6:54 AM
Hi
Can anyone help with a complex number question ?

7:04 AM
A JKL map is an open continuous surjection $f:X\to Y$ from a noncompact Hausdorff space $X$ to a compact Hausdorff space $Y$ such that every fiber is finite with the same size (i.e. $|f^{-1}(y)| = n$ for each $y\in Y$). It's known there isn't such a map once $Y$ is first countable but the existence is unknown in general.
any interest in this @Jakobian ?
note that the conditions on JKL map are carefully chosen so that the existence is nontrivial.

7:31 AM
hello all. I am wondering what result is used to obtain (1.2)? I think it should be some standard result of Lie theory, but I have only worked through some of Hall's text, which does not go through Lie theory in full abstraction.
I thought maybe that there exists a finite covering $\tilde{G}_0$ is a consequence of the fact that $G_0$ is compact (since it is a subgroup of a compact group), but I do not understand what the finite abelian group $A$ is doing.
or, would this all be answered if i read up on a section of classifications of compact lie groups?

8:24 AM
yes, that should all be in a book on lie theory, although i don't know of a reference off the top of my head, particularly one that would harmonize with hall. i understand that some books adopt different definitions (depending e.g. on how abstract they get) and sometimes present the material in a different order.
the finiteness might arise out of something like math.stackexchange.com/questions/3360023/… where somewhere out there, from compactness of G, lie theory gives you an abelian T and a simply connected semisimple G' and a surjective map from T x G' onto G that is nice enough (by abstract properties of G, T, G') to be a finite covering map.
and then some lie theory tells you that G' has to look like that K_1 x ... x K_n.
if you know via abstract nonsense that lie algebra of a connected compact G splits as abelian + semisimple, then T = exp(abelian) and G' = exp(semisimple) are good candidates for that kind of idea

Hi,
If i have two points(x,y,z) and one of them is moving, how can I tell which axis I am moving along
I am not looking for direction vector, I want to know if I am moving along x or y or z axes

@onepotatotwopotato there are multiple results in dimension theory that tell if a certain open surjective maps exists that has nice fibers, then dimension is not changed. This reminds me of that a bit
@fido9dido isn't this physics

@Jakobian more like vector math or computational geometry(it has many names) but not physics

You said its moving. So it can move in some crazy way I imagine. Unless we are in physics world or something
Besides even if a point is rotating then why would it move with respect to x, y or z axis

8:40 AM
when i said moving, I meant one point is fixed and the other can be at an arbitrary location, sorry but English is not my native language

Doesn't clarify anything
If you take a point rotating around the origin for example, it moves in a plane but not necessarily xy, yz or xz plane

let's say Point A is at (0,0,0)
and point B can be anything like
B is (10,1,1) then i want something to let me know it's X axis
B is (2,20,5) and here Y axis etc
I can look at the max and min values but I wonder if there's a better way

You need to practice your problem explanation skills

Agreed

I still don't understand you

8:49 AM
nvm then, thanks for trying^^

2 hours later…
11:07 AM
I'm reading a proof of the monotone convergence theorem (only the comments of the post are relevant). It is claimed that the union of the $E_n$'s is $X$. I struggle with verifying this. In the comments it is claimed that:
Since $0\leqslant s\leqslant f$ and $0<\varepsilon<1$, clearly $(1-\varepsilon)s<f$. As $f=\sup_n f_n$, there exists $N$ such that $(1-\varepsilon) s \leqslant f_N(x)$ for all $x\in X$, hence $X=E_N$ (and $E_N=\bigcup_{n=1}^\infty E_n$ as $E_n\subset E_{n+1}$ for all $n$). — Math1000 Aug 31, 2023 at 20:39
I doubt what is written in parentheses; isn't $E_N=\bigcup_{n=1}^N E_n$ as $E_n\subset E_{n+1}$ for all $n$?

@psie E_n?

