/sci/ - Science & Math » Thread #12893590

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Anonymous Sun 28 Mar 12:01:40 2021 No.12893590 View Reply Original Report

Quoted By: >>12896063 >>12897093 >>12900509 >>12900637 >>12900655

Teach the controversy.

Anonymous

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Anonymous Sun 28 Mar 2021 12:04:24 No.12893592 Report

Quoted By: >>12893593 >>12893919

Spread the Finitist gospel all over the world.

Anonymous

Anonymous Sun 28 Mar 2021 12:05:14 No.12893593 Report

Quoted By:

>>12893592
People need to know the bad news.

Anonymous

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Anonymous Sun 28 Mar 2021 12:06:51 No.12893597 Report

Quoted By: >>12897093

>They hated him because he told them the true.

Anonymous

Anonymous Sun 28 Mar 2021 12:25:11 No.12893632 Report

Quoted By: >>12893637 >>12897093

What does wildberger think about infinitesimals?

Anonymous

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Anonymous Sun 28 Mar 2021 12:26:12 No.12893634 Report

Quoted By:

>his nature is to lie. If his mouth is moving, he is lying. He is the original liar and, therefore, the father of lies. Every lie was and is birthed in him. However, deception is all he has in his arsenal against Finitists.

Anonymous

Anonymous Sun 28 Mar 2021 12:28:51 No.12893637 Report

Quoted By: >>12894526

>>12893632
He has a video on them, quoting from the description:
Is there a modern way to establish these mysterious quantities without resorting to philosophical or logical hand-waving? Yes there is, and it involves yet another application of the remarkable Dihedron algebra that we introduced in the previous Famous Math Problem 21 on the true complex numbers.

Anonymous

Anonymous Sun 28 Mar 2021 13:47:25 No.12893786 Report

Quoted By: >>12893879

>an introductory math text fails to define R to the satisfaction of a professional mathematician

Anonymous

Anonymous Sun 28 Mar 2021 13:48:39 No.12893789 Report

Quoted By: >>12893792 >>12893989 >>12897093

I can’t write down the decimal expansion of 1/3, does it also not exist?

Anonymous

Anonymous Sun 28 Mar 2021 13:50:13 No.12893792 Report

Quoted By: >>12893850

>>12893789
It can be expressed as a ratio of integers.

Anonymous

Anonymous Sun 28 Mar 2021 14:08:32 No.12893850 Report

Quoted By:

>>12893792
Not him, but does the decimal expansion of 1/3 exist?

Anonymous

Anonymous Sun 28 Mar 2021 14:18:03 No.12893879 Report

Quoted By: >>12893929 >>12897093

>>12893786
Yeah I don't know what this proves. Conway's book on Numbers and Games says Landau's construction takes 100 pages and in order to be complete would require a few hundred more. What intro analysis book would waste 300 pages on this? Of course there will be no satisfactory definition.

Anonymous

Anonymous Sun 28 Mar 2021 14:30:19 No.12893919 Report

Quoted By:

>>12893592
PRAISE THE HOLY WILD BURGER!

Anonymous

Anonymous Sun 28 Mar 2021 14:33:44 No.12893929 Report

Quoted By: >>12893935 >>12897093

>>12893879
Your days of preaching infinity are over, SODOMITE! We begin a new and enlightened era of finitism! We shall purge your filth from the text books.

AND WE SHALL RECLAIM CONSTANTINOPLE FOR THE ONE TRUE FAITH!

Anonymous

Anonymous Sun 28 Mar 2021 14:35:27 No.12893935 Report

Quoted By: >>12893946

>>12893929
But isn't god infinite?

Anonymous

Anonymous Sun 28 Mar 2021 14:39:59 No.12893946 Report

Quoted By:

>>12893935
We of the ONE TRUE FINITE FAITH dont take kindly to strangers poking around and asking awkward questions.

Anonymous

Anonymous Sun 28 Mar 2021 14:58:32 No.12893989 Report

Quoted By: >>12897093

>>12893789
Geometric series are fine according to him, since he vets p-adic computation

Anonymous

Anonymous Sun 28 Mar 2021 17:39:54 No.12894526 Report

Quoted By: >>12894650

>>12893637
yeah he's fine with purely algebraic definitions of infinitesimals (and infinity)

Anonymous

Anonymous Sun 28 Mar 2021 18:19:21 No.12894650 Report

Quoted By: >>12895868 >>12897093

>>12894526
Does he care that we don’t know if pi+e can be expressed as a ratio of two integers? Or is that just a meme?

Anonymous

Anonymous Sun 28 Mar 2021 23:15:06 No.12895868 Report

Quoted By: >>12896059

>>12894650
I think he cares more that no closed form exists other than pi + e.

Anonymous

Anonymous Mon 29 Mar 2021 00:15:54 No.12896059 Report

Quoted By: >>12896083

>>12895868
does he care that the closed form for 1 / 2 is 1/2?

Anonymous

Anonymous Mon 29 Mar 2021 00:17:33 No.12896063 Report

Quoted By: >>12900623

>>12893590
Which video is this from?

El Arcón

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El Arcón Mon 29 Mar 2021 00:21:53 No.12896073 Report

Quoted By: >>12896306 >>12897093 >>12898154 >>12898249 >>12899422 >>12900783

The controversy is that Norman assigns greater significance to his own opinion that he does to the opinions of people that are far more respected in his field than he is.

Anonymous

Anonymous Mon 29 Mar 2021 00:26:40 No.12896083 Report

Quoted By: >>12896090

>>12896059
No, because negative numbers are defined by (equivalence classes of) 2-tuples of naturals, just like how (positive) rationals are.

Anonymous

Anonymous Mon 29 Mar 2021 00:31:16 No.12896090 Report

Quoted By: >>12896110

>>12896083
how does that relate to 1 divided by 2 having a closed form of 1/2? isn’t that the same as saying e plus pi has a closed form of e+pi?

Anonymous

Anonymous Mon 29 Mar 2021 00:40:35 No.12896110 Report

Quoted By: >>12896116

>>12896090
3 divided by 6 also has a closed form of 1/2. There's an amount of work you can do to put a rational number in lowest terms, given in terms of coprime integers.
Hell, you can get at algebraic numbers if you find their minimal polynomial.
No such work exists for transcendentals.

