Stack Exchange
log in

Daniel Donnelly

 Mathematics

Associated with Math.SE; for both general discussion & math qu...
5
Daniel Donnelly
Jul 8 12:16
Dang, I looked back, but can't really find tracks of your conversation so shouldn't / can't really comment further :0
Daniel Donnelly
Jul 8 12:15
:)
Daniel Donnelly
Jul 8 12:15
Pointed space, I know that one
Daniel Donnelly
Jul 8 12:14
then I'll dualize
Daniel Donnelly
Jul 8 12:14
what's fibrant mon
Daniel Donnelly
Jul 8 12:14
@Thorgot what's cofibrant
Daniel Donnelly
Jul 8 12:06
😭
Daniel Donnelly
Jul 8 12:03
@Vincent
Daniel Donnelly
Jul 8 11:53
@Faoler that looks like some AnNT
Daniel Donnelly
Jul 8 07:26
This room is rife with topologists and complex analysts usually, is everyone down for the night?
Daniel Donnelly
Jul 8 07:25
*in the abstract algebra book
Daniel Donnelly
Jul 8 07:25
Figured you topologists would like something they forgot to put in the book. Should be a topology
Daniel Donnelly
Jul 8 07:24
0
Q: If affine $n$-space $\Bbb{A}^n$ over a field $k$ can be topologized with Zariski's topology, then what is the topology of $k[\Bbb{A}^n]$ the ring?

Daniel DonnellySince there's the Zariski topology in which closed sets are the affine algebraic sets of the form $Z(S)$ for some $S \subset k[\Bbb{A}^n]$ the coordinate ring, and there's Hilbert's Nullstellensatz at work: I'm wondering if the radical ideals of the coordinate ring $k[\Bbb{A}^n]$ are also closed...

abstract-algebra general-topology algebraic-geometry ring-theory zariski-topology
Daniel Donnelly
Jun 16 21:49
@Thorgott just count them :>
Daniel Donnelly
Jun 16 21:48
0
Q: How can we typeset inference rules on this site using MathJax/KaTeX standard libs?

Daniel Donnelly Here is a picture. I would like the fractions' horizontal bars aligned nicely like they are here, if possible. In other words, I'm looking for the standard way, as my KaTeX-parsing code will work with that firstly. Attempt. $$ \begin{align} &\dfrac{\dfrac{}{\cdot \text{ ctx}}\text{ctx-EMP}}{\vda...

support mathjax typesetting
Daniel Donnelly
May 19 05:08
That's mathematical fascism. The only people allowed to work on certain problems can be counted on 10 fingers.
Daniel Donnelly
May 19 04:56
It's like you're forcing people to only be interested in certain math by upvoting textbook problems while downvoting creativity in harder areas. That's not democratic at all, that's preservation of what math is already well-known. Essentially: don't ask any homework questions, but make sure that's all you ask about.
Daniel Donnelly
May 19 04:53
@EmmaBee in general the site should have a subsite for people (newbies) to work on prize problems without negative sentiment. These prize problems are what drives the newcomers to learn more math. When they get downvoted to oblivion for asking a good question, just because it is a well-known open problem, it's more nazi over-moderation than good site upkeep.
Daniel Donnelly
May 19 04:45
The reason for the repeating sequences is simple. Those are the offsets that you must add to get to the next non-solution to $x^2 - 1 \mod {p_i}$. The $*$ operation is to combine them in a union way
Daniel Donnelly
May 19 04:43
So the above formulation is closest to a "combinatorics on words" approach, but researching that and they don't really cover this topic.
Daniel Donnelly
May 19 04:42
I can count them easily, but can't prove the counting formula doesn't just vanish
Daniel Donnelly
May 19 04:41
E.g. while twin primes involves "$x^2 - 1$" there's the $x^2 +1$ is prime i.o. problem. Ie. they're related
Daniel Donnelly
May 19 04:39
It's not just twin primes. It's many prime problems. If you can solve one you've likely found a general method
Daniel Donnelly
May 19 04:39
It appears to be very similar to the Post Correspondence Problem (a family of instancs of it), but not quite. So it does seem decideable.
Daniel Donnelly
May 19 04:38
Because 6 gets sieved out by the 5
Daniel Donnelly
May 19 04:37
So the first entry for $\widehat{5} * \overline{6}$ is of course 12.
Daniel Donnelly
May 19 04:37
lol oh
Daniel Donnelly
May 19 04:36
Yes, but this is even simpler than Fermat's
Daniel Donnelly
May 19 04:36
borders?
Daniel Donnelly
May 19 04:35
It's just strange that I can present this problem as a kid-level counting problem, yet, our most advanced mathematics can't solve it. I.e. a question about repeating natural sequences and their least common subsum's first entry. That's my point, is all. That we can't solve this simple problem.
Daniel Donnelly
May 19 04:34
Not sure what's that, bitbucket is a code repository
Daniel Donnelly
May 19 04:33
Where $*$ is the op and the sequences are $\overline{6}$, $\overline{2,1,2}$ (5), ... $\overline{2, 1,1,1,\dots, 2}$ ($p_n$).
Daniel Donnelly
May 19 04:32
But the only entry in the result of the operation is the first entry and that should be $\lt p_{n+1}^2 - 2$.
Daniel Donnelly
May 19 04:31
The operation that computes the common subsums of two periodic natural sequences is associative.
Daniel Donnelly
May 19 04:30
That is the twin prime conjecture... if your bound is $\leq p_{n+1}^2-2$ where $p_n$ is the highest prime involved.
Daniel Donnelly
May 19 04:29
Suppose you have $a_n = \overline{2,1,2}$ and $b_n = \overline{2,1,1,1,2}$ and the like. How can you compute an upper bound for $\min \{ \sum_{i = 1}^n a_i\}\cap \{ \sum_{i=1}^m b_i\}$ i.e. something that's less than $5\cdot 7$?
Daniel Donnelly
Apr 19 12:22
Found problem weaker than two prime problems simultaneously:
https://math.stackexchange.com/questions/5057649/forall-i-1-dots-p-n12-2-exists-prime-q-in-i-such-that-gcdq2-p
Daniel Donnelly
Apr 8 10:07
I would tear that book to shreds or write all over it.
Daniel Donnelly
Apr 8 10:06
Math books causing psychosis these days...
Daniel Donnelly
Apr 8 10:04
They made their money, and now you're losing your mind
Daniel Donnelly
Apr 8 10:04
I hate that. It's like... you like a book then they screw it up with some bad writings.
Daniel Donnelly
Apr 8 10:02
What a waste of your time
Daniel Donnelly
Apr 8 10:02
@psi looks like a typo yes. They should have not even put that particular proof in if they're going to half-ass it
Daniel Donnelly
Apr 8 05:59
No, A means you ate matrices
Daniel Donnelly
Apr 8 05:58
@leslietownes C meant you "C how it works", "B means you became a matrix at one point". "A means you are a matrix now."
Daniel Donnelly
Apr 8 05:56
MSE chat is popping tonight
Daniel Donnelly
Apr 8 05:52
Is a context tree the way to go... ?
Daniel Donnelly
Apr 8 05:51
Anyone here know how Proof assistants work internally?
Daniel Donnelly
Apr 8 05:48
@PM2Ring 25) Spitting image of Robin Williams
Daniel Donnelly
Apr 1 07:17
I don't think AI's will take our job as creative maths for a very long time, like at least 100 years or so