@Loong Whoa I didn't even hear of that!

I'm not in superheavy element research but I image those guys are happy!

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ about him I just teased him ;) and I know. about the quote your welcome, that's a favorite of me too

@0celo7 iupac.org/cms/wp-content/uploads/2016/06/…

can a set be a subgroup of a group?

@Loong I already looked it up

@Obliv ...what

all groups are sets

so all subgroups are sets because subgroups are groups

oh i thought they were ordered pairs

of sets with operations

groups?

a group is a set with an invertible associative binary operation

right so I thought to be a subgroup one had to be a subset under the same operation

and if the operation wasnt explicitly defined it couldn't be a subgroup

wasn't explicitly defined?

the kernel is defined as a set in this text and I'm told to prove it is a subgroup of something. So, I was wondering if a set could be a subgroup without an operation explicitly defined @0celo7

kernel of a group homommorphism?

yeah

of course its a set

because its a subset of the group

@Loong thanks for sharing

"So, I was wondering if a set could be a subgroup without an operation explicitly defined"

I don't know what this means

if you have some subset of the group the operation is inherited on the subset

@ACuriousMind A mathematical analog would be interesting.

Tautological bundles etc.

isn't the kernel of a homomorphism just a set of 1 element? Say $G,H$ are groups $\varphi:G \to H$ is a homomorphism. The kernel of $\varphi$ is $\{g \in G~|~\varphi(g) = I_H\}$ isn't there only 1 element in this kernel, which is the identity element in $G$? Like say $\varphi(ab) = \varphi(a)\varphi(b)$ where $\varphi(b) = I_H$ then $\varphi(ab) = \varphi(a)I_H$ only 1 $b$ such that $\varphi(ab) = \varphi(a)$?

@Obliv No.

Think a bit harder. Recall how I told you about trivial homomorphisms.

Also, I suggest you ask all these questions in the Mathematics chat ;)

@Danu the math chat is full of people who hate people

it's not a good place

And this is?

It's very good

well mostly they don't ever answer my questions :D @0celo7

and when they do, it's either mike who is really cool or arctictern who probably hates my questions :p

Mike is too brusque

he makes @Danu look like a sweetheart

Implying I'm not. (?!)

You're a bully

Take that back!

@Danu used to be really cool and fun but he suddenly became all serious.

shots_fired

@3075 :D

(also I was joking about taking that back, don't worry. I know I'm your favorite bully)

@Danu No.

→ 1 message moved to Trash

I've had enough of your crying wolf

→ 1 message moved to Trash

The dynamics of the two rooms is totally different

Woops

lol wtf is going on

→ 1 message moved to Trash

@0celo7 Oh, I intended to move those.

There used to be plenty of real bullies in the math room.

:D removed mine

→ 3 messages moved to Trash

Trust me ;)

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ like that one guy, what's his name

uh

the math prof

Terry Bollinger?

Sort of

No

Ted Shrifin?

@0celo7 If you're referring to your recent ban, I'm sure you're aware that since I'm not a PSE moderator I did not have anything to do with that.

@0celo7 lol the "dude"?

He's ok

@0celo7 Ted is a super nice guy! :)

^

@Danu No

@0celo7 What'd he do to you?

Just don't piss him off

@Danu No I didn't know that

@0celo7 OK. So now you know.

@Danu No I'll forget

That's fine---there is a transcript for a reason.

Noooo not Taylor

??

Better

@danu I don't see what you mean by the trivial homomorphism. If there are multiple elements in $G$ that the image of which is the identity in the target set, doesn't that mean $G$ has multiple identity elements?

@Obliv No.

Also, the irony of a German pop song only being blocked on German YouTube is great.

@Danu HAH

@0celo7 You took it to the non-English level...

Is LaFee still around?

No idea who it is...

The singer of the song I linked

:O

@0celo7 Steen is hilarious

me right now:

how can $\varphi(gh) = \varphi(g)\varphi(h)$ be satisfied where multiple elements $g \in G$ satisfy $\varphi(g) = I_H$ without $g$ being the identity in both $G,H$?