Anonymous

Anonymous Mon 29 Mar 2021 00:42:50 No.12896116 Report

Quoted By: >>12896130

>>12896110
but what can you do with 1/2? isn’t e+pi like a reduced form of transcendental? no amount of work will reduce either of those

Anonymous

Anonymous Mon 29 Mar 2021 00:46:33 No.12896130 Report

Quoted By: >>12896133

>>12896116
You can add 1/2 with other rational numbers and get a closed form. 1/2 + 1/3 = 3/6 + 2/6 = 5/6. The result is still given by two numbers, even though you performed addition with four.

Anonymous

Anonymous Mon 29 Mar 2021 00:47:39 No.12896133 Report

Quoted By: >>12896137

>>12896130
how is that different than e+pi + 2e+3pi = 3e+4pi ?

Anonymous

Anonymous Mon 29 Mar 2021 00:49:47 No.12896137 Report

Quoted By: >>12896146

>>12896133
Every other number is not given in terms of e or pi unless you assume the reals

El Arcón

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El Arcón Mon 29 Mar 2021 00:50:58 No.12896141 Report

Quoted By:

Anonymous

Anonymous Mon 29 Mar 2021 00:52:55 No.12896146 Report

Quoted By: >>12896154 >>12896166

>>12896137
but i mean like for 1/2. it’s a lowest form you can’t do anything with it. 1 divided by 2 doesn’t give you anything other than 1/2. bear with me here but isn’t e+pi the exact same thing? it’s like a lowest form you can’t do anything with.

Anonymous

Anonymous Mon 29 Mar 2021 00:55:33 No.12896154 Report

Quoted By: >>12896158

>>12896146
pilpul

Anonymous

Anonymous Mon 29 Mar 2021 00:57:16 No.12896158 Report

Quoted By:

>>12896154
> Pilpul is the Talmudic term used to describe a rhetorical process that the Sages used to formulate their legal decisions.
i’m sorry?

Anonymous

Anonymous Mon 29 Mar 2021 00:59:01 No.12896166 Report

Quoted By: >>12896179 >>12896235

>>12896146
I get what you mean, but how do you propose getting either e or pi in terms of natural numbers?
If you use some series form, all you get are rational numbers until you assume that your infinite sum has "finished", and that's a pretty strong assumption. Not to mention that series are the opposite of n-tuples

Anonymous

Anonymous Mon 29 Mar 2021 01:01:16 No.12896171 Report

Quoted By: >>12897093

Found out last week that Wildberger helped prove a particular case of Horn's conjecture in 1993. The conjecture was proved by Tao in 1998.
>Wildberger forever btfo

Anonymous

Anonymous Mon 29 Mar 2021 01:04:51 No.12896179 Report

Quoted By:

>>12896166
i’m not that advanced, i was more thinking about it like maybe the reason e+pi doesn’t combine into something different is because they have no common “factors” like 2 and 3 don’t.

Anonymous

Anonymous Mon 29 Mar 2021 01:31:32 No.12896235 Report

Quoted By: >>12896284

>>12896166
so i was thinking a bit more, 2+3 can be reduced to 5 but 2/3 can’t be reduced to anything but 2/3. so can we say that two natural numbers can’t be combined by division unless they have a common factor, and two irrational numbers can’t be combined by addition (or division or anything else) unless they have a common factor? if this is true, does it matter?

Anonymous

Anonymous Mon 29 Mar 2021 01:51:19 No.12896284 Report

Quoted By: >>12896315

>>12896235
"Irrational" isn't quite strong enough. Let's focus on algebraic numbers first.
If you have the roots of some polynomials and combine them in some fashion, you can construct a new polynomial that has a root at that combination. For example, WolframAlpha tells me that the expression $\sqrt 2 + \sqrt 3$ has minimal polynomial $x^4 - 10 x^2 + 1$ . All the coefficients of that polynomial are still integers, even if it's more difficult to express than $x^2 - 2$ .
Analytic numbers like pi and e on the other hand are much harder to work with. All we really have are series, and they come from observations of operators. For example, e is nice because its exponential function is invariant under the derivative; pi is nice because it can be seen in the integral $1 \over 1 + x^2$ , which has a very simple series. But it's very difficult to express these numbers in any other way, at least not in a tidier way like in algebra.

Anonymous

Anonymous Mon 29 Mar 2021 01:58:32 No.12896306 Report

Quoted By:

>>12896073
spoken like the good little cock sucker that you are

Anonymous

Anonymous Mon 29 Mar 2021 02:03:01 No.12896315 Report

Quoted By: >>12896380

>>12896284
wow this is really cool, integrate -infinity to infinity 1/(x^2+1) is pi? what?

Anonymous

Anonymous Mon 29 Mar 2021 02:34:14 No.12896380 Report

Quoted By:

>>12896315
Well yes, but it's nicer if you don't immediately go integrating over the whole function.
$ {1 \over 1 + x^2} = 1 - x^2 + x^4 - x^6 + ... = \sum_{i=0}^\infty {(-1)^nx^{2n}} $
Formally integrating term-by-term gets you
$ <script type="math/tex; mode=display"> \int {1 \over 1 + x^2} = x - {x^3 \over 3} + {x^5 \over 5} - ... = \sum_{i=0}^\infty {(-1)^n x^{2n+1} \over 2n+1} $
But we also know this integral should evaluate to arctan from trig identites (which also have their own series)
$ \int {dx \over 1 + x^2} = \int{\sec^2(u)du \over 1 + \tan^2(u)} = \int du = u + C = \arctan(x) + C $
Since arctan(0) = 0, choosing C = 0 coincides with the formal series above, meaning that
$ \phantom{{\pi \over 4} =,}\arctan(x) = \int_0^x{dt \over 1 + t^2} = \sum_{i=0}^\infty {(-1)^n x^{2n+1} \over 2n+1} \\ {\pi \over 4} = \arctan(1) = \int_0^1{dt \over 1 + t^2} = \sum_{i=0}^\infty {(-1)^n \over 2n+1} $
The exceptional part of this is "plugging in 1" for a formal series, but it turns out to be justified.

Anonymous

Anonymous Mon 29 Mar 2021 05:03:52 No.12896756 Report

Quoted By: >>12897107 >>12897302 >>12897309

Which current philosophers/logicians best represent the finitist view? Ones that publish peer reviewed papers not youtube videos, please.

