@nitsua60 What is Jackson?

[Random]

it's an author

@Semiclassical I guessed that.

Michael?

no

I forget his first name. he wrote an electrodynamics text which is standard at the graduate physics level.

not so much because it's a good book but because there's really no other text out there which covers the same range of material.

@Semiclassical Ah.

I hate racism.

I mentioned a last name on another chat and a user said it was "too black of a last name" and it really upset me and now I've been banned.

welcome to the new age.

@Dodsy I take it there were some other events/comments that transpired in between.

Well

So my cousin's name is matt

and there was a guy named matt

so i asked if his last name was my cousins last name

(Like, maybe you should have refrained from responding, and just flagged the post that upset you....)

and he said "no that's too black of a last name"

and I said 'what does that mean"

and someone else joined in saying it was a black name

and I said no no you don't understand, it isn't a traditional black name it would be a name given by slave owners

then i quoted a really good quote about using the term "black"

and the guy laughed a me

@Dodsy I really don't think rehashing it here is a good idea.

It has absolutely nothing to do with math.

and called me Rachel Dolezal

@KasmirKhaan yes

well, I've been here a long time.

hi Demonark

Hi demonark.

@Dodsy 5 months, one post on the whole network?

?

alright thanks for that.

I'll say instead then

@Dodsy I'm just sayin'. I know of plenty of cases of users complaining about chat bans in other rooms and getting the situation escalated so they get banned more broadly or longer or suspended. I don't know of any cases where the complaints gave anyone a nice rosy glow of satisfaction.

this isn't even other rooms

this is discord

why did you ask me if you didn't want me to answer?

jesus.

@Dodsy I didn't ask you anything.

Read the transcript.

@Dodsy I take it there were some other events/comments that transpired in between.

this is an invitation for story time

this is legit what I've been dealing with all night.

@Dodsy Ohhhhh. So, not SE. I get it.

yeah but I've only been here 5 months, so fuck me right?

@Dodsy No, not at all.

And don't swear, please.

But I don't quite understand what you meant by "I've been here a really long time." (a) I thought you were talking about an SE chat ban, so (b) I thought you meant a long time on the SE network.

Many people consider the "f" word offensive @Dodsy.

do you?

were you the one who got me banned from here earlier today?

@Dodsy Only if someone says it to me, otherwise I'll ignore.

for saying "omfg"

I spent a good chunk of time earlier today puzzling out how moderation works in the SE chatrooms (it's in this very room; you can check the transcript) so when you started talking about a ban I naturally started thinking of SE chat bans....

@Dodsy That's offensive too.

it really isn't.

I was talking about something unrelated to anybody

@Dodsy It's disrespectful to God.

I DON'T BELIEVE IN GOD

is that disrespectful?

@Dodsy But there are other users who do :)

I don't care,

@Dodsy No, that's your opinion.

@Dodsy Chat rooms and communities are based on agreement. So when you're out of agreement and strongly assert your disagreement, you will get rejected.

I don't get offended when they practice their beliefs

it is also your opinion that omfg is offensive

@Dodsy Define "offensive."

so are you offended if I am muslim?

@Dodsy No

if i said "jesus doesn't exist"

is that offensive

no it isn't

so why is it any more offensive to practice my belief of not believing in God?

does that offend you?

@Dodsy there's a chat room for this. Take your discussion there, please.

No.

I was banned today for saying "o.m.f.g"

I am sick of this chatroom bs.

"o..g" is offensive @Dodsy.

that offends me

@Dodsy Calm down.

@anon, can you please move the discussion regarding offensiveness/unoffensiveness to the chatroom I linked above?

that you find that offensive.

@secret

so i met an aussie today

I forget his uni name but he's from the south.

@anon, it's essentially everything since Dodsy entered the room several minutes ago, except a couple isolated posts.

Basically, the chat can continue without the the use of swear words @Dodsy :)

@Dodsy Adelaide maybe...

Hi and good morning @LeakyNun

first of all, if you think it's okay to impress your belief in god onto me, then it's okay to impress my unbelief in God onto you. He doesn't exist so there's nobody to offend.

omfg therefore offends nobody, not even fake god.

@Dodsy You're creating an argument out of nothing. Literally.

how does that feel?

You are deliberately trying to be offensive.

to have somebodies beliefs shoved down your throat

I never impressed my belief on anyone :(

Didn't you?

Guess what, you will get banned that way.

you said it offends God.

@Dodsy No, I didn't

Well, I'm sick of it, Wildcard

@Dodsy Then leave.

and you aren't the ambassador of the chatroom

@Dodsy It offends other people because it seems to offend God.

because you told me too?

as if..

