Anonymous at Fri, 14 Mar 2025 15:47:05 UTC No. 16618797

>>16618792
Because you're a pseud.

Anonymous at Fri, 14 Mar 2025 15:48:46 UTC No. 16618800

>>16618792
pseudo calc ; ^(
operational calc B^)

Anonymous at Fri, 14 Mar 2025 15:49:47 UTC No. 16618802

>>16618800
>operations research
>pseudo research

Anonymous at Fri, 14 Mar 2025 15:54:07 UTC No. 16618803

>>16618792
Does this imply that Russell engaged in pseudomathematics when he claimed set theory didn't work? Are the ZFC axioms pseudomathematics according to definitions a hundred years ago? Or did Newton & Leibniz, or when inventing calculus without the epsilson-delta formality and rigor of mathematics engage in pseudomathematics?

Anonymous at Fri, 14 Mar 2025 15:57:18 UTC No. 16618805

academics trying to cope while their paper takes 3 years and 16 people to publish

Anonymous at Fri, 14 Mar 2025 17:15:36 UTC No. 16618860

>>16618803
derivation or equivalent to "constructive proof" or invention > ur shitty le "rigorous" proofs

Anonymous at Fri, 14 Mar 2025 18:59:41 UTC No. 16618917

>>16618792
A pseudo mathematician is just called a philosopher.

Anonymous at Fri, 14 Mar 2025 19:01:29 UTC No. 16618919

>>16618917
and they aren't bound by the rules of mathematics because they realize that math is just a human concept and the laws of the universe are beyond our comprehension.

Anonymous at Mon, 17 Mar 2025 12:06:40 UTC No. 16621564

prime numbers aren't pseudo-variables
they're quasi-variables

Anonymous at Tue, 18 Mar 2025 23:24:07 UTC No. 16623077

>>16618803
Russel didn't claim set theory didn't work. He is specifically famous for trying and failing very hard to make set theory + logic the perfect foundation for math. Then Kurt Godel showed there isn't a perfect a perfect mathematical foundation: they all either have something they can't prove or disprove (i.e. they are incomplete), or are otherwise total garbage where you can prove every statement is both true and false(i.e. they are inconsistent)

ZFC is not pseudomath but some people take issue with it. The axiom of choice in particular gives some people pause since you can conclude some WILD shit using the axiom of choice. In practice, in math, it's rare to bump into any part of ZFC that might have have a sharp corner if axiom of choice is wrong. Might need to get it replaced by some new formalism someday if we ever show that axiom of choice is wrong, but most of the stuff in math people give a shit about will be unaffected because we'll just choose our new formalism to leave that stuff alone. It's useful stuff! We got to the moon and back, invented computers, and discovered the higgs boson all using that stuff, which is currently sitting on ZFC. A lot of people like to think of "the collection of math" as a big tower where current proofs rest on old proofs like higher bricks on lower bricks. It's a useful analogy, but a limited one. If you somehow managed to pull out one tiny brick at the bottom, it's not like the whole tower will come crashing down, and all is lost. Realistically we'll probably debate over it for a few decades and then settle on a new brick that works better.

Anonymous at Thu, 20 Mar 2025 09:01:16 UTC No. 16624173

>>16623077
>since you can conclude some WILD shit using the axiom of choice
"Meanwhile, it would be a form of confirmation bias to discuss only counterintuitive consequences of the axiom of choice, without also discussing the counterintuitive situations that can occur when the axiom of choice fails. Although mathematicians often point to what are perceived as strange consequences of the axiom of choice, a fuller picture is revealed by also mentioning that many of the situations that can arise when one drops the axiom of choice are perhaps even more bizarre.
For example, it is relatively consistent with the axioms of set theory without the axiom of choice that there can be a nonempty tree T, with no leaves, but which has no infinite path. That is, every finite path in the tree can be extended to further steps, but there is no path that goes forever. This situation can arise even when countable choice holds (so countable families of nonempty sets have choice functions), and this highlights the difference between the countable choice principle and the principle of dependent choice, where one makes countably many choices in succession. Finding a branch through a tree is an instance of dependent choice, since the later choices depend on which choices were made earlier."
1/2

Anonymous at Thu, 20 Mar 2025 09:05:23 UTC No. 16624177

>>16624173
"Without the axiom of choice, a real number can be in the closure of a set of real numbers X ⊂ R, but not the limit of any sequence from X. Without the axiom of choice, a function f : R R can be continuous in the sense that every convergent sequence xₙ x has a convergent image f(xₙ) f(x), but not continuous in the ε, δ sense. Without the axiom of choice, a set can be infinite, but have no countably infinite subset. Indeed, without the axiom of choice, there can be an infinite set, with all subsets either finite or the complement of a finite set. Thus, it can be incorrect to say that ℵ0 is the smallest infinite cardinality, since these sets would have an infinite size that is incomparable with ℵ0.
Without the axiom of choice, there can be an equivalence relation on R, such that the number of equivalence classes is strictly greater than the size of R. That is, you can partition R into disjoint sets, such that the number of these sets is greater than the number of real numbers. Bizarre! This situation is a consequence of the axiom of determinacy and is relatively consistent with the principle of dependent choice and the countable axiom of choice."
2/3

Anonymous at Thu, 20 Mar 2025 09:07:01 UTC No. 16624179

>>16624177
"Without the axiom of choice, there can be a field with no algebraic closure. Without the axiom of choice, the rational field Q can have different nonisomorphic algebraic closures. Indeed, Q can have an uncountable algebraic closure as well as a countable one. Without the axiom of choice, there can be a vector space with no basis, and there can be a vector space with bases of different cardinalities. Without the axiom of choice, the real numbers can be a countable union of countable sets, yet still uncountable. In such a case, the theory of Lebesgue measure is a complete failure.
To my way of thinking, these examples support a call for balance in the usual conversation about the axiom of choice regarding counterintuitive or surprising mathematical facts. Namely, the typical way of having this conversation is to point out the Banach-Tarski result and other counterintuitive consequences of the axiom of choice, heaping doubt on the axiom of choice; but a more satisfactory conversation would also mention that the axiom of choice rules out some downright bizarre phenomena — in many cases, more bizarre than the Banach-Tarski-type results."
— Joel David Hamkins, Lectures on the Philosophy of Mathematics
https://mitpress.mit.edu/9780262542234/
>>16623077
i ain't in dissagrement with your post, im just adding context to that tidbit i quoted

Anonymous at Thu, 20 Mar 2025 11:16:21 UTC No. 16624200

>>16618792
No it doesn't.

Anonymous at Thu, 20 Mar 2025 13:53:04 UTC No. 16624255

>>16618792
It doesn't?

Anonymous at Thu, 20 Mar 2025 15:47:36 UTC No. 16624305

>>16618792
> recognized as extremely hard by experts
oh wow!
> attempts to apply mathematics to non-quantifiable areas
such as?

Anonymous at Thu, 20 Mar 2025 15:52:56 UTC No. 16624310

>>16623077
>they all either have something they can't prove or disprove
Is it a bad thing that they cannot prove nonsensical things?

Anonymous at Thu, 20 Mar 2025 15:56:09 UTC No. 16624313

>>16624305
That's what the "Talk" section from the Wikipedia article is for. Let them know your questions
https://en.m.wikipedia.org/wiki/Talk:Pseudomathematics

Anonymous at Thu, 20 Mar 2025 15:57:00 UTC No. 16624315

>>16624313
Consider them your own.