Noah Schweber

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$Mathematics$ CURED

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Noah Schweber

May 26 04:20

I suspect more to come along these lines: math.stackexchange.com/questions/5070282/…, math.stackexchange.com/a/5070280/28111

Noah Schweber

Mar 20 17:21

C/D math.stackexchange.com/questions/5047844/…

Noah Schweber

Mar 9 04:15

"Is Useful?" troll is back, this time with some set theory: math.stackexchange.com/questions/5043702/greater-than-infinity

Noah Schweber

Mar 5 18:13

User 1586619 has plagiarised two existing questions: see the comments under math.stackexchange.com/questions/5042436/…, math.stackexchange.com/questions/5042417/….

Noah Schweber

Feb 3 05:57

Actually, it's now pretty clear that this is AI garbage: math.stackexchange.com/a/5030808/28111

Noah Schweber

Feb 3 05:12

This answer "feels" AI-generated but I'm not competent in the relevant area; can someone take a look? math.stackexchange.com/a/5030808/28111

Noah Schweber

Dec 17, 2024 18:47

AI-generated garbage: math.stackexchange.com/questions/5012684/…

Noah Schweber

Nov 22, 2024 00:37

Delete (crank banned from physics.SE physics.stackexchange.com/users/457578/user77952, now trying out garbage here): math.stackexchange.com/questions/5001738/sophit-ideology

Noah Schweber

Aug 1, 2024 20:47

@amWhy Notice that I explicitly mentioned that I'd answered it in my comment here, and explained why I reopened it at the post itself as well. What would you have preferred I do?

Noah Schweber

Aug 1, 2024 20:29

which is true but doesn't explain the diagonal lemma at all). To be clear I would not be surprised if this is a dupe after all, I just can't find a duplicate. I'm posting here since I didn't realize my reopen vote would unilaterally reopen it.

Noah Schweber

Aug 1, 2024 20:28

FYI I've just reopened math.stackexchange.com/questions/4952882 (having answered it); the dupe target selected was not in fact a duplicate of the question, nor does the answer to the target address the original question (the one sentence of the answer relating to the proof of the diagonal lemma is "It turns out that if you calculate the number of this formula, you get exactly the number you get by starting with the number 𝑘 and performing the operations described by the statement"

Noah Schweber

Jul 21, 2024 16:12

Close and delete math.stackexchange.com/q/4948735/28111 (repeated Godel crankery).

Noah Schweber

Jul 12, 2024 18:52

@Peter I disagree with this. There's nothing wrong with that answer; a now-deleted comment criticizes it for taking ultrafinitism seriously, but (and I'm far from an ultrafinitist FWIW) that doesn't make it a bad answer. I think using CURED in this way comes dangerously close to an abuse of its purpose: we shouldn't ask for downvotes on answers just for countenancing philosophical positions we disagree with.

Noah Schweber

Jun 29, 2024 01:47

The usefulness continues: math.stackexchange.com/q/4939263/28111

Noah Schweber

Jun 27, 2024 02:30

More "is useful" garbage: math.stackexchange.com/questions/4938306/…

Noah Schweber

May 8, 2024 19:16

@Peter "the sense in which $a=a+1$ shoould hold is not clarified at all" There is nothing that needs clarification. The question states that a is the cardinality of the set A; both "=" and "+1" have completely standard meanings in the context of cardinality. (Note that "cardinality" is not the same as "cardinal" in the context of choiceless set theory - cf. "Scott cardinality.")

Noah Schweber

Apr 21, 2024 06:15

Close/delete: math.stackexchange.com/q/4902872/28111

Noah Schweber

Mar 30, 2024 03:34

@XanderHenderson Thank you. Would it be possible for my original comment to Peter (which included the disclosure that I had answered the question in question) to be un-trashed? Separately, would it be possible to delete my comment of a few minutes ago beginning "Also, it seems" - that was written in annoyance, and in retrospect was rude, but too much time has passed for me to delete it (and sorry to @Saad re that).

Noah Schweber

Mar 30, 2024 03:30

@Ѕᴀᴀᴅ I explicitly pointed out that I had answered the question, in my initial comment to Peter.

Noah Schweber

Mar 30, 2024 03:26

(Also, it seems disingenuous to both chide me for asking why something happened in CURED and chide me for creating a new chat room to ask you why you moved messages to trash. No opacity was intended, but I'm genuinely not sure how I was supposed to go about this!)

Noah Schweber

Mar 30, 2024 03:25

@Ѕᴀᴀᴅ I just want to make sure I understand: it is inappropriate to ask why someone wants a question closed (or deleted or etc.) here? Can I at least voice a contrary opinion?

