Nah. I meant Prob with Calc

Maybe Ross level?

YOU ARE AN ISI STUDENT ?!

May be yes! (to "Ross Level?")

Cool

Guys, quick question - what is e to the power of j?

What is j?

@nitstorm

j as in the imaginary component @KannappanSampath

@nitstorm engineer? :)

@Ilya trying to be one.. :P

icic. I think only they use j instead of i

lol :P would you happen to have an answer to my question?

cos (1 rad)+ j sin (1 rad)

@nitstorm

@KannappanSampath Thanks :D

no mention

$1 \operatorname{rad} \approx 57^\circ$ :D

quite warm

@Ilya The answered turned out to be wrong

which&

that subspace problem

uc

@Ilya as in U See?

@JasperLoy How so?

I have Highland Park 15 yrs.

ELU?

Ah. I did not make rules for all the chatrooms

Hey guys! As Mandelbrot set is a subset of the complex plane, do you know of any fractal that is a subset of a spherical surface?

I found this very cool image earlier, that they say to be of a fractal, and seems to be what I want: miqel.com/images_1/fractal_math_patterns/simple-fractal/…

but I don't know how to build it

@JonasTeuwen grocery, hah!

@Ilya 8-).

@lvella take the image of Mandelbrot set to the Riemann sphere

That's part of the groceries...

@Jonas Gall and Gall?

@Ilya Yeah.

There is also "Wines and Whisky's" in Delft.

20% discount today?

@lvella welcome to the real life

@Ilya 25% if you have a Gall & Gall card.

what about the figure? any idea on what it might be?

@Brian

Are you around, I'd like to have a small exchange with you.

I’m mostly watching Matt’s room, but I am here.

Alright. Do you know of a reference for complemented space problem

I’m not even sure what the complemented space problem is.

on finite vector spaces I presume? ;) math.stackexchange.com/questions/107389/…

@BrianMScott OK, forget it!

@anon Nah, That will be Complementary Subspace Problem :)

I got it all wrong, -4! that just stabbed me!

well then I have no idea what the complemented space problem is

@anon

@KannappanSampath At least it was halfway balanced out by the +2.

You should have deleted it before it got that low! That's what I've done. At least the total score wasn't at -3, or else you would have got the Peer Pressure badge :)

@anon True, anon. I was assuming, I'll be able to fix real quick.

But, that has been this long before, I figured out on my own that this is where I went wayward?

In fact this answer and this answer I felt the need to delete, clean up, and undelete just in the past few days.

I’ve done that a time or two.

Is that last sentence ^ supposed to be a question Kanna?

Brian, you commented that my generating function answer was nice when it still was erroneous ;)

@anon No. A typo

I'll now write up something beautiful in that place. Do yoou still see the answer?

"?" is not a typo here.

Yes 10k goggles = see deleted questions/answers.

Do, you think It's fine as it stands?

(A minor edit has gone into it)

Let me actually read it now

Criticise it thoroughly. I'll fix it as you point out mistakes,

@anon (Had to go look at the edit to see what you’d done.) You’re right: I knew that the approach was right, liked the form of the explanation, and didn’t check the details.

A bit of Ctrl+C and Ctrl+V has gone into it @anon

I did it to get some base to improve it in my style! :)

@Kanna: Your second to last paragraph is almost a direct quote of Grigory's answer, that's too copious to put off as your own writing. Don't mention the problem in full generality unless (a) it's after you've already presented the answer to the particular problem or (b) you're going to actually do the problem in full generality. You say "we can prove this number is precisely equal to formula" but then never prove it (maybe rephrase?). Finally, after "namely," just to be on the safe side

[...] you might want to explain why we're dividing N5 by N2 and N3. Also, I don't see a need to boldface Theorem and Definition when there's only one of each.

@anon A bit. I'll write up more into it. I'll then let you know. Two more attempts: We'll be fine to roll it.

As for defn and thm, I wanted to add more, that is why.

Ah, I thought so. Then that makes sense.

I was a bit bored when I started to edit

@Brian Your apostrophe is all Y, Why?

What do you mean?

@Kanna: If your browser freezes a lot when writing things on MSE I would recommend saving your edits alot, because the system doesn't autosave edits like it does answers.

