definition it all. What it does is to say "let's PRETEND there exist such an object" without actually explaining what it is or how to deal with it. Such a "definition" isn't worth shit and is completely meaningless, unless you can actually show what it means, which you can't, by Godel.
Also the cope that "at least we haven't proven its inconsistency" so laughable. Godel showed you can have as many different consistent definitions of arithmetic as you want, which give you different answers to supposedly "concrete" questions if you believe in the completed infinite, as long as one of the axiomatic systems are consistent. There is no real reason to prefer one over the other.
You think Godel showed inherent limitations of mathematics, but that's only because you have been indoctrinated to believe in the completed infinite, like I was at some point in time. Once you get rid of such superstitions, Godel's result become much clearer and you realize that you have simply been mistaken about what "real mathematics" is.

>>12463756
>mathematicians struggled to model the continuum
>wanted a system of arithmetic to include pi and e, and to make sense of infinite sums
>people start getting angry at analysts for talking bullshit and not making any sense with their "infinites", even prominent geniuses like Abel accuse them of being charlatans and not making any sense.
>analysts start looking for a way to make their theories logically sound
>develop set theory in which asserts that infinity can be completed without actually proving it
>claim it properly explains what they're actually doing when they're manipulating infinities
>actually it doesn't explain shit, people discover paradoxes and logical inconsistencies in this set theory
>best mathematicians at the time like Poincare, Kronecker recognize set theory as the joke that it is.
>logicians upload a "patch" to the set theory where now the word "set" is actually meaningless and all you're doing in this "set theory" is just manipulating formulas according to some predetermined rules
>mathematicians naturally assign semantics to concepts in set theory and discover that obvious bullshit follows from this set theory, like the existence of "arbitrarily large infinites", or numbers that can't be described in any way, and suddenly you can't add rational numbers anymore, not even natural numbers can be added with this "set theory", also you get objects without any size, and you can decompose a sphere into many different spheres of the same kind.
>big battle develops in the foundations over the meaning of set theory and its place in mathematics. Hilbert vs Intuitionists vs other schools somewhere in between. People start asking whether "for all natural numbers n, something is true" is even a meaningful proposition, and what does it take to prove or disprove such propositions.

>>12463969
>the completed infinite seems more and more dubious to people investigating the foundations, many prominent mathematicians interested in foundations realize that this whole debate arises because the inherent ambiguity involved in the concept of the "completed infinite".
>Godel confirms their suspicious by proving that if any axiomatization of the completed infinite is consistent, then there are many other mutually exclusive extensions of this system which are also consistent, and which answer differently to the question of whether a given algorithm halts, with no real way to distinguish between them.
>demonstrates that it's actually impossible to define the true completed infinite, and that questions about it are actually meaningless
>multiple questions in set theory that were once thought to be meaningful, even about objects as simple as real numbers, turn out to be meaningless. Cohen shows the question of how big the set of real numbers is is impossible to answer. Other logicians show that similar questions, such as the existence of different models of the real line with similar properties are also unsolvable.
>mathematicians keep clinging to this set theory and being unaware of the foundational issues and debates, comfortable assign semantics to their meaningless statements, deluding themselves.
>Current mathematics is dominated by Hilbertian approach, which is crypto-Platonism. Hilbert won out because his mathematics "looks simpler" at the cost of being meaningless. Mathematicians completely unaware that a lot of their subject can be put on logically firm meaningful foundation, such as Wildberger did with trigonometry.
>People like Wildberger who try to point this out and try to improve the state of math get called "cranks", as opposed to the believers in the completed infinite.

>>12463974
and I say...

PRAISE THE HOLY BURGER!

For He shall lead us out of the darkness inhabited by those...those...THOSE GOD CURSED INFINITY LOVING SODOMITES!

..and into enlightenment of the ONE TRUE FINITE FAITH!

Amen.

>>12463503
>I want it to be a well-defined logically sound concept I can understand. Unfortunately nobody has offered such a definition for me.
because its a primitive notion you fucking retard
you cant define a set in terms of anything simpler, since there is nothing simpler than it
learn some goddamn foundations before you start talking shit about it

>>12461651
I have terrible mixed feelings...
I'm beginning to suspect he actively censors discussions in the comments of his videos: There was a heated discussion with ron maimon in the comments on one of his videos which was really awesome to read, but none of ron's comments are there anymore. I don't know if njw removed them intentionally, but I really hope that's not the case. I've loved wildberger ever since /sci/ introduced me to him.