@Obliv el magico

$\varphi$ need not be injective, that's now

if it's not injective, you're telling me there are multiple identity elements in $G$, no?

i'm looking at this wrong brb gonna take a walk

@Obliv no

@Obliv ok

@Danu that doesn't seem to be a German song...

but LaFee isn't around... not that I know

@Vogel612 The song 0celo7 posted is.

hmm.... yea...

@Vogel612 do you have a script that calls you when someone says "German"

lol

@0celo7 nope... I just can see chat-flags

ffs who is flagging now

No worries, I'm on it ;)

@Danu abuse != on it

well, I guess it is

but not in a good way!

@0celo7 Remember when you went on your anti-swearing rant? You oughta sympathize.

sidenote: music discussion is welcome in "Off the record" anytime:

</shameless plug>

lol

@Danu hmm?

Who swore

You

Shock and horror!

I doubt that

You do it all the time

Nice try

Without thinking

@Danu You better watch out.

@0celo7 2 chainz the real gangster

Some people take automatic offence to the F word. That's just the way it is.

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ I know

Like me

whatever

@Danu realler than you

3real5me

expect flags then, gangsta

@Danu Maybe you should go to sleep

@0celo7 This is too easy.

In other news, that was not the original Protect Ya Neck. Corrected now.

I really don't understand many of the rules here on stackexchange

particularly on meta

Askaway

@Danu Why is there a tea kettle in the background

@0celo7 In the corrected link, there is not. I don't know the song I first linked (and it didn't sound nearly as good as the older song).

yeah it's there in the old one too

Really? A tea kettle?

when sb can close a question? how can he/she realize it's a homework type q or not for example

I didn't spot it...

3:53

I'm there right now

and here this F word argument

Should 'fuck' be present in review audits ?!

@0celo7 The song I linked (again, the corrected one) has a picture as "video".

@2physics Link?

obviously it should !

@Danu I know!

hold up for a moment, you about to see some greatness

I'm going to stop paying attention now.

:(

I was going to write a rap :(

damn i got like 8 more mins left to learn why a kernel isn't a set of identity elements in $G$

@Danu wts the invitation for?

@Obliv why do you think it is

@2physics Did I invite you for something? I'm sorry, that must've been a mistake.

en.wikipedia.org/wiki/Kernel_(algebra) here it shows (under group homomorphisms) that its only injective if and only if the kernel is the singleton set $\{e_g\}$

(removed)

@Danu the trash

you invite people to the trash when you abusively delete messages

But my line of thinking is that unless there were other identity elements in $G$, there cannot be any other elements such that $f(g) = I_H$

it's insulting, really

i'll think more about it tomorrow i have to go :\

what

the homomorphism need not be injective though

@Obliv I just told you. Think about the trivial homomorphism.

what are you talking about

idk we'll see

Send every $g\in G$ to $e\in G'$, for arbitrary groups $G$, $G'$.

Everything is in the kernel.

Isn't it obvious that there can be nontrivial elements in the kernel from this example?

@Obliv that's a homomorphism because $\varphi(ab)=e=e^2=\varphi(a)\varphi(b)$

^

@0celo7 stop being so overly sensitive

You've done worse

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ I'm not sensitive at all

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ I don't think so :/

whatever

nvm

Just remember mod=god

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ I tempt the lord every day

Enough said.

I only recognize two gods @Sᴋᴜʟʟᴘᴇᴛʀᴏʟ

That ^ looks promising

neither are mods

Did you find my meta post protesting your ban @@0celo7?

Did you even look?

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ Yes I looked, I could not find it.

They stripped your username from it :(

can you please link it

I can't find it

But whatever

Wait till after the ama @0celo7

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ what is that

and why am I waiting

We need to hang low for awhile

dude just link it please

did it get deleted?

what's the title

what is the content?

Ask Me Anything

I'm going through ALL posts and I cannot find it

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ no of the protest

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ what, why? The AMA is still 6 days away and there's no particular reason to wait for it anyway

yes sir

and just for the record, saying things like that isn't going to improve my impression of you

@DavidZ why would you have a bad impression of him

he's always well behaved