@anon Thanks for the hint. It just did. I am having to retype all again!

heh :)

@BrianMScott I'm here is like IYm here, in Matt's Room @Brian

@anon Should I add how is the Gaussian Coefficient enumerated?

Looks fine to me. I’m using curly quotes, though, so you may have to change the character encoding.

Sure. It should only take a few sentences if you're concise enough.

True, I'll do so and I'll add Gaillard's Comment. Then, I'll tell you @anon

Don't switch between "we" and "you." Just use we the entire answer.

@anon Where, exactly?

"This gives you the claim."

sorry, I'm eavesdropping :)

No, I have no problem with that.

I am editing bit by bit

Ah. I still can't see deleted stuff.

@anon I'd like to mention two interesting results but not directly connected with the problem, should I?

what are they?

@DylanMoreland You'll see it in a few hours! :)

@anon $\binom n k_q=\binom n {n-k}_q$

sure

and, $\lim_{q \to 1} \binom n k_q=\binom n k$

@anon BTW, the second needs a bit of icing, like analytic extension

@anon are you around, or held up with sth?

@DylanMoreland $\stackrel{\stackrel{\searrow\hskip{6pt}\swarrow} {\huge\bullet\hskip{8pt}\huge\bullet}}{\hskip{1pt}\huge\smile}$ Hi Dylan.

that latter one is pretty much by definition, and I doubt it would help in solving the problem

sorry my internet dropped out

@anon It does not help but is interesting, no?

seems too... tautological. [n]->n implies [n]!->n! implies $\binom{n}{k}_q\to\binom{n}{k}$.

A q-analog is supposed to approach what it's analogous to as q->1

What is [n]? @anon

$[n]_q = 1+q+\cdots+q^{n-1}=\frac{q^n-1}{q-1}$

May be interesting to me, because, I learnt it on my own with some experimentation ?

And $[n]_q! = [n]_q [n-1]_q \cdots [2]_q [1]_q$. See the Wikipedia page on q-analogs for more.

Alright, there's whole world of $q$ analogs :)

Oh yes.

Then I won't add the latter!

@BrianMScott I'm putting the final touches on our consecutive multiples discussion, what do you think of this wording, Sir: "Consecutive multiples of any real number are multiples of that number by consecutive integers."

Yes, that works.

@BrianMScott Do you have any suggestions to make it better?

I honestly think that using only words and no symbols makes it a bit harder to understand than is really necessary. I’d probably say something more like this: If $x$ is a real number, consecutive multiples of $x$ are multiples of $x$ by consecutive integers, i.e., numbers of the form $nx,(n+1)x,(n+2)x,\dots$ for some integer $n$.

I also personally prefer that style.

"Consecutive multiples of a are multiples of a by consecutive integers."

Looks good.

Short and sweet?

@anon Where should I head now? (I have Gaillard's comment in mind, apart from that?)

@BrianMScott Would "Consecutive multiples are multiples by consecutive integers." be too short?

@Skullpatrol This sound vacuous and will require second reading for mathematically immature people

I prefer the previous version, ‘Consecutive multiples of a ...’.

I/we all agree that "Consecutive multiples of a are multiples of a by consecutive integers." is the best wording?

I agree

Yes, for a short, compact statement.

@Kanna: I don't see the relevance of Thm 0 and you still have Grigory's words copied too exactly to be your own. Other than that the only issues are with English style and I could for example edit that later (too lazy to explain it all)

@BrianMScott Thank you.

@anon Grigory's answer will be edited. I want a road map. So, now I should venture into Grigory's answer?

@Skullpatrol You’re welcome.

K: Yes.

And thank you both Kannappan and Jasper.

@Skullpatrol You spelt my name right! +1

@JasperLoy An opposite, most certainly not my own!

"I came across the following challenging problem in my self-study:..."

...

hi everybody

:-)

"..." means "and so on"

oh no, no my problem. There exist a user here that ask lots of questions in that way

I assume that it’s to keep people from asking whether the question is homework.

@JasperLoy math.stackexchange.com/questions/107405/… math.stackexchange.com/questions/107402/… math.stackexchange.com/questions/107404/…

@Skullpatrol indeed and so on...