Noah Schweber

Mar 29, 2024 22:46

Personally, I think that in general the decision to vote to close a question (or request for others to do the same) has a higher obligation of explanation than the decision to answer a question. Of course in neither case is that obligation serious - Peter is perfectly free to ignore my question - but it's also perfectly fine for me to ask why he thinks it should be closed.

Noah Schweber

Mar 29, 2024 22:44

I answered it because I thought - and think - that it is a good question about mathematics that does not seem to be an exact duplicate of another question, and to which I have an answer. I don't really know what you want me to say here. Do you think it's a bad question? If so, why?

Noah Schweber

Mar 29, 2024 19:50

@Peter, re: the independence-of-CH question, why do you want it closed? It seems perfectly fine to me. (Full disclosure: I have answered it.)

Noah Schweber

Feb 8, 2024 19:48

@rschwieb's example is a different instance of the same thing.

Noah Schweber

Feb 8, 2024 19:48

Suspended user (SirLatin) sockpuppet: math.stackexchange.com/questions/4859463/…

$Mathematics$ Discussion on question by Christopher…

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Noah Schweber

Feb 19 12:35

@PyRulez Does my answer resolve your question?

$Mathematics$ Discussion on question by oggiman: Ca…

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Noah Schweber

Feb 9 21:48

You're basically just describing a non-Archimedean ordered semiring (possibly with exponentiation as well). Lots of these exist. However, whether or not such a thing is appropriate to your purposes depends on what exactly you're doing. You're tacitly assuming that there should be a "best" way of thinking about infinity, but that's not correct.

$Mathematics$ Discussion on question by Daniel Donn…

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Noah Schweber

Jan 5 10:16

@DanielDonnelly "The theory generalizes in more places than one" Cool, so you should be able to give at least one interesting example. "Let its effect on generalizing the entire theory speak for itself." This sort of grand sweeping claim absent any justification or example misses a key part of why the "abstract" approach in mathematics is so successful: we don't just pointlessly generalize existing definitions purely for the sake of generality itself. (A certain remark by Girard occurs ...)

Noah Schweber

Jan 5 10:16

@DanielDonnelly That's not John's question. He's asking for examples of this phenomenon in the first place - that is, why should we care about this additional generality?

$Mathematics$ Discussion on answer by Noah Schweber…

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Noah Schweber

Dec 25, 2024 04:30

@zaq Over the next few minutes I'll go ahead and add (a version of) this to my answer, since I think it might be helpful for readers and comments are ephemeral.

Noah Schweber

Dec 25, 2024 04:30

That said, since in the construction of $L$ we do allow parameters at each stage, it actually is the case that $L_\alpha$ is "appropriately-definable" in $L_\beta$ whenever $\alpha<\beta$; specifically, there's a formula $\lambda(x,y)$ such that whenever $\alpha<\beta$ are ordinals we have $$\{x: L_\beta\models \lambda(x,\alpha)\}=L_\alpha.$$ But this is neither obvious (it's easy to prove for $\beta$ limit, but takes some care for $\beta$ a successor) nor necessary to the specific question here.

Noah Schweber

Dec 25, 2024 04:30

@zaq Oh, I see! Yes, the two-sortedness is a bit different although not material to this specific situation. The issue is that if $\mathfrak{A}$ isn't an $\{\in\}$-structure there's not an obvious way to construe $\mathfrak{A}\sqcup\mathcal{P}_{def}(\mathfrak{A})$ as a single-sorted structure, and so the two-sorted approach is a fix we don't need here.

Noah Schweber

Dec 25, 2024 04:30

Or maybe I'm misunderstanding. When you write "we need...," what are you saying we need this for?

Noah Schweber

Dec 25, 2024 04:30

@zaq I don't understand. It's generally not true that $L_\alpha$ is definable (without parameters) in $L_\beta$ for $\beta>\alpha$. But this doesn't impact the issue you're looking at: already for a relatively simple structure such as $(\mathbb{Z};+,1)$, two "$L$-like steps" is already different - even at the level of definable subsets of the domain! - than one "$L$-like step."

Noah Schweber

Dec 25, 2024 04:30

If this is helpful I'll add it to my answer!

Noah Schweber

Dec 25, 2024 04:30

However, it is definable over $\mathfrak{M}_2$ (so is an element of $\mathfrak{M}_3$ in an appropriate sense): this is because $x$ is positive iff for every $\mathfrak{M}_1$-definable set (= element of $S$) $A$, if $0\in A$ and $a\in A\wedge a\not=x\implies a+1\in A$ then $x\in A$. Similarly, the set of positive primes is definable over $\mathfrak{M}_2$, which is even more striking since (unlike the positive integers themselves) this goes beyond what Presburger arithmetic can do (note that $(\mathbb{N};+)$ interprets $(\mathbb{Z};+,1)$).