Anonymous

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Anonymous Mon 29 Mar 2021 07:16:03 No.12897093 Report

Quoted By: >>12899092 >>12899138

>>12893590
>>12893597
>>12893632
>>12893789
>>12893879
>>12893929
>>12893989
>>12894650
>>12896073
>>12896171

Anonymous

Anonymous Mon 29 Mar 2021 07:23:28 No.12897107 Report

Quoted By:

>>12896756
>Ones that publish peer reviewed papers not youtube videos, please.
Idiot. There may be some, but in general you won't find any good papers challenging a dogma that got past review, that's what makes it a dogma. If you aren't competent to evaluate a thing yourself, you have no future in mathematics, or any sciences really.

Anonymous

Anonymous Mon 29 Mar 2021 09:02:05 No.12897302 Report

Quoted By:

>>12896756
Bendegem_1993_How Infinities Cause Problems in Classical Physical Theories.pdf

How Some Infinities Cause Problems in Classical Physical TheoriesDavid Atkinson and Jeanne PeijnenburgUniversity of GroningenThe NetherlandsPublished in: Patrick Allo and Bart Van Kerkhoeve (eds.)Modestly radical or radicallymodest. Festschrift for Jean Paul Van Bendegem on the Occasion of his 60th Birthday.London: College Publications, (2014) 1-10.AbstractIn this paper we review a 1992 excursion of Jean Paul Van Bendegem into physics, ‘How InfinitiesCause Problems in Classical Physical Theories’, in the light of two later models concerning collidingballs, of P ?erez Laraudogoitia and of Alper and Bridger, respectively. We show that Van Bendegemanticipated the model of Alper and Bridger by six years, but we also argue that his conditions for theavoidance of problems in these models are not entirely adequate. For although a veto on actual infinityseems to be required, allowing a potential infinity remains a viable option.Keywords: Zeno balls, finitism, potential infinity.1 Finitism in Classical MechanicsWe all know it: Jean Paul Van Bendegem does not like infinity. In his view, both mathematicsand physics can do extremely well without the concept of an actual, or even of a potentialinfinity. And although he realizes that there is a downside to relegating infinity to the scrapheapof mathematical history, he has always insisted that the advantages outweigh the drawbacks.Far be it from us to question the feasibility of Jean Paul’s program: his ideas contain manyvaluable insights that should be taken seriously.

Anonymous

Anonymous Mon 29 Mar 2021 09:03:08 No.12897306 Report

Quoted By:

We do not challenge the consistency of thestrict finitist reconstruction of large parts of mathematics; nor have we the temerity to denythat infinity has given rise to many a headache for the physicist. Indeed, we concur with hisclaim that:“. . . infinities cause all sorts of bizarre problems in the framework of classical me-chanics.” (Van Bendegem 1992, p. 33).Yet we will argue that, in classical mechanics, only actual infinities give rise to difficulties, whilepotential infinities are not only harmless, but in fact quite useful. That explains the title ofour paper, which differs by only one word from the title of Van Bendegem’s cited 1992 paper,‘How Infinities Cause Problems in Classical Physical Theories’.

Anonymous

Anonymous Mon 29 Mar 2021 09:06:51 No.12897309 Report

Quoted By: >>12897317 >>12897368

>>12896756
HOW INFINITIES CAUSE PROBLEMS IN CLASSICAL PHYSICAL THEORIES

Jean Paul Van Bendegem

Introduction

Although it may sound as some sort of confession, I must warn the reader that I am a strict finitist. I hold the position that mathematics can do (extremely) well without the notion of infinity, whether actual or potential. As to the technical feasibility of such an undertaking, I must refer the reader to Van Bendegem [1987], [1992] and [1993a]. As it happens, this is not the subject of this paper, it is therefore not important whether the idea of strict finitism is ludicrous or not. The subject that concerns me here is how well "the other side" is doing. Let me clarify this last statement. Surely it must be an additional argument in support of strict finitism, if it can be shown that within the classical infinitary theories themselves these infinities give rise to rather serious problems. As I already indicated, I will not discuss this problem from within mathe-matics, but instead I will concencrate my efforts on one of mathematics most beautiful and most successful applications: physics. In particular, classical Newtonian mechanics is the main subject I want to deal with. The aim of this paper is to show that infinities cause all sorts of bizarre problems in the framework of classical mechanics. The core problem is the loss of determinism. To be quite clear about the matter, what I do not show is that all infinities should be eliminated in order to restore deter-minism. Actually, I will mostly deal with infinities "in the large" and not "in the small". It is thus not a defense of strict finitism (in certain parts of physics), as said, it just adds some other arguments in its favour. On the conceptual level, I will use and rely on a theoretical device

Anonymous

Anonymous Mon 29 Mar 2021 09:08:25 No.12897317 Report

Quoted By:

>>12897309
that probably most philosophers have declared obsolete: supertasks1• To be quite honest, until the publication of a paper by Victor Allis and Teunis Koetsier [1991], I shared this attitude. However, having read the Allis-Koetsier paper, I was quite astonished to see that (apparently) the last word had not been said or written about supertasks. In fact, this paper will add some new ideas to the subject. Thus, it can just as well be read as the "re-opening" of a classified subject.

Anonymous

Anonymous Mon 29 Mar 2021 09:19:49 No.12897333 Report

Quoted By: >>12897335

REFERENCES

Vrije Universiteit
Brussel Belgium

Victor ALLIS and Teunis KOETSIER: "On Some Paradoxes of the Infinite", The British Journal for the Philosophy of Science, 42, 2, 1991, pp. 187-194.

John D. BARROW: Pi in the Sky. Counting, Thinking, and Being. Ox-ford University Press, Oxford, 1992.
JohnEARMAN: A Primer on Determinism. Kluwer Academic Publisher, Dordrecht, 1986.

---------: World Enough and Space-Time. Absolute versus Relational
Theories of Space and Time. MIT, Cambridge, Mass., 1989.

Tom ETTER: "Zeno Ball", ANPA-West, Volume 3, number 1, 1992, p. 5.

David GALE:-"An Indeterminate Problem in Classical Mechanics", American Mathematical Monthly, May 1952, pp. 291-295.

Adolf GRUNBAUM: Modern Science and Zeno 's Paradoxes. Allen and Unwin, London, 1968.

Adolf GRUNBA UM: Philosophical Problems of Space and Time. Reidel, Dordrecht, 1973.

John NORTON: "The Hole Argument". In: Arthur FINE & Jarrett LEPLIN (eds.): PSA 1988, volume 2. PSA, East Lansing, 1989, pp. 56-64.