@BrianMScott Do you know of any branch of linguistics that studies the relationship between mathematics and natural language?

Other than math education, of coarse.

People have looked at the question of whether human language is context-free, but in general there’s not much connection.

@BrianMScott I guess math education is that connection, on a specific given language basis, right?

I’m not sure what you mean: I don’t really see how language comes into math education, apart from the fact that we speak or write in order to teach.

Hey there,

@BrianMScott That is what I mean: "we speak or write in order to teach"

Okay; I don’t think of that as having much of anything to do with linguistics.

Why the power set of an uncountably finite set is finite?

There is only one empty set. It has zero members, and zero is certainly finite!

@BrianMScott Can they not find better ways through their linguistic knowledge?

I meant power set, sorry @BrianMScott.

@Skullpatrol That’s not really a linguistic question; it’s more of a psycholinguistic question.

@Gigili What do you mean by uncountably finite set? If a set is finite, it can’t be uncountable.

A set which is uncountable but finite, according to my book.

@Gigili Please stop reading that book!

@BrianMScott Have you ever heard of psycholinguistic math education?

@Gigili Kannappan’s right: if it really says that there is such a set, get rid of it!

A set is defined to be uncountable if it is not countable. THIS IS THE DEFINITION.

Like $\mathbb N$?

Some books will say that "countable" has to mean "in bijection with the natural numbers" and then they'll say "denumerable" or something to mean "finite or countable".

@Skullpatrol Not in those terms, no. But there are people in the field of education who study how students learn mathematical concepts, what kinds of language work best, and so on.

I have to read it for my exam, sorry!

So uncountable might mean: "finite or (infinite and not countable)".

Finite is countable.

@DylanMoreland Yes. Most of us use countable to mean finite or countably infinite. And in my experience no one uses uncountable to mean not countably infinite.

I agree.

=\

I'm just offering an interpretation. I've seen this done.

I've never seen uncountable mean that but it seems consistent with the definition of countable that I mentioned.

@DylanMoreland You have? Ye gods an little fishes.

Again, don't do this in mixed company.

I have a doubt: Uncountable means not countable. Right?

@Dylan @Brian

@KannappanSampath Normally it means not finite and not countably infinite.

I agree with Brian.

@BrianMScott Do you know what that field is called? "the field of education who study how students learn mathematical concepts, what kinds of language work best"

Glancing at Rudin he defines uncountable to mean that. Even though countable implies infinite for him.

Nobody cares about finite sets.

Kinda confusing.

@AsafKaragila Life is a finite set.

Here we go: Uncountable means what Brian Says, {I had that in mind}

This is horribly uninteresting. It's just definitions.

I asked a senior of mine: What are group actions?

@Gigili If your book says that "uncountably finite" means "finite", then a normal person would phrase that assertion as "the power set of a finite set is finite". That's a true statement.

But I sure hope it doesn't say that.

He said: What can it be more than a definition?

I hate such people!

@Skullpatrol So far as I know, it’s just part of math education. One of our part-time instructors at my former university was doing his doctoral research in that area, but I don’t think that he referred to it by any special name.

@KannappanSampath People who breath?

Some things are not just definitions.

But you'd need to be a bit more specific before anyone could say anything interesting in response to that question.

@DylanMoreland Aha, I should check it again to make sure. Thank you.

@AsafKaragila I love them, if they don't exhale fire instead of $CO_2$!

@Gigili I mean, if you search for that phrase the only stuff that turns up is junk.

@DylanMoreland Right, I'll be more careful next time.

@BrianMScott Thanks again.

No problem.

Oh, wait, maybe there's something

wiki.answers.com/Q/What_is_infinity_used_for_IN_MATH

@KannappanSampath You should know that fire only hurts if you're made out of wood. If you are made out of wood then you float on water, therefore you weigh like a duck. A WITCH!!

@DylanMoreland You mean my question should be a bit explicit as to I am not expecting such an answer.

He seems to relate this phrase to cardinality? But this is not the most reputable source, and if Asaf doesn't recognize it then surely this isn't a real definition.

Huhu, I have become a true authority.