@Jakobian yes, those are sets defined in the proof; Rudin uses $E_n$ too, here is his proof for reference, but the relevant part is why the union of the $E_n$ are $X$.

@psie whats $E_n$
If $X = E_N$ then certainly both are equal $X$

11:23 AM
I wonder why $E_N=\bigcup_{n=1}^\infty E_n$. $X=E_N$ is clear, but I don't understand why $E_N=\bigcup_{n=1}^\infty E_n$.
Anyway, maybe the comment doesn't make sense, Rudin provides another motivation, but it's not a lot of motivation

11:40 AM
@psie If $X = E_N$ is clear then obviously $X = E_N\subseteq \bigcup_{n=1}^\infty E_n\subseteq X$, no?

true indeed :)
but the reverse inclusion remains, i.e. $E_N\supseteq \bigcup_{n=1}^\infty E_n$?

huh?
aren't $E_n$ contained in $X$ by definition?

yeah, maybe you showed it

I don't think you need to "show it"
they are literally subsets of $X$

yeah 👍

11:46 AM
I don't understand your problem here
even from technical standpoint this seems obvious assuming that $E_N = X$ is clear

now upon further thought, it is clear, thanks

try to think about those things more before posting here. And don't take comments at face value

3 hours later…
2:49 PM
Is the serial downvote correction automatic? I just got four downvotes in quick succession.

@Shaun Yes.

Cool. Thanks :)
How's your weekend going, by the way?
@XanderHenderson

It is a weekend.
I got home yesterday from a conference.

What kind of conference? How was it?

@Shaun ArizMATYC / MAA sectional joint converence.
It was good.

2:52 PM
Great :)

Though the main reason I went was for the spring Articulation Task Force meeting.

I have three conferences coming up: one for Computational Group Theory, one is the Postgraduate Group Theory Conference, and the other is the GAP Days in August.
@XanderHenderson I don't know what that means.

@Shaun In the state of Arizona, the community colleges have agreements with the three state universities regarding how certain classes will transfer to the universities.

I bought extra spicy ketchup
its more spicy than the usual spicy ketchup I find in stores

So, for example, if a student at my colleges takes calculus from me, the three state universities are required (by law, even) to accept that class as a one-to-one equivalent for the classes they teach. For the purposes of transcripting, it is essentially as though they took the class at that university (it counts towards credit hour requirements, prerequisites, programatic requirements, etc).
Each subject area has a statewide articulation task force which is charged with determining which classes will transfer, and how they will transfer.
I am a member of the mathematics articulation task force.
We meet twice per year to discuss changes to the statewide curriculum.

3:02 PM
are there going to be some major changes?
if thats not private information

@Jakobian There are almost never major changes.
The only thing that is kind of on the horizon (and which has been developing over the last several years) is that the colleges are creating pathways to degrees which do not require calculus. So there are now course options which don't lead to calculus, and the community colleges are struggling a bit how to offer new classes which fit these roles.
E.g. several of the CCs are developing data science classes (essentially introduction statistics classes with a bit of programming).

whats a CC?
community college?

Clan castle

It sounds like a hassle, @XanderHenderson. It's kind of interesting though.

@SoumikMukherjee you play clash of clans?

3:09 PM
I used to play a lot

I see. I have no knowledge of that game

@Shaun A hassle? Not at all. I love it. And I love that the community colleges in Arizona have a voice in how students are taught.
@Jakobian Yes.

2016-2022, coc was an integral part of my life, then I got bored of it

@Jakobian Kind of.

3:13 PM
Did they finally include category theory into undergraduate studies?
or was that included before already

In the US system, community colleges serve communities. They teach students who live in the area, and tend to focus on lower-division coursework and vocational training, as well as non-credit bearing "community outreach" classes (such as "sculpture" and "bird watching").
Typically, a student who attends a community college can, at most, earn an associates degree, with the expectation that they will transfer to a "four year" college or university to complete a bachelors degree.
But about half of our students are not even in transfer degree programs---they are in vocational programs (such as welding or cosmetology), and have no plans to complete a bachelors degree.
Though we do now offer three bachelors degrees.
(The second two are official as of this week, assuming no problems in the next month or two.)