Roger PENROSE: The Emperor's New Mind. Concerning Computers, Minds, and the Laws of Physics. Oxford University Press, Oxford, 1989.

Christopher RAY: Time, Space and Philosophy. Routledge, London, 1991.

Wesley C. SALMON (ed.): Zeno 's Paradoxes. Bobbs-Merrill, Indianapo-lis, 1970.

Ian STEWART: Does God Play Dice? The Mathematics of Chaos. Black-well, Oxford, 1989.

Jean Paul VAN BENDEGEM: Finite, Empirical Mathematics: Outline of a Model. Werken uitgegeven door de Faculteit Letteren en Wijsbe-geerte, R.D.Gent, volume 174, Gent, 1987.

---------: "Strict Finitism Meant to Please the Anti-Finitist", ANPA-West, Volume 3, number 1, 1992, pp. 6-17.

Anonymous

Anonymous Mon 29 Mar 2021 09:20:52 No.12897335 Report

Quoted By:

>>12897333
---------: "Strict, Yet Rich Finitism". In: (forthcoming) Proceedings of the First International GtJdel Symposium, Pergamon Press, New York, 1993a.

---------: "Ross' Paradox is an Impossible Super-Task". To appear in The British Journal for the Philosophy of Science, 1993b.

---------and Gustaaf CORNELIS: "Three-Body Collisions and Supertasks: Where Infinities Meet". Submitted for publication, 1993.

Zhihong XIA: "The existence of noncollision singularities in newtonian systems". Annals of Mathematics, 135, 1992, pp. 411-468.

Armen H. ZEMANIAN: Infinite Electrical Networks. Cambridge D niver-sity Press, Cambridge, 1991.

Anonymous

Anonymous Mon 29 Mar 2021 09:31:11 No.12897341 Report

Quoted By: >>12897350 >>12897872

Explain the controversy in terms a midwit with no higher education in mathematics can understand.

Anonymous

Anonymous Mon 29 Mar 2021 09:39:15 No.12897350 Report

Quoted By:

>>12897341
Wildberger at least tries to do this in his videos on Sociology and Pure Mathematics.

Anonymous

Anonymous Mon 29 Mar 2021 09:51:52 No.12897368 Report

Quoted By: >>12897541

>>12897309
Why should mathematics care if it is useful to physical science? If they don't like mathematics they can invent their own system to use. Mathematics doesn't have to correspond to the physical world.

Anonymous

Anonymous Mon 29 Mar 2021 11:19:56 No.12897541 Report

Quoted By:

>>12897368
Spoken like a GOD CURSED SODOMITE!

Listen up, HERETIC! We of the ONE TRUE FINITE FAITH no longer have to endure your infinity LIES!

Anonymous

Anonymous Mon 29 Mar 2021 13:27:39 No.12897872 Report

Quoted By: >>12897906

>>12897341
Basically, you have numbers. 1 2 3 etc. Then you have more numbers in between. 1.5, 2.75, 1.33.... etc.
Keep sprinkling more abstract bullshit and you end up with pure autism like $\pi$

How do you define all of the above such that it's not borderline schizophrenia and an actual definition that can be used as a foundation? You can't, but you can approximately define it by not taking your pills and deciding to cut the number line in two. That definition doesn't actually do anything but people pretend that it does because anti-conformism requires significantly more calories than just passive conformism.

So how is this acceptable? It's not, which is where the controversy comes from, and it's only a controversy because people adamantly refuse to address it.

Anonymous

Anonymous Mon 29 Mar 2021 13:39:45 No.12897906 Report

Quoted By: >>12898208 >>12898296

>>12897872
Are there two Wildberger camps? One where constructible algebraic numbers qualify as numbers and one where they don't?

Anonymous

Anonymous Mon 29 Mar 2021 15:10:09 No.12898154 Report

Quoted By:

>>12896073
based tooker

Anonymous

Anonymous Mon 29 Mar 2021 15:29:26 No.12898208 Report

Quoted By: >>12898243

>>12897906
"Constructable" in an algebraic sense requires you only think in terms of conics (quadratics) and straight lines. The famous problem of trisecting the angle doesn't exist if you work within a different framework
https://plus.maths.org/content/trisecting-angle-origami
And besides, even if it was a problem, polynomials let you express numbers in a more general way than allowed by Euclidean geometry

Anonymous

Anonymous Mon 29 Mar 2021 15:37:51 No.12898243 Report

Quoted By:

>>12898208
Then are there two Wildberger camps? One where polynomials qualify as numbers, and one where they don't?

Anonymous

Anonymous Mon 29 Mar 2021 15:38:48 No.12898249 Report

Quoted By: >>12898308 >>12898491

>>12896073
>assigns greater significance to his own opinion
most people do, though

Anonymous

Anonymous Mon 29 Mar 2021 15:47:32 No.12898296 Report

Quoted By: >>12898392

>>12897906
There should be conferences just for cranks. And then you would surely get to see some fierce fighting. It would be fun.

Anonymous

Anonymous Mon 29 Mar 2021 15:49:12 No.12898308 Report

Quoted By:

>>12898249
Most people do not refuse to confront reality though.

Anonymous

Anonymous Mon 29 Mar 2021 16:07:05 No.12898392 Report

Quoted By:

>>12898296
>There should be conferences just for cranks
There are already plenty of conferences organized by infinitist schizos
https://www.conference-service.com/conferences/mathematics.html

Anonymous

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Anonymous Mon 29 Mar 2021 16:28:46 No.12898491 Report

Quoted By: >>12898589 >>12900659

You know how sometimes a child will pretend to have a speech impediment because they think it's cute to talk like Elmer Fudd, or whatever? Norman's schtick is the adult version of that.

>>12898249
IMO, most academics are extremely careful not to prejudice their work with their opinions. In a report, opinions would appear in a "discussion" section but Norman's whole thesis here about "satisfaction" is nothing but his opinion to begin with. Are we to believe that Rogawski gave a definition of R which Rogawski did not find satisfactory? Are we really to value Norman's opinion of satisfaction about Rogawski's? I do not! In general, Norman's whole thesis about the shortcomings of R are just his opinions because coming up short or not is only a matter opinion. There is no objective standard what definition of R is "good enough."