>>12461659
Andrew Wakefield
Luc Montagnier
Didier Raoult
All more academically credited than him, all pseudo-science retards.
>>>/x/

>>12463969
>infinity can be completed
Strawman

Actual infinity [math]\not=[/math] completed infinity.

>>12463969
>>12463974
>>12463904
>>12462397
>>12462327
Write an expository paper on this subject already. Would be glad to read it.

>>12461651
It's just a metaphor.
Through it really sounds like he's getting close to understanding the real numbers maybe he'll get there one day

>>12462101
if e and pi arn't numbers then why can you approximate them in terms of rationals?
e is simply the name give for an infinite series
it really doesn't matter if infinity "exists". We assume infinity exists and there is no good reason to drop it. You may point to "paradoxes" "caused" by infinity but any system of axioms will generate paradoxes. Remove induction remove law of excluded middle and you get the same shit. It's just computable now.

>>12462119
Would you say the same for a difficult recursive function.

>>12462119
what do you think the symbol "5" is defined as retard

>what is 5?
its 1+1+1+1+1
>now calculate it
5

>what is pi+e
this sum
>now calculate it
pi+e

>>12462655
the answer was already stated

>>12466851
I'm wrote the last two posts you quoted.
Take a look here:
>>12466642
If you want more details about what I believe Wildberger would say (I wrote all the posts from his point of view in that thread). Not a paper, but I definitely think it's more comprehensive about what he'd say (I'm almost solely using things from his videos).

>>12466917
Yes. Too many people like to make the unwarranted assumption that all primitive recursive functions are total. While this makes sense in the ideal world of infinitary mathematics of the completed infinite they like to deal with, after some point it stops having any meaning and it's nontrivial to figure out what is actually meant by these "functions".

>>12466334
I've heard of youtube comment removal shenanigans before where the comments disappear without the author actually removing them, so I wouldn't immediately assume they were removed by Wildberger. There could be a more charitable interpretation of what happened.
As to the particular discussion with Ron Maimon, do you remember the gist of their arguments? What was Wildberger's opinion on Ron Maimon's suggestion?

>>12461651
>mfw I was dumb enough to try and explain his shit to my math teacher in high school 9 years ago
I was fucking dumb

>>12467374
Why dumb? Because math teachers refuse to listen?

>>12467367
>As to the particular discussion with Ron Maimon, do you remember the gist of their arguments? What was Wildberger's opinion on Ron Maimon's suggestion?
lol here I compiled it for you pic-related

>>12467595
BTFO

>>12467595
This Ron Maimon guy is quite misguided. I will write up my thoughts later.

>>12466334
It's pretty obvious the other guy realized his error and no longer wanted those comments associated with his name in public.

>>12467749
what error?

>>12467595
LOL Wildberger can only repeat his canned responses when his lies are exposed.

>muh introductory textbooks

>>12467595
His example of a "noncomputable RN" is a joke. What he actually does boils down to providing an algorithm that generates a sequence of strings of digits in which some digits can change from 0 to 1 but never from 1 to 0.
There is NO REASON to think this is a "number" of any kind. Any belief in such a "number" that this sequence approaches can only be supported by the dogma of completed infinite through taking limits which require infinite amount of works, and also the belief that the question of whether an algorithm halts is even meaningful.
If this is what he calls "explicitly showing him an uncomputable RN" then "0 if Continuum hypothesis is true and 1 if Continuum hypothesis is false" must also be an explicit natural number to him. How ridiculous!
His "proof" of the Fundamental Conjecture of Algebra is a joke as well. He mentions Bishop's book on constructive analysis, and surprise surprise, it doesn't actually prove the theorem Ron Maimon thinks it does.
The theorem picks some circle on the complex plane such that the polynomial is bounded below in this circle. It uses the lemma which gives you a sequence of circles with radius converging to 0 at the rate 1/n and the polynomial's "zero" is inside of the circle. It doesn't satisfy Wildberger's formulation of the theorem because it doesn't give explicit bounds to Q(p(z)).
Also Wildberger is completely correct about the axiom of choice. Ron Maimon talks here about measure theory, which is completely different from what Wildberger is talking about and isn't actually about randomness. The statement of Axiom of Choice is exactly about this, you can pick an element from each set in a collection, and so according to AC you can go on picking until you picked infinitely many elements, which is ridiculous. In almost every application of Axiom of Choice I've seen, the (pseudo)semantic idea behind the proof is picking infinitely many things at once.

>>12461901
So what? Ted was great mathematician.