Oh. We don't have something like the associates degree here to my knowledge. There's nothing in between high school diploma and Bachelor's degree

@Jakobian I wouldn't regard it as something "between" high school and a bachelors degree.
Many (most?) people who end up with a bachelors degree don't ever get an associates degree.
And most of our associates-degree-earning students are earning "applied" degrees (again, welding, cosmetology, etc), and will probably not ever bother to go to college for a bachelors degree.
An associates degree is a post-secondary degree, but it isn't exactly in the hierarchy of bachelors -> masters -> doctorate.
It is a kind of "side path" (typically).
Though a student who earns an associate of arts or an associate of science here can transfer to a state university as a third year student (they will basically be given credit for completing the first two years of a bachelors degree program).

in Poland you typically go to a vocational school after elementary school as an alternative to high school after which you would go to a university

I'm really glad you did something you loved recently :)
Too few people can say they have.

3:25 PM
and also technical schools after which you also can go to a university or begin to work
it was elementary school -> gymnasium -> high school or vocational school or technical school
and now its elementary school -> high school or vocational school or technical school after the change in education now that elementary schools fit the roles of gymnasiums as well (for better or worse for the kids...)
and high school or technical school -> university after getting "matura" which is a high school degree basically

In the US system, there are vanishingly few "specialized" schools for students under the age of 18. Basically every student goes through the same general curriculum from kindergarten through high school.
The goal of this primary and secondary education is to give students a basic foundation for life---some academic skills, some vocational skills, and some life skills.
Specialization into a career or academic path only begins after high school.

yeah... if you go to a high school you're basically doomed to go to a university here

2 hours later…
5:23 PM
If you can a^x then x is the exponent, but what is a called?

base

Thanks. What would be the exponential "term"?

@Simd What are you asking exactly?

@Jakobian is a also the exponential term?
@Jakobian I want to refer to the value a

define exponential term
are you asking what exponential term is?
according to this site it would be the whole expression "$a^x$"

5:31 PM
@Jakobian thank you. That is very helpful
Is a also the "exponential base" ?

this should be the terminology, yes

5:44 PM
Or "the base of the exponent".
In the exponential expression $b^e$, the variable $b$ is the base, and the variable $e$ is the exponent.

4 hours later…
9:18 PM
i wish ted were here
9
i have a question about differential equations and he always has the most insightful responses

@Allie It's not the same without Ted.
2

WHAT HAPPENED

@XanderHenderson some would say the goal of primary and secondary education is to be daycare so parents can work outside the house

9:39 PM
Where is Ted?
3

@Derivative Those people are typically either (a) cynical, (b) politically motivated, or (c) bad parents.

@Derivative it certainly works as that nowadays but its not the only function of it, and I wouldn't call it a goal. A goal would be to educate students and school does provide that, for as much as you are able to provide knowledge to a massive amount of people

@XanderHenderson in my experience, never blame commission when omission is a possibility...
even very smart people can be very dumb

9:54 PM
@copper.hat I think I covered that with "cynical". :)
Bad parents, too. Negligence is usually the issue.
Kind of like my ex-wife, who seems to think that public school is a babysitting service. :/

i actually know everything and all the correct opinions

What's a correct opinion

the right one, duh.

As opposed to the left one?

no actually leftism is cooler so thats the right one
TED DDDDDDD

9:59 PM
But rightism is hotter

i suppose if you mean global temperature
then youre correct

I mean the sex appeal

i actually find right wingers very ugly people

I thought we were talking about handedness

LOL

10:06 PM
How's the conference going? @XanderHenderson

10:45 PM
@user85795 Oh, it's over. It was only two days. I got home yesterevening.

11:07 PM