If Norman wrote papers instead of making youtubes, those papers would contain catalogs of historical information complemented with Norman's feels but they would not contain any original contributions to either mathematics or the philosophy of mathematics. All he does is say, "This isn't good," but he never says what would be good instead. This is the difference between shit-flinging and constructive criticism. Norman is just a shit-flinger and he places far more value on his opinion that it's not good than he does the very large of number of people who opine otherwise. He never says, "This isn't good though thousands of better mathematicians than myself find it perfectly satisfactory." He handwaves over that bar *big time.*

Does Norman think we should stop using calculus because R is not defined to his satisfaction? Obviously he does not and R *is* defined to his satisfaction. He's just got this schtick he likes to do about being a contrarian.

Anonymous

Anonymous Mon 29 Mar 2021 16:57:41 No.12898589 Report

Quoted By: >>12899209

>>12898491
>he never says what would be good instead
Then why did he put together online classes containing what he believes is a better foundation for calculus? Why are ghosts of departed quantities so frightening if they have a reliable description in linear algebra?
>Does Norman think we should stop using calculus because R is not defined to his satisfaction? Obviously he does not and R *is* defined to his satisfaction. He's just got this schtick he likes to do about being a contrarian.
Calculus was used for centuries before its modern justification came into view. Not only that (and this might come as a shock), but non-standard analysis is a thing. You don't have to axiomatize the computationally impossible to make math work

Anonymous

Anonymous Mon 29 Mar 2021 19:07:48 No.12899092 Report

Quoted By: >>12899109

>>12897093
I always wonder what happened to Ron

Anonymous

Anonymous Mon 29 Mar 2021 19:13:59 No.12899109 Report

Quoted By:

>>12899092
His time was finite.

Anonymous

Anonymous Mon 29 Mar 2021 19:21:46 No.12899138 Report

Quoted By:

>>12897093
I wonder if he really hasn't read Bishop's analysis? I haven't either, but I would certainly hope that someone interested in constructive mathematics would at least have some familiarity.

Anonymous

Anonymous Mon 29 Mar 2021 19:39:41 No.12899209 Report

Quoted By:

>>12898589
>he put together online classes containing what he believes is a better foundation for calculus?
I am not aware of Norman's attempt to give a definition of R which would meet his arbitrary personal criterion of satisfaction and I think what you wrote is a red herring. Has Norman given a definition of R that I didn't see? I think all he does is shit on other people's definitions of R. I thought his thing about calculus was "calculus without R" or something. This would address my supposition about him thinking we should stop doing calculus but it does not speak to my main point about how all he does is shit on other people's definitions of R without proposing something of his own or identifying any problems other than inconsistency with his opinion.

>You don't have to axiomatize the computationally impossible to make math work
This sentence is appears to me to be a profoundly stupid platitude. Maybe if you say more about that I will understand what you meant.

Anonymous

Anonymous Mon 29 Mar 2021 20:31:38 No.12899422 Report

Quoted By:

>>12896073
just that alone isn't a bad thing, the inverse would be accepting authority figures just because, which is a fallacy. His approach is sound as long as he has the evidence to back it up.

Anonymous

Anonymous Tue 30 Mar 2021 00:27:56 No.12900264 Report

Quoted By: >>12900307 >>12900310 >>12900336 >>12900411

I keep trying to understand his point of view, but he really does just seem to want to be a contrarian. He seems to reject axioms completely. He says that mathematics should "investigatethe mathematical reality of the world in which we live". If that's the case then shouldn't we reject far more than just the real numbers?
It also seems that he's concerned about computability, and laments that computer science is disconnected from mathematics and that we need a theory of algorithms, etc. Seems to me the more I read about theoretical computer science and such though the more similar it seems to the mathematical logic/axiom systems he's against. I don't see computer scientists rejecting infinity and such. Lots of it is in the Art of Computer Programming for example.
I just really don't understand because he never fully proposes an alternate system.

Anonymous

Anonymous Tue 30 Mar 2021 00:39:28 No.12900307 Report

Quoted By: >>12900324 >>12900417

>>12900264
>but he really does just seem to want to be a contrarian.
I'm convinced that's all that he really is.

Anonymous

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Anonymous Tue 30 Mar 2021 00:41:40 No.12900310 Report

Quoted By: >>12900317 >>12900406

>>12900264
>he really does just seem to want to be a contrarian
Yes, clearly. He just thinks it's cute to do his thing and he's got some base that fangirls for him. (More on that below.)

>laments that computer science is disconnected from mathematics
I don't know what papers Norman is reading. Practically the only CS paper I ever read was Based Codd's paper on the foundations of relation databases and it was an exercise in pure linear algebra with basically nothing other than math in it:
"A Relational Model of Data for Large Shared Data Banks"
https://www.seas.upenn.edu/~zives/03f/cis550/codd.pdf

Another CS paper I read, maybe the only other one, was this one from Oracle which is actually where I got the table structure format for my arithmetic axioms:
"Extended Real Intervals and the Topological Closure of Extended Real Relations"
https://www.oracle.com/technetwork/systems/extended-real-150017.pdf

I put together a nice system here in which think I do a "satisfactory" job of definition R:
"Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis"
https://vixra.org/abs/1906.0237

In fact, Norman's recent attempt to call into question whether or not Euclid's Elements of Geometry are a "satisfactory" foundation for mathematics, ignoring that they are *indeed* the foundation, is his attempt to undermine my own reliance on Euclid in the paper I linked above. Norman is certainly affiliate with the Loyal White Knights of the Ku Klux Klan, the worst of all the Klan orgs, but I would not be surprised to learn that he is an agent of the P2 freemasons as well.

Anonymous

Anonymous Tue 30 Mar 2021 00:43:31 No.12900317 Report

Quoted By:

>>12900310
>"A Relational Model of Data for Large Shared Data Banks"
This paper was *great* by the way.

Anonymous

Anonymous Tue 30 Mar 2021 00:46:44 No.12900324 Report

Quoted By: >>12900373 >>12900397

>>12900307
Why do I come to this board when half the people think it's funny to shill this guy and I wasted hours listening to him. And the other half just want to pretend its pol and append 'scientifically speaking'? Yet I still somehow decide oh I should go there.

Anonymous

Anonymous Tue 30 Mar 2021 00:49:53 No.12900336 Report

Quoted By:

>>12900264
>He says that mathematics should "investigatethe mathematical reality of the world in which we live".
No one tell him about physics.

Anonymous

Anonymous Tue 30 Mar 2021 00:57:14 No.12900373 Report

Quoted By: >>12900393

>>12900324
Because as shitty and futile as this board is, everywhere else is even worse.