Please, can we all calm down in here.

@Dodsy Because you're a rude, disrespectful person who came into a MATH chat room to pick a fight that has absolutely NOTHING to do with math.

That's why.

No I didn't

you directed hatred towards me

@Dodsy Okay, then let's talk math.

because you've been here longer

> Don't vent frustrations by lashing out at people.

@Dodsy Evidently this is hatred:

yes

that's rude

or are you literally that socially inept

I was wondering what you meant.

2 years? doesn't even know anybody on the chat?

Quite a few flags from here.

@Dodsy Rude is not hatred. That wasn't hatred. And I don't think it was even rude.

@Dodsy Really, let's talk math.

because you don't think it was rude, it wasn't rude

If you want an argument, let's have a knockdown, drag-out argument about math.

@MartinSleziak welocome to math chat

@Dodsy I reeeeeeally just don't care.

basically abcd is flagging me all day

???

and saying how he feels

seriously, can we talk about math now?

but I can't do anything about it

sure

@Dodsy Do you think infinite cardinalities make sense?

@Dodsy all day?

Thank you for welcoming me, but it's not my first time here.

@Abcd Just drop it.

yes

(My advice.)

you were here when I was banned earlier

@Wildcard Yeah, sure.

and now I've been flagged?

such a joke.

Please, can we stop arguing, shouting, and insulting each other. SE's be nice policy applies everywhere, including in chat. Let's drop the issue, I don't want to have to call in some mods.

@Dodsy Do you think it's necessary to prove that 1+1 = 2 or should it be taken as axiomatic?

I hope you get what you deserve

@Dodsy Do you think it is sensible to treat a cauchy sequence as though it were an actual number?

@Dodsy So...you didn't come to pick a fight, but you're ignoring all my math-related questions....

I guess you're just killing time?

Yeah I came here to get pick a fight

you asked me what was up

realized it was about race

told me to shut up

@angussidney Please feel free to; before this he was complaining about a ban on some other site, so I don't think this is going to change.

and told me I haven't been here long

please bring a mod

actually please

because look at how combative you are

stop @ing me

stop talking to me

leave me alone

@Dodsy I'm using the "reply" button.

why?

@Dodsy Because I'm replying.

stop talking to me

hi @AlessandroCodenotti

please bring math into this room to stop this nonsense

@LeakyNun Feel free to chime in on any of the questions I wrote above.

I think we could have a really interesting discussion from any of them.

@Wildcard what is a number is the equivalence class of cauchy sequences

modulo "sameness of limit" defined in terms of the sequences

@Wildcard you have issues

so no, a sequence itself isn't a number

@LeakyNun See, I think that's total nonsense. (Now we're talking!)

@Wildcard why so?

@Wildcard so is a function a number too?

@Dodsy You told me to stop talking to you. I did. Now you're pinging me. You have misquoted me several times already, yet claim you didn't come here to pick a fight. Answer one of my math questions above or do not address me again (except perhaps if you wish to acknowledge this chat message).

@Wildcard the "actual numbers" that make up the sequence are also coded as sets most likely in this context

your math questions are meant to provoke

I literally wish you would shut up and do actual math

@Dodsy You came to pick a fight. So I thought I would give you a fight about math.

it seems that you've only the slightest understanding of the subject.

and even that is fleeting.

Glad you've got all of your pals around you

nice chat

@Dodsy I started frequenting this chat room like yesterday. I wonder why you apparently believe that I have "pals" and that you don't? Could it be your own perception of the world that adds hostility into every discussion? Could it be that other people really aren't out to get you? Could it just be that you're reading antagonism into people's words when it's not there? (Of course, that easily becomes a self-fulfilling prophecy. But I am even now not hostile to you in the slightest.)

@azureai Yup :D

so you started here yesterday

then decided to make me feel bad

for not posting much on the actual SE

but talking here a lot

@Wildcard would you answer (any one of) our responses towards your math questions?

@Dodsy Read the transcript. If you really think that's what happened, I feel sorry for you. You are reading malicious and hostile intent into ordinary questions and statements.

@LeakyNun Yes, yes. Sorry. Wow, interesting to have so much drama....

Hey all. Not sure what's going on here, but let's remember the be nice policy.

@AlessandroCodenotti I don't quite understand this statement.

@LeakyNun This I can agree with.

We expect community members to treat each other with respect … even when they don't deserve it.

@Abcd I don't know what you're saying "yes" to but I agree with your statement.

@Wildcard I copy-pasted that from the Be Nice page because people weren't visiting the page I guess.

