Mathematics

If $f:F \rightarrow L$ and $g:L \rightarrow F$, is it at least OK to say that $fg=id_L$ since they agree on $B$?

you can say it if you can explain why that is enough :-)

Is it because $B$ is a basis for $L$ and the uniqueness thing?

then sure, you can

I'm still thinking about $gf$ though. Grrrr

7:17 AM

well, $B$ as a subset of $F$ has a property... use it

Oh god

OK thanks a lot

I don't know how the hell I didn't see that

now go write an answer to your question which you can understand

and accept it

(youwill have to wait a day or so, to accept your own answer, tho)

That would be too embarrassing

no, it is not

if you must, tell the world that I forced you

So would you say that using the Yoneda lemma for this result is going a bit too far?

7:22 AM

not really

but if you do not understand the lemma or the way it is used here, then it is useless

the Yoneda lemma is the abstraction of this result (and many others like it)

Interesting

makes me want to learn category theory

don't

?

the best moment to learn category theory is when you already know it

4

and you still don't :-)

Another question - what's with the quotes on the right hand side of the screen?

3

7:25 AM

I should go to bed... I am speaking in apothegms...:-/

what do you mean?

well

who puts the sentences up there

people can "star" things we say here

and then they get put there

each of out lines here is in a box: put the pointer to the right of that box

a star will show up

ah thanks

if youclick on it, then you have starred the line

for some reason, people in stackexchange seem to looooove the :hover property

John Senior

Good morning all

7:29 AM

hello sir

hi

@MarianoSuárez-Alvarez Hi

Hello Ben

@MarianoSuárez-Alvarez I have a lie theory exam tomorrow :D

cool :-)

7:32 AM

Just proved that if $G$ is connected

then $Z(G) = \ker Ad$

@MarianoSuárez-Alvarez How come you don't hang out so much in chat anymore?

well, I do have a job :-)

@MarianoSuárez-Alvarez You met Peter Tamaroff?

these last few days, for example, I am reading a thesis

Ah ok fair enough

@MarianoSuárez-Alvarez I find Lie algebras exciting

they are very nice

7:34 AM

You learn that if $G$ is connected

I did meet him

and he came to my office last week too

then you have a galois correspondence thingy happening between normal subgroups and ideals of the lie algebra

@MarianoSuárez-Alvarez So lucky he is

Thankfully I can invade Jarod's office at any time

@MarianoSuárez-Alvarez I asked a question on linear algebraic groups

have you seen the book by malle ?

after you are done with your test and all, you should browse a bit Serre's book on lie groups and lie algebras

you'll probably enjoy it

not familiar with the book, but I've seen it

@MarianoSuárez-Alvarez I am going through questions from here

@MarianoSuárez-Alvarez But I do say that without a knowledge of differential geometry, it is hard to see what is going on behind

nimbus roman font, ugly! :-P

7:37 AM

What I like about this course is

Algebraic topology is coming in

Differential geometry is coming in

Like today we proved that if G is simply connected then a map of lie algebras induces a unique lie group homomorphism

@MarianoSuárez-Alvarez Can they really be summed?

lie groups is a nice subject because it mixes up everything

we used the fact that G simply connected implies if you have $f : K \to G$ a covering space map then $K$ is isomorphic to G

Yeah

Like I keep hearing about flows, submanifolds and smooth immersions :D

Issac M

$f : A --> R$, with $A \subset R$. What do we call $f(a)$ where $a \in A$?

@GustavoBandeira, what do you mean?

7:40 AM

@GustavoBandeira Forget about that guy

You can only talk about the limit of partial sums

Jayesh Badwaik

@GustavoBandeira You can only talk of limit of partial sums.

yunone

@IssacM The image of $a$ under $f$?

You look at $s_N$, and the infinite sum is defined to be $\lim s_N$

Jayesh Badwaik

@BenjaLim Damn! We have posted exact similar message.

Issac M

@yunone Ok so it's fine to use image even though image is also defined as $\{f(a) : a \in A\}$?

7:41 AM

@MarianoSuárez-Alvarez I must say that in these more advanced courses

@JayeshBadwaik @BenjaLim He's really stoned then?

They do demand that you have an overall understanding of what is going on in general in maths

@GustavoBandeira He is talking nonsense

@GustavoBandeira Like in Fourier theory

so many times you deal with infinite integrals and things like that

what makes you so sure you can just do a change of variables?

@MarianoSuárez-Alvarez "can you point to any reference where an 'infinite sum' is considered?" He said it's in Rudin's book - but he didn't say in what page lol

well it's because in your infinite integral, you are taking the limit as $x \to \infty$

yunone

@IssacM I could call that set the image (or range) of $f$. But I could call $f(a)$ the image of $a$ under $f$. Notice the slight difference in wording.

7:42 AM

and certain operations commute with limits

and then you're fine.

Issac M

@yunone Perfect answer. thank you.

yunone

@IssacM Sure thing.

Jayesh Badwaik

Well I'll be off for lunch.
@GustavoBandeira See you around later.