Anonymous

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Anonymous Tue 30 Mar 2021 01:02:51 No.12900393 Report

Quoted By:

>>12900373

Anonymous

Anonymous Tue 30 Mar 2021 01:03:30 No.12900397 Report

Quoted By:

>>12900324
why is this in reply to my post

Anonymous

Anonymous Tue 30 Mar 2021 01:06:40 No.12900406 Report

Quoted By: >>12900475

>>12900310
>Norman's recent attempt to call into question whether or not Euclid's Elements of Geometry are a "satisfactory" foundation for mathematics
meh, parts of euclid have been ripped to pieces before. nothing new
> ignoring that they are *indeed* the foundation,
that's a different meaning of foundation than he's using and you full well know that
> Norman is certainly affiliate with the Loyal White Knights of the Ku Klux Klan, the worst of all the Klan orgs, but I would not be surprised to learn that he is an agent of the P2 freemasons as well.
lmao what

Anonymous

Anonymous Tue 30 Mar 2021 01:07:38 No.12900411 Report

Quoted By: >>12900523

>>12900264
it's not that hard to understand. he basically agrees with wittgenstein's criticisms of set theory and foundations in general. see here:

https://plato.stanford.edu/entries/wittgenstein-mathematics/#WittInteCritSetTheo

https://plato.stanford.edu/entries/wittgenstein-mathematics/#WittLateCritSetTheoNonEnumVsNonDenu

Anonymous

Anonymous Tue 30 Mar 2021 01:09:31 No.12900417 Report

Quoted By: >>12900461 >>12900475

>>12900307
anyone who strongly disagrees with the orthodoxy on any topic whatsoever gets called a contrarian. this claim is always vacuous

Anonymous

Anonymous Tue 30 Mar 2021 01:20:15 No.12900461 Report

Quoted By:

>>12900417
I'm fine with him disagreeing with things. I think people say 'contrarian' just to mean that his disagreements have little substance, and he's probably just trying to make a name for himself.

Anonymous

Anonymous Tue 30 Mar 2021 01:22:54 No.12900475 Report

Quoted By: >>12900491 >>12900498

>>12900406
>parts of euclid have been ripped to pieces
No they haven't. Try supporting your claim. When you do, you'll see it does not stand up to scrutiny,

>>12900417
It's not always vacuous. If the contrarian has some other idea, then the claim is vacuous. I the contrarian is just saying, "This sucks" and doesn't propose something else, the claim is not vacuous at all.

Anonymous

Anonymous Tue 30 Mar 2021 01:27:42 No.12900491 Report

Quoted By: >>12900536

>>12900475
he handwaves intersections of circles
the way he uses them works, but that doesn't change the fact that it's not gone over sufficiently

Anonymous

Anonymous Tue 30 Mar 2021 01:29:45 No.12900498 Report

Quoted By: >>12900536

>>12900475
he produced an entire course of lectures on calculus without real numbers so he has offered other ideas: https://www.youtube.com/playlist?list=PLIljB45xT85CSlgGh36810KdTcOd21JFh

Anonymous

Anonymous Tue 30 Mar 2021 01:33:34 No.12900509 Report

Quoted By: >>12900536 >>12900552 >>12900867

>>12893590
What controversy? Wildberger is technically correct on everything he says. It is true that "we can't imagine real numbers, can only imagine that we can imagine them" but that's the kind of problem that we'll deal with when we hit a wall.

If we keep going in the direction of real analysis and find a proof that 1 = 0 then we'll just backtrack and fix. That's literally how math has been done since the beginning of the universe. I don't see any point in not using our strongest tools just because they are too powerful. Sometimes you just have to nuke Japan to end the war.

Anonymous

Anonymous Tue 30 Mar 2021 01:38:54 No.12900523 Report

Quoted By:

>>12900411
>But instead of interpreting Cantor’s diagonal proof honestly, we take the proof to “show there are numbers bigger than the infinite”, which “sets the whole mind in a whirl, and gives the pleasant feeling of paradox” (LFM 16–17)—a “giddiness attacks us when we think of certain theorems in set theory”—“when we are performing a piece of logical sleight-of-hand” (PI §412; §426; 1945). This giddiness and pleasant feeling of paradox, says Wittgenstein (LFM 16), “may be the chief reason [set theory] was invented”.
set theorists BTFO

Anonymous

Anonymous Tue 30 Mar 2021 01:45:13 No.12900536 Report

Quoted By: >>12900545 >>12900547 >>12900558

>>12900491
>sufficiently
Sufficiency is a matter of opinion. In my opinion, Euclid is sufficient. Citing your own opinion doesn't rise to the level of "tearing Euclid to shreds." Do you have any criticisms that don't hinge on your opinion?

>>12900498
As far as I know, none of those things offer an alternative to the definitions of R which he flings shit at. Norman is a cunt, please deal with my opinion.

>>12900509
>technically correct on everything he says
He is not. In the OP image, it shows "Norman" saying that Rogawski's definition of R is not satisfactory. That is not "technically correct" because satisfaction is not a technical matter, Almost nothing Norman says is technically correct except when he is repeating what other people have done.

Anonymous

Anonymous Tue 30 Mar 2021 01:47:31 No.12900545 Report

Quoted By: >>12900560

>>12900536
the alternative to real numbers is to do mathematics without real numbers. not sure what your point is.

Anonymous

Anonymous Tue 30 Mar 2021 01:48:25 No.12900547 Report

Quoted By:

>>12900536
>an alternative to the definitions of R which he flings shit at
He doesn't believe there's an alternative, so why would he advocate one? The "alternative" is using algebraic techniques that came into common practice after people started fellating set theory

Anonymous

Anonymous Tue 30 Mar 2021 01:49:28 No.12900552 Report

Quoted By:

>>12900509
Turing had the same objection to Wittgenstein, he said that if there are contradictions then someone will build a bridge somewhere and it will collapse.
The fact is no one is going to worry about the issues until there is one. Real numbers are a great model, sure they don't physically exist, but they are useful. Besides if mathematicians really decided to change they way they defined real numbers it would only make everything more complicated and you'd lose a lot of nice properties. Only to find out that physicists, for example, are just ignoring the changes and continuing to use calculus as they always have.

Anonymous

Anonymous Tue 30 Mar 2021 01:51:15 No.12900558 Report

Quoted By: >>12900564 >>12900568

>>12900536
>That is not "technically correct" because satisfaction is not a technical matter

But Norman defines 'satisfactory' quite clearly. He specifically wants all mathematical actions to be expressed in a finite number of steps. This is even a practical requirement of math because if you can't write a proof down in a finite number of steps, you'll never finish your proof.

