@TedShifrin I only know about Bruce Lee and John M Lee, lol.

Ooopsie @Kevin ... I wrote garbage in a comment the other day, but Donkey corrected me.

@MikeMiller How do you even get that?

I don't see it in user profile.

Basic arithmetic, @Balarka

Twice we've told him, @Mike

I hate it when everyone does that.

Kids these days...

@BalarkaSen Just go to your votes and filter ot only upvotes. It tell you the number of those. Then do the same but filter by only downvotes.

I couldn't take it anymore. Had to put myself out of my misery.

(Bottom right of userpage)

@KevinDriscoll Now here's someone helpful.

@KevinDriscoll Wrong method, lol.

@BalarkaSen Wrong method, lol.

@BalarkaSen See bottom right of user profile, lol.

Too hard, @Kevin: As Mike said, look at bottom right.

Oh, OK.

I really love to lol, lol.

@Jasper: Google Ang Lee — very famous, award-winning director, born in Taiwan.

I don't understand why books require the "has the 0 vector" requirement of a vector space

It follows from scalar multiplication (and that your vector space is nonempty)

Easier for students to check than nonempty @Mike.

grr

And easy to rule out some examples (like affine subspaces)

@Ted @Jasper The two methods are actually inconsistent. The summary page says I've cast 40 votes, 8 of which are downvotes. But if I got to my votes, I only see 1 downvote. I guess the summary page aggregates across various SE sites whereas my method restricts itself ot math.se

@MikeMiller In mathematics, we don't understand things, we get used to them, lol.

@JasperLoy Bullshit.

When you start teaching, @Mike, you'll get it.

.14 of downvotes. Ha!

@Ted why do they require that $1x=x$ ? /troll

what? @G.T.R

@G.T.R That is an important axiom.

Because otherwise you could have different actions @GTR

Maybe even that isn't right. I just went to my physics.SE page and it have even different vote numbers.......#confuzzled

@TedShifrin I think it's conceptually better to think of it as nonempty... that it necessarily follows that there's a 0 vector is interesting

(also I think you folks got trolled)

Pedagogically you lose @Mike ...

@KevinDriscoll They didn't do their basic arithmetic right I guess.

@TedShifrin Pedagogically I think students should have an exercise where they see that these other axioms are equivalent.

High-school math mistake.

They need an arithmetic number theorist @Balarka

How is it trolling, 1x=x is not required, it is necessary. As we define 1 to be the multiplicative identity, "the thing that when we do the thing denoted multiplicatively to another thing results in the second thing"

@TedShifrin Definitely not me.

@Ted @JasperLoy I'm not convinced. Can you find an example where all the other axioms are true, but not $1x=x$ ? /troll

@G.T.R What is 1? x?

In a ring I'm guessing?

what is multiplication?

oh shaddup you people

@MikeMiller "STAHP" - Peter Tamaroff.

@MikeMiller Flag, lol.

@BalarkaSen see axioms there en.wikipedia.org/wiki/Vector_space

Hmm, I miss @Pedro :)

Oh in a vec space, yes it is,because of distributivity from the field the vec space is over.

yeah, where did that guy go?

Seriously guys if I can do this, it's not hard.

Tragic car accident, @BalarkaSen

@MikeMiller really?

@MikeMiller tsk tsk

Did you go to the Funeral?

Of course not, I'm not made of money.

@AlecTeal Why not just ask Pedro?

If it is true he'll never respond.

@TedShifrin He had a haircut yesterday.

It could be true thogh, math.stackexchange.com/questions/827196/… 10 minutes an no answer (I really hope you guys are joking about his death, for whatever distasteful reason)

I was there @Jasper: Just one hair.

@AlecTeal Not if he left an imprint of his echo

Better to joke about my death — closer to imminent, and it'll make dozens of students happy :)

nerds

In This Thread

@Ted are you teaching over the summer?

Noooo .... Only 4 informal reading courses.

Someone upvoted my quintic answer. After such a long time.

@BalarkaSen Do you know my favourite question on this site?

No.

I didn't know it was posted ...

"only 4"

@BalarkaSen math.stackexchange.com/questions/203061/… I asked and answered it myself.

This just occurred to me: Minkowski space is not a traditional vector space because the norm is not positive definite. What is it then?

Vector space defn says nothing about norm.

@JasperLoy So there was a time when you asked questions and answered non-lhfs?

Oh wait it doesn't? I thought $x \cdot x = 0$ had to imply that $x = 0$

Hence semi-Riemannian geometry modeled on indefinite metrics.

Oh ya I guess thats a different thing?

@TedShifrin What's a semi-Riemann geometry?

You're defining an inner product space ... More structure on a vector space.

@BalarkaSen Well, I answer some slightly more difficult questions now and then. Two other users who answered that question were forced to delete their answers when I pointed out the flaw in their logic.

@Ted I just never thought about it because we still call all the quantities "4-vectors"

They are @Kevin.