@KannappanSampath I don't know. It seems like asking what a function is. Or what a group is.

@DylanMoreland Isn't the set of real numbers infinite?

@AsafKaragila Huehuehue, yes you have.

@Gigili I sure hope so!

Why do witches burn?

@AsafKaragila I am made of living cells. If I am made of dead cells (wood), it hurts, by your claim. Living cells have life (Tautology). fire hurts wood (your claim). So, living cells are hurt more!

@Gigili Is this a real book I can look up? I'm super curious now.

@KannappanSampath Soon you'll tell me that coconuts cannot migrate.

@DylanMoreland Yes, it is. I wrote down my questions, I should find it in the book. I'll ping you when I get back.

@AsafKaragila Good Heavens, this is more abstract than those Grassmanians I defined the other day I defined in my class!

@KannappanSampath Thus proving that you are in fact a witch!

@DylanMoreland Typos: countably finite should be countably infinite, and uncountably finite should be uncountably infinite. (At least I certainly hope that they’re just typos.)

In my introduction to general topology course I started the exam with a definition of a "badger topology" where badgers are basic open sets, and under the assumption that the world is a big badger I showed that it is indeed a topology, but it is not normal. I then said that it is homeomorphic to the topology of ducks in which every human is compact and therefore a witch.

@AsafKaragila tells himself this is what happens when you are talking to a set theorist in a Music Seminar

@ASaf Theorem: The space of absolute fantasy is metrisable in which any increasing sequence is bounded and converges to an element called Asaf Karagila

The space of absolute fantasy was discrete until Asaf Karagila came along and became the point at infinity in the one-point compactification.

I'd like to think of myself as something which cannot be approached by sequences, only by nets.

@BrianMScott That's just not true. Fantasy is continuous.

@AsafKaragila By men in which jackets with nets!

@AsafKaragila Any space admits a discrete topology! So, Fantasy can be thought of discrete for fantasy!

@KannappanSampath Not every topology is discrete. This is just fantasy.

@BrianMScott Elmer Fudd??

Does anybody understand what Didier is trying to say? math.stackexchange.com/questions/107512/…

@JonasTeuwen He's trying to tell you to shut up and do more set theory.

@AsafKaragila That was supposed to be men in white jackets.

Oh.

@JonasTeuwen I think that he’s saying that your suggestion to the OP is the standard approach to the problem.

@AsafKaragila But in the space of fantasy, if every topology was not discrete, there is no fantasy about it. This will contradict that the space is space of fantasy and since, self contradicting objects don't exist in Math, the space cannot exist.

@BrianMScott That is a more positive interpretation than mine 8-).

This is like saying that there can only be one model of ZFC so there is no such thing as independence results such as the continuum hypothesis etc.

@AsafKaragila You mean saying that every topology is not discrete, I know!

@JonasTeuwen Yes, I don’t think that he had any problem with your comment; it was the OP’s comment that bugged him.

SET THEORY FOR LIFE . Those who say yes, leave a T as the response, others may use F

@BrianMScott Good, thanks :-).

F

I’ll see you folks later; I need to run off and do some chores.

@Brian Your response b4 you leave?

$\frac12(T+F)$.

May be You can explain your stand later @Brian

@Nunoxic It takes a while to get used to, admittedly...

@JonasTeuwen Yeah, I read it the same way as Brian, even if it is the usual Didier brusqueness...

@HenningMakholm Hi.

Is someone going to review the $\lambda > |T|$ edit? :)

Not me, I'm busy giving a second answer to a question... :)

double-dipping eh?

I'm just remarking on the fact the edit has been open for review for 2 hours but nobody's been around to understand it.

@anon Only Canadians use the expression "eh."

Clearly your statement is false.

@anon Well, it's a bit different. You'll see what I mean when it pops up.

"ping-pong lemma" This sounds fun. And I was just wondering about a slick way to prove a basis for PSL(2,Z) too.

@JasperLoy Life is a FINITE set.

prove it

prove "prove"

In the statement "life is a finite set" there is nothing to prove.

In the statement "life is an infinite set" there is nothing to prove.

Argument by assertion, I love that one.

More like argument by exertion.