He complains that what real analysis does is hide infinite number of steps in special symbols that are able to perform those infinite steps but in just one symbol. It is not false that this is what real analysis does. It is true that if you want your math to be devoid of these tricks then no definition of real number is satisfactory.

I'm not saying I agree. I'm just saying I understand.

Anonymous

Anonymous Tue 30 Mar 2021 01:52:28 No.12900560 Report

Quoted By: >>12900565

>>12900545
Please tell me how to do real analysis, the backbone of all of modern mathematics, without real numbers. You are retarded. You are probably Norman, I reckon.

Anonymous

Anonymous Tue 30 Mar 2021 01:53:33 No.12900564 Report

Quoted By: >>12900572

>>12900558
>all mathematical actions
this is an infinite list of things. try again, fucktard.

Anonymous

Anonymous Tue 30 Mar 2021 01:53:35 No.12900565 Report

Quoted By:

>>12900560
>real analysis, the backbone of all of modern mathematics
this is what analysts actually believe

Anonymous

Anonymous Tue 30 Mar 2021 01:55:14 No.12900568 Report

Quoted By: >>12900574

>>12900558
What is the maximum number of steps you can use? It's interesting that if you formulate a system with a maximum number of steps x for example, there are statements that cannot be proved in fewer than x steps. What then? This keeps going on forever. Either we make thousands of special rules or we simplify things by using the concept of infinity. So far the infinity thing has worked great and been of use to lots of applications and allowed everything we have without finding any inconsistencies.

Anonymous

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Anonymous Tue 30 Mar 2021 01:56:25 No.12900572 Report

Quoted By:

>>12900564
>mfw when I want an infinite number of things to require a finite number of steps

Anonymous

Anonymous Tue 30 Mar 2021 01:57:44 No.12900574 Report

Quoted By: >>12900584 >>12900587

>>12900568
"Unbounded" doesn't mean infinite

Anonymous

Anonymous Tue 30 Mar 2021 02:01:58 No.12900584 Report

Quoted By:

>>12900574
Yes it does. The notation
$\lim\limits_{n\to\infty}$
is literally read as "the limit as n increase without bound."

Anonymous

Anonymous Tue 30 Mar 2021 02:02:35 No.12900587 Report

Quoted By: >>12900600

>>12900574
Yes it does. The notation
$\lim\limits_{n\to\infty}$
is literally read as "the limit as n increases without bound."

Anonymous

Anonymous Tue 30 Mar 2021 02:06:13 No.12900600 Report

Quoted By: >>12900621 >>12900645

>>12900587
Which is why it's rigorous to just plug in the value infinity, yeah?

Anonymous

Anonymous Tue 30 Mar 2021 02:14:12 No.12900621 Report

Quoted By: >>12900684

>>12900600
It's rigorous because it means "as n increases without bound" which is a rigorous idea. It means "for an unbounded increasing monotonic sequence of n." You could put an arrow pointing to a smurf below "lim" and it would still be rigorous if the smurf meant "increases without bound."

Anonymous

Anonymous Tue 30 Mar 2021 02:14:17 No.12900623 Report

Quoted By:

>>12896063

Anonymous

Anonymous Tue 30 Mar 2021 02:18:57 No.12900637 Report

Quoted By:

>>12893590
>real numbers: defined
>thot status: patrolled

Anonymous

Anonymous Tue 30 Mar 2021 02:19:49 No.12900642 Report

Quoted By:

Why did he retire by the way?
Also: 'Norman, who features on a list of the most famous mathematicians in Australia ...'
The state of mathematics in Australia!

Anonymous

Anonymous Tue 30 Mar 2021 02:20:55 No.12900645 Report

Quoted By: >>12900684

>>12900600
But, if perhaps I have missed your point, I think the only "rigorous" use of the INF symbol is as the limit of a non-zero fraction whose denominator approaches zero. I wouldn't want to the think of the limit as n increases without bound as "the limit as n approaches the limit of 1/x as x approaches zero," but I suppose you could. For this reason, however, the rigorous take on a limit approaching infinity is usually that it is understood as an increase without bound. This is written in shorthand with the infinity symbol not strictly dependent on the limit definition of infinity as a fraction's denominator approaches zero. It's just better for brevity to write "n->INF" than "as n increases without bound."

Anonymous

Anonymous Tue 30 Mar 2021 02:24:19 No.12900655 Report

Quoted By:

>>12893590
>Teach the controversy
We do teach it, in the history of mathematics. His ideas are ones we resolved a century ago. His new idea is mainly to apply constructivism to the way we teach mathematics to young people.

Anonymous

Anonymous Tue 30 Mar 2021 02:25:21 No.12900659 Report

Quoted By:

>>12898491
>There is no objective standard what definition of R is "good enough."
and this is the meme you fell for? how dare you mock us CSlets, get your shit together

Anonymous

Anonymous Tue 30 Mar 2021 02:34:31 No.12900684 Report

Quoted By: >>12900741 >>12900763

>>12900621
>>12900645
Admittedly I wasn't very clear. I meant "unbounded but still finite", or more accurately, a process which eventually halts. And we know it's impossible for a general procedure to tell us whether any given process halts. The Ackermann function halts for any finite input, but the number of steps it'll take can grow to be arbitrarily large.

El Arcón

El Arcón Tue 30 Mar 2021 02:57:09 No.12900741 Report

Quoted By: >>12900761 >>12900762

>>12900684
Infinity relates to numbers, not processes. I assume you're talking about the number of steps for a process to halt. If a process does halt, it halts after n steps. n is always bounded by n+1.

>"unbounded but still finite"
This is an oxymoron and a logical contradiction. "Unbounded" and "infinite" are synonyms in math and I'm not familiar with any other field's bastardized jargon. The whole idea of "halting" seems completely stupid to me because it is much simpler to talk about counting. Either you count to a number and then stop or you keep counting forever. There is no need to add some algorithmic layer to decide if you keep counting or if you stop. If you're talking about boundedness or unboundedness, it can't matter why do or don't stop counting, only that you do or don't. The only thing you get by adding an algorithmic computation layer is a reason for why you stopped or did not stop, which is irrelevant.