@Abcd :D

@LeakyNun Honestly, I'm not hugely interested in debating such things. I think we can have a better conversation than that about interesting puzzles and such. But I thought it would be a good way to change the subject from a fight that wasn't math related, to a fight that was. I mean, if we're going to have a fight anyway, we may as well fight about math.... :)

But I will state my views, since I brought it up:

Dodsy left...

@Abcd Noted.

@Wildcard in a context in which you're interested in a formal construction of the real numbers via Cauchy sequence of rationals you should also worry about what thw rationals are

My views: I think it's perfectly fine to play with cauchy sequences and infinite cardinalities and so forth, but it's not something you can really ever do anything with. I get the logic—I admit it has self-referential validity and "consistency" and so forth—but you can't apply it as cauchy sequences and as infinite cardinalities to the real world.

There's a fantastic quote by Knuth that I love; let me dig it up....

I mean in the most common axiomatic formalization of maths there's only sets, no "actual numbers" at all

> I don't know why it's important to me if something relates to practice or not. There are mathematicians who never think about anything finite, and they hardly ever come down to countably infinite—they publish terrific papers just talking about kinds of infinity that are mind-boggling and they're able to make sense out of it and that gives them satisfaction.

> And there are similar things like that in algorithms. But for me I'm turned on much more by the ideas that I would be able to use in my machine.

the context of cauchy sequence is to make the system consistent; whether it is applicable to the real world is irrelevant

— safaribooksonline.com/library/view/coders-at-work/9781430219484/…

@LeakyNun Right. That's what I disagree with as an ideal.

That consistency is more important than workability.

And now, I have to step out. Thanks for the chat!

when did anyone say that it is more important?

Hello @LeakyNun. How are you?

not bad

Are you in college/ university @LeakyNun?

not yet

@LeakyNun High School!?

finished

Okay, so I guess you are studying independently @LeakyNun.

no, uni starts in oct

Okay.

@LeakyNun In what country? Iceland?

ucla starts either at the end of sept or beginning of oct, depending on the year

Doesn't it get cold though?

I mean I would expect it to start earlier so people don't freeze to death trying to find their classes on the first day

@JennaSloan see my profile

@LeakyNun Your country and university aren't stated in your profile

@Abcd but my university (hence my country) is

it is

I can't see it @LeakyNun

I mean math.SE profile

Please send link @LeakyNun

math.stackexchange.com/users/328173/kenny-lau?tab=profile

@LeakyNun is from London.

I'm from Hong Kong

@LeakyNun Imperial college is in London too :P

@Abcd I'm going to London

lol, okay :-)

Did anyone notice Prof. Ted Shifrin here today?

How to get unit vectors through Math Jax?

Can't find anywhere.

$\widehat{n}$

okay.

$\hat{n}$

$$\oint_{\{z \in \Bbb C : |z| = 1\}} \dfrac 1 z \ \mathrm dz$$

Let $z=\exp(i\theta)$ where $\theta \in [0,2\pi)$.

Then, $\mathrm dz = i\exp(i\theta) \ \mathrm d\theta$.

Our integral becomes $$\int_0^{2\pi}i\ \mathrm d\theta$$

which becomes $2\pi i$.

Hello

Am I doing something wrong?

Because this answer isn't one of the possible ones

Or is it right? Because isn't this condition the same as $a^2+b^2 \neq 0$ ?

@Evinda I don't

G=(0,infinity) is a group under multiplication. can someone tell me any one subgroup of G

Powers of 2 with exponents in Z

A ok @LeakyNun

Let $V$ be a basis of $\Bbb R$ as a vector space over $\Bbb Q$. Then, a subgroup of $G$ is characterised by $U$a subset of $V$ with $\{u_1^{a_1} u_2^{a_2} \cdots u_n^{a_n}: a_i \in \Bbb Z, n \in \Bbb N, u_i \in U\} \le G$.

In @Alessandro's example, we have $U=\{2\}$. (cc @NV-US)

Hi, Demonark

Hello @Evinda. I remember you. Aha!

Hi @Jasper How are you?

@Evinda Same, which means still sick.

:(

Have you finished your degree now?

I am doing my master. I haven't finished yet. @Jasper

@LeakyNun Not every subgroup is of that form though. Also I don't see why fixing a basis is needrd rather than taking arbitrary elements

@AlessandroCodenotti for example?

@Evinda Well done! I hope you become a great mathematician some day!

You're excluding things like $\{2^a3^b:a,b\in\Bbb Z\}$

@AlessandroCodenotti oh, right. Disregard my elaborate nonsense.

Thanks :) @Jasper

As well as infinitely generated subgroups I think

Isn't $2^q$, for rational $q$ a subgroup as well?