Noah Schweber

Dec 25, 2024 04:30

(Actually that's not quite true; $S$ should have all the $\mathfrak{M}_1$-definable finite-arity relations on $\mathbb{Z}$. But meh.) Now what happens when we build $\mathfrak{M}_3$? Well, we can now do things like quantify over the $S$-part, which amounts to quantifying over the definable sets in $\mathfrak{M}_1$. This is definitely not "collapsible" to a formula in the original $\mathfrak{M}_1$. Here's a concrete example of this: it's known that $<$ is not definable over $\mathfrak{M}_1$ (see here). (cont'd)

Noah Schweber

Dec 25, 2024 04:30

@zaq (Don't worry, I didn't think it was you!) The issue is that we're not just adding on a bunch of definable relations - we're also treating these additional relations as objects over which we can further define things. So, for example, the right analogue is the following: we start with $\mathfrak{M}_1=(\mathbb{Z};+,1)$ (you'll see why I added 1), and then $\mathfrak{M}_2$ is a two-sorted structure $(\mathbb{Z}, S; +,\in)$ where $S$ is the set of all sets of integers which are definable in $\mathfrak{M}_1$ and $\in$ relates the $\mathbb{Z}$- and $S$-parts in the obvious way. (cont'd)

$Mathematics$ Discussion on answer by Vadym Vashche…

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Noah Schweber

Dec 21, 2024 16:20

Re: your opening line, I didn't downvote but more is not necessarily better. (And indeed in my opinion, this answer provides less insight - and with more circuitous explanation - than the previous answers.)

$Mathematics$ Discussion on question by Ismael: Is …

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Noah Schweber

Oct 30, 2024 12:36

@IThinkHighlyOfEiligh "300 pages of the most advanced Analytic NT ever devised" Zhang's paper is 54 pages long. Regardless, what a weird hill to pick ...

$Mathematics$ Discussion on question by Sho: Issue …

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Noah Schweber

Sep 24, 2024 15:06

Try to show that if $\Lambda$ is the least inaccessible cardinal, $\kappa<\Lambda$, and $V_\Lambda\models$ "$\kappa$ is inaccessible," then $\kappa$ is in fact inaccessible - contradicting the assumption that $\Lambda$ was the least inaccessible.

$Mathematics$ Discussion on answer by Mikhail Katz:…

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Noah Schweber

Sep 23, 2024 12:24

"Halmos's attitude is untenable, as mathematicians always preferred and still prefer to avoid the axiom of choice in their arguments" is a very strong claim; backing it up with a single (if important) mathematician's opinion isn't at all convincing. In my experience, worries about AC (especially among non-logic-oriented mathematicians) are extremely rare. Until more evidence is provided, I think this answer makes far too strong a claim.

$Mathematics$ Discussion on question by Gustav Stre…

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Noah Schweber

Sep 23, 2024 05:32

"making it possible to prove incorrect values as limits as well as to prove that valid values are not limits" Can you give a detailed example of such a proof?

Discussion on question by ResearchMat…

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Noah Schweber

Jun 30, 2024 10:10

@gparyani I did not know that, thank you.

Noah Schweber

Jun 30, 2024 10:10

Without commenting on the post, how were you given -100 rep? You only received 6 downvotes, which correspond to -12 reputation.

$Mathematics$ Discussion on question by Shaun: Alle…

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Noah Schweber

Apr 28, 2024 13:16

@jjagmath Quibble: it's not the axiom of union that's needed for that, but rather the axiom of pairing. The axiom of union doesn't go "$A,B\leadsto A\cup B$" but rather "$\color{red}{\{} A_i:i\in I\color{red}{\}}\leadsto\bigcup_{i\in I}A_i$" - you have to already have formed the set of sets you're trying to union together.

Trash

Where the trash goes.

Noah Schweber

Mar 29, 2024 22:50

@amWhy (Sorry, forgot to notify)

Noah Schweber

Mar 29, 2024 21:45

@amWhy I wasn't picking a fight, I was asking a question and stating that I do not currently see a rationale. I believe it is entirely fine to ask why another user wants a question to be closed.

$Mathematics$ Discussion on question by AUTIST INC:…

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Noah Schweber

Mar 8, 2024 12:35

While (3) happens to be true because the consequent is true, as a general step in a proof it is nonsense: replace $P$ for example by $\{1,2\}$. Then $\exists X\exists Y(X\in\mathbb{N}\wedge Y\in P\wedge Y>X)$ is true but $\forall X\exists Y(X\in\mathbb{N}\wedge Y\in P\wedge Y>X)$ is blatantly false. So how do you plan to justify (3) in the case $P=$primes without first proving the infinitude of primes anyways?