For example, this halts:
N=rand(100000)
jj=0;
kk=1;
for jj=1:N
jj=kk;
kk=kk+1;
end

This doesn't halt:
jj=0;
kk=1;
while jj is INT
jj=kk;
kk=kk+1;
end

All algorithms are bound to be a glorified version of one algorithm or the other and each is a just glorified version of counting.

El Arcón

El Arcón Tue 30 Mar 2021 03:04:31 No.12900761 Report

Quoted By:

>>12900741
>for jj=1:N
should start with zero, obviously

Anonymous

Anonymous Tue 30 Mar 2021 03:04:34 No.12900762 Report

Quoted By: >>12900772

>>12900741
tooker you ok man? you seem very lucid today

El Arcón

El Arcón Tue 30 Mar 2021 03:05:49 No.12900763 Report

Quoted By:

>>12900684
Infinity relates to numbers, not processes. I assume you're talking about the number of steps for a process to halt. If a process does halt, it halts after n steps. n is always bounded by n+1.

>"unbounded but still finite"
This is an oxymoron and a logical contradiction. "Unbounded" and "infinite" are synonyms in math and I'm not familiar with any other field's bastardized jargon. The whole idea of "halting" seems completely stupid to me because it is much simpler to talk about counting. Either you count to a number and then stop or you keep counting forever. There is no need to add some algorithmic layer to decide if you keep counting or if you stop. If you're talking about boundedness or unboundedness, it can't matter why do or don't stop counting, only that you do or don't. The only thing you get by adding an algorithmic computation layer is a reason for why you stopped or did not stop, which is irrelevant.

For example, this halts:
N=rand(100000)
jj=1;
kk=1;
for jj=1:N
jj=kk;
kk=kk+1;
end

This doesn't halt:
jj=1;
kk=1;
while jj is INT
jj=kk;
kk=kk+1;
end

All algorithms are bound to be a glorified version of one algorithm or the other and each is a just glorified version of counting.

El Arcón

El Arcón Tue 30 Mar 2021 03:07:59 No.12900772 Report

Quoted By: >>12900779

>>12900762
Man, your thinking is not very clear if you think implying that I am usually not lucid is good for your interests and/or the interests of your ancestors.

Anonymous

Anonymous Tue 30 Mar 2021 03:09:11 No.12900779 Report

Quoted By: >>12900796

>>12900772
is that a threat? you wanna go or something?

Anonymous

Anonymous Tue 30 Mar 2021 03:10:20 No.12900783 Report

Quoted By: >>12900796

>>12896073
thats fucking rich coming from you

El Arcón

El Arcón Tue 30 Mar 2021 03:13:54 No.12900796 Report

Quoted By: >>12900825

>>12900779
yes. yes.

>>12900783
I am extremely careful to qualify statements of my opinion, with "in my opinion" and the things I use to destroy my detractors are facts that don't depend on my opinion. You never see me whining about some bullshit "satisfaction" or anything like that pseud Norman usually goes on about.

Anonymous

Anonymous Tue 30 Mar 2021 03:23:49 No.12900825 Report

Quoted By: >>12900857 >>12900873

>>12900796
I'm new here are you really that crazy bearded guy in Atlanta I've seen videos of?

El Arcón

El Arcón Tue 30 Mar 2021 03:32:10 No.12900857 Report

Quoted By:

>>12900825
where did you find this video? I might need to file a lawsuit

El Arcón

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El Arcón Tue 30 Mar 2021 03:32:59 No.12900858 Report

Quoted By: >>12900913

For instance, it's not my opinion that the only possible definition of R which Riemann might have been using in the 1850's was Euclid's. It's not my opinion that Riemann could not have been using Dedekind's 1872 cuts definition of R in the 1850's. It's not my opinion that Cantor's 1872 definition of R by Cauchy equivalence classes was not available to Riemann in the 1850's. These are facts.

To the contrary, Norman says I can't have solved RH because my solution is not "satisfactory." That's an opinion. Another fact is that Clay defines the problem they have a bounty on. It's a matter of opinion if Clay has a bounty on the problem Riemann had in mind but, in fact, Clay spells out plainly the problem they have a bounty on:
http://www.claymath.org/library/annual_report/ar2004/04report_prizeproblem.pdf

It is my opinion that Clay implicitly cites the definition of R which Riemann would have had, and I think my opinion is well motivated in this regard because they use Riemann's name to title the problem which is the object of their bounty and they don't say anything about a requirement for some framework of R which did not exist when Riemann first posed his hypothesis. If Clay changes it to say they will only accept solutions formatted for systems of R defined in 1872 or later, then I will be happy to have identified a previously undiscovered corner case and will be glad to see my paper appear in the Annals of Mathematics where such a previously unreported corner case in "the most important unsolved problem in mathematics" belongs. Again, this is only my opinion that a stunning new result which causes Clay to change it's statement of "the most important unsolved problem in mathematics" should appear in the Annals but, in fact, such a result would be good enough to at least appear on arXiv which has described my result as "devoid of scholarly content." In fact, if Clay changes the definition of their problem in response to my paper, the scholarly content is self-evident.

El Cabrón

El Cabrón Tue 30 Mar 2021 03:35:06 No.12900867 Report

Quoted By:

>>12900509
but we do have a proof that 1=2 in analysis

El Arcón

El Arcón Tue 30 Mar 2021 03:38:11 No.12900873 Report

Quoted By: >>12900900

>>12900825
I'm not a crazy bearded guy, so no. Also, I live in Antarctica and you would do well to distinguish between Atlanta, North America and Atlanta, Antarctica. It's like how the University of Georgia is in Athens, GA but that's a different Athens than Athens, Greece. When you just say "Atlanta" people will think you mean Atlanta, North America.

El Cabrón

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El Cabrón Tue 30 Mar 2021 03:46:31 No.12900900 Report

Quoted By:

>>12900873

El Arcón

El Arcón Tue 30 Mar 2021 03:52:49 No.12900913 Report

Quoted By:

>>12900858
>http://www.claymath.org/library/annual_report/ar2004/04report_prizeproblem.pdf
wrong link!
https://www.claymath.org/sites/default/files/official_problem_description.pdf

Anonymous

Anonymous Tue 30 Mar 2021 03:54:31 No.12900917 Report

Quoted By:

I wish tooker would teach me to become a mathematics chad.

Anonymous

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Anonymous Tue 30 Mar 2021 11:22:36 No.12901775 Report

Quoted By:

>work in first order logic
>construct a model where the reals are countable
>Wait, construct models of ALL infinities so they're all countable
>Never have to deal with R

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