@AlessandroCodenotti @LeakyNun thank you

@AlessandroCodenotti right

my whole question as is given in the textbook is to find subgroups of G=(0,infinity) that are compact. how can i proceed?

Compact means closed and bounded for subsets of $\Bbb R^n$, I suggest you start looking for bounded subgroups

@NV-US in the usual topology?

sorry, metric induced from R

@AlessandroCodenotti can u give me any one example of a subgroup of G which is compact. i need an example, then i will start my own thinking, i cant think of one

$\{1\}$ is a compact subgroup

If you can't think of any nontrivial example maybe you should try to prove that there is none

non trivial

so there is none?

Maybe, it was a general suggestion, if you can't find examples of a mathematical object you should wonder whether there exist any

@NV-US think by yourself.

i was thinking like, let H be a subgp of G, then H is compact implies H is closed and bounded. Since it is bounded, H must have finite order. so if such a subgp exist, it will be of finite order. will i be right in saying this?

Hello!! Does someone of you have an idea about my question: math.stackexchange.com/questions/2422392/… ?

@AlessandroCodenotti @LeakyNun

why does bounded imply finite order?

@LeakyNun Hello

@Mr.Xcoder hi

because they are numbers, and because of closure, all of their multiples must be in the set

i'm confused, please give me any one example, so that i can know what they look like

If a subgroup contains $a$ it must contain $\langle a\rangle$

@NV-US all of their multiples?

I can't give you any example because they are all trivial

ok

so {1} is the only one?

yes, but you need to prove it

i will, thank you.

was i wrong in saying that order of H can only be finite? (above)

@NV-US it can only be 1, so I'm not sure where you're getting "finite" from

bounded does not imply finite for arbitrary subset of the real numbers

ok

That ********** koolman is now in h bar

looks like somthing big is going to happen

Hello guys i got a question

@samjoe just ask

Is there a theorem in maths about centroid of area drawn on top of hemisphere?

Let H be a subgp of G, and let H be compact, then H must be closed and bounded, so i let a belong in H, a not equal to one, then all multiples of a must be in H, upto order of a. but all elements of G has infinite order, except 1, so H will be unbounded. therefore no subgp's of G are compact, except the trivial one. am i right in saying this? @LeakyNun

@NV-US all multiples of a?

yes, upto order of a

powers of a

sorry

is it correct now?

yes

thank you

@LeakyNun I was looking for formula similar to this

A is arbitrary area on sphere surface

uniform distribution of mass on Area A

B is projection of Area A on Base of hemisphere.

Formula says the Y coordinate of Centroid is A/B times R

Where does this formula come from?

Does it have a name?

hi we know that $R^n$ isomorphic to $R^m$ need not imply m=n for non comm rings, but can we extend the result to say that f.g free module isomorphic to infinitely generated free module.

What's the point of proving a polynomial to be irreducible over integers ? Is there any number theoretic consequences of it ?

hopefully leaky can handle koolman

That Bomb is still not being in used yet

and I don't want to use it

what is the bomb?

Codename: Infinite expanse

and what do you mean by handle? @Secret

cc: @BalarkaSen this

koolman is quite help vampire-ish, at least a year ago

I have not seen him for long until just recently for this year, and he is still rather help vampirish

I am glad you and other people have handled him well by guiding him to show his effort

@Secret you do know how to use the "ignore" option, right?

There's a reason I don't use that button

For now, I will let you to figure out what it is...

I meant in life, pal.

same answer to that

suit yourself

paying attention to something that annoys you is a waste of your energy

it's sort of like why "hate" destroys the hater

So if we have an outer measure $\varphi:2^X\to[0,\infty]$ it is continuous from below, meaning that for an increasing sequence $\{E_j\}_{j\in\Bbb N}$ of measurable sets we have $\varphi\left(\bigcup_jE_j\right)=\lim_j\varphi(E_j)$ and from above, meaning that for a decreasing sequence $\{F_i\}_{i\in\Bbb N}$ of measurable sets with $\varphi(F_1)<+\infty$ we have $\varphi\left(\bigcap_iF_i\right)=\lim_i\varphi(F_i)$

Can this be interpreted as $\varphi$ being continuous wrt some (ideally natural) topology on $2^X$?

please ignore that ^

(semi-removed)

(removed uncountably many times)

(removed $\aleph_0$ times)

$\aleph_0$ is too small

(removed $\mathbf{c}$ times)

:P

(removed)

Actually, we need a cccoo-mbbboo breaker

@skullpatrol I agree pal, but sometimes something messes you up so much you have no choice but to pay some kind of attention to it.