Mathematicians care, too, @Mike. See $O(p,q)$, $U(p,q)$

Stop making snide comments, @MikeMiller

@Ted ya sorry didnt mean to imply that it wasn't just that I never thought about it. Its not a normed vector space though and until I thought just now those two were entirely equivalent in my mind.

But, yeah, I'd be glad to say

physicists

@Mike: My favorite model of hyperbolic space is a quadric hypersurface in Lorentz space.

(Symmetric space structure)

@TedShifrin I had meant to write something longer but hit enter too early :P

(And then I deleted it because the longer thing wasn't funny either.)

@TedShifrin Pic?

You're rarely funny.

Pic?

Of a quadratic hypersudrafe in Lorentz space!

See this

Your typing is worse than @Pedro's, @Mike

@TedShifrin Mean

@TedShifrin EH, isn't it enough to be getting on with Lobachevsky?

Not always, no @Balarka

That model looks so differential. Ack. No algebraic representation.

It's totally algebraic: Quotient of Lie group by closed subgroup

@TedShifrin Ah?

That's interesting.

Go away, Lie groups. I'm not ready for you yet.

$SO(n,1)/SO(n)$

Oh, no. Not my type of Lie.

Dual symmetric space to sphere $SO(n+1)/SO(n)$

Lobachevskian model is the most algebraic.

They're all isomorphic.

Answered another lhf.

@TedShifrin Special ortho groups are more differential than algebraic.

I am being a whiner. I know.

Nonsense.

Well, probably I am whining because it's not number theoretic.

Yes, you are indeed.

Your number theory is special to dim 2.

@TedShifrin "special to dimension 2"?

In the hyperbolic plane, not in $\Bbb H^n$, $n\ge 3$

This is why I prefer to hang out here: very few people come in and start 'pop-math' discussions that cause reasonable people to disagree about silly things like the arbitrary definitions of imprecise words. Someone in physics asks about whether something casts a shadow and you have to discuss what your definition of a shadow is......

@TedShifrin Yeah. That's kinda true.

just complaining

@TedShifrin Now that you mention it, I am not familiar with multidim modforms acting over $\mathcal{H}^n$ for $n > 2$.

I thought generally math people were FAR more pedantic than physics! My physicist friends tell me so.

@TedShifrin I wouldn't extend my statement to the purely professional part of the field. The kinds of things I'm talking about usually involve professionals, students, and laymen because they're 'popular' questions.

I should go to sleep right now. It's late and I am a bit ill today.

Hey quick question: what's the verb for the opposite of pruning a graph? E.g., adding trees to the graph with existing vertices as roots.

Night, @BalarkaSen

Grafting? @Joebot ... I know no graph theory.

I like grafting. Also totally unknowledgable.

Hmm, perhaps "graphting"

LOL

I spoke botanically.

Hehe. Well thanks Ted & Kevin.

@Joebot Don't thank me until you're sure you won't get yelled at for what I ttold you.

@KevinDriscoll Ah but isn't that what math is for? Yelling?

In Calc II my teacher walked out to infinity to teach us about series and he had to really yell to be heard.

Haha, maybe some folks try ot yell. I get leave when physics people start ot yell. I find that theyre WAY too prone to raising their voices for my taste.

Good question title: "good morning I want to prove that I want to calculate the determinant"

LOL

@DanielFischer Vote to move to Computer Science as equivalent to the Halting Problem

Nice, @Kevin.

@DanielFischer Have you ever wished you could go back to some point in your life and do things differently?

@JasperLoy Yes. Frequently when playing chess.

@DanielFischer LOL. I have many regrets in life. I wish I could go back to the time I was not crazy.

(But also in the intended way.)

Hello

Another question, lol.

i'm soory but can someone help me

[math.stackexchange.com/questions/825955/…

There is a lot of work to do there (brb)

hehe, no problem, the success will embrace me in the end. :-)

Hey @IlanAizelmanWS

It's way past @Ilan's bedtime ... Surely he isn't here.

Doesn't follow, @Ted. I've been here way past my bedtime too.

well, @DanielF, it appears you have no bedtime. But you're not in the army, either.

@TedShifrin Indeed. Army wasn't my cup of tea.

nor would I have it allowed it to be mine ... was ready to flee.

@TedShifrin I saw him flying in, which is why I pinged him.

it's like 2 or 3 am there, @Jasper

@TedShifrin Well, it's 6 am here, lol.

yeah, but you don't have to be alert in the military all day, @Jasper

@TedShifrin I never got enough sleep back then.

@TedShifrin sigh... two more homework stacks to grade before I'm done

Gets tiresome, doesn't it, @Mike?

@TedShifrin It's fine until you lose hope, which was about 3 weeks ago, I think.

@Jasper: I lied; it's only 1 AM there. You made me suspicious of my original guess when you told the time in Singapore.

I've been grading papers for ... um ... approximately 40 years, @Mike.

Thankfully not for every course.

@TedShifrin Well, I'll regain hope when the next class starts.