00:00 - 10:0010:00 - 23:00

12:12 AM
It might be nice to have, in the FAQ, some advice related to asking questions here.
It's hard to articulate but there are quick questions that work here and things which really, really ought to be on the main site.

test
@DylanMoreland Yes, agreed.
@DylanMoreland There's another way chat can help: you can ask here whether the question is suitable for main, or how to make it suitable.

1:23 AM

1:44 AM
Is there an elementary expression for extracting polynomial coefficients? I would have guessed no, since I've never seen monomials used as an orthonormal basis...

2:40 AM
@user1123950 That comment makes no sense whatsoever.

2:59 AM
I finally have a gold badge!
for doing nothing but watching the site :-)
@ZhenLin Other than $\frac{1}{n!}\frac{\mathrm{d}^n}{\mathrm{d}x^n}P(0)$?

@robjohn The OP has produced a multivariate generalisation of that, but to be honest that's not very useful...

@ZhenLin Yeah, but it's all I could think of at the moment.

I thought of one which exploits the orthonormality of the Fourier basis: $$\frac{1}{2 \pi} \int_{-\pi}^{\pi} e^{-i t} P(e^{i t}) \, d t$$
It has the advantage of using integration instead of differentiation, but the disadvantage of requiring functions defined on the complex plane...

Unfortunately, I don't think there is a function on $[0,1]$ that kills all polynomials whose $x^n$ coefficient is 0.
or other convenient interval.
I think we're stuck with the complex integral.
For example, find a function orthogonal to all polynomials so that $P(0)=0$

@robjohn Congratulations! I have been 307 consecutive, but just earned 1 badge instead of 3. So unfair.

3:09 AM
I have to run and pick up dinner for my family.
@Tim I missed one day a while back

I have to cook dinner for myself too.

@Tim I missed it because I didn't know that editing an answer didn't keep my count going and it took a couple of days to write up the answer.

@robjohn Oh, that is even more unfair.

2 hours later…
4:51 AM
Wow, almost empty. O_O

@robjohn Congrats, @robjohn!

hi folks

Hey.
Everyone is showing up now. Was it something I said?

hi Bullmoose.

what did @robjohn get congrats for>
?

4:54 AM
You are the "AEP using Chernoff bounds" guy, right?

yes, yes I am that idiot

I think he got a badge or something.

@Bullmoose I congratulate him every night. It's like good night here. :-)

@Srivatsan Thanks! I worked hard for it :-)

@robjohn Of course, you did. Don't tell your manager though. =)

4:56 AM
@Srivatsan I found out about Chernoff bounds a few days ago

@Bullmoose I can't get to sleep otherwise.

@Bullmoose Oh, I liked the question btw. That's why I remember it.

and, well, there is a saying: if you have a hammer, everything looks like a nail

Oh, Chernoff bounds is a good hammer to have.

I don't want to poop in the party, but if anyone wants to answer an elementary, high-school level math question, I'm looking for advice. Anyone have 5 seconds?

4:57 AM
(also, let me join the everyone in congratulating @robjohn!)

@KorganRivera 5.... 4.... 3.... 2.... 1.....

@KorganRivera I suppose 5 seconds is an exaggeration, but go ahead.

yes, Chernoff bounds are neat if you know how to use them correctly :)

Well here it is. math.stackexchange.com/questions/96741/… I rewrote the question so go ahead and ignore the feedback I've received so far.

4:59 AM
actually that's the wrong link. hold on....

@robjohn Have you seen this question, sir? backwards epsilon

goodness
Raiders

@KorganRivera The $\epsilon$ is multiplied by $b$

5:01 AM
@Bullmoose Thanks for the condolences

i spent two months in the hospital under the care of two great nurses who (along with their husbands) were huge Raiders fans (their husbands were from Oakland originally and used to be in the Black Hole at every home game until moving to NY). Those months included January 2001....

@robjohn you're begging the question.

@Bullmoose Al Davis destroyed us, before he passed away ...
RIP

@KorganRivera Sorry, I was responding to this question

@robjohn b?
@robjohn ah, ok :) yeah sorry my mistake.

5:06 AM
they were some the gentlest people I've ever met, and really took care of me during my recovery. So, I always think of them when I see a Raiders game on TV
I think Al Davis deserves a lot of credit for the successes of that organisation
he just didn't step down in time...
RIP

I'm new here, so would it be fair to ask a little about everyone here? Just the basics: where you are, what you do, favourite colour, &c. :)

@Bullmoose No team has gone from Super Bowl contender to 7 straight seasons of 11 or more losses ... time to rebuild ...

hmmmm Buffalo?

@Bullmoose that's what I thought but the record was set in 2009

well, at least your Raiders won a few Superbowls :)

5:11 AM
@robjohn, did you see my other link?

@Bullmoose True ;-)

@KorganRivera yes,

btw, can someone answer a very very elementary question re: Gamma functions for me?
it's so laughably simple that I don't think it deserves a question
what is the order of Gamma(x-1/2)/Gamma(x)?
I'm getting lost in the factorials :(

@KorganRivera $\frac{f(g(x+h))-f(g(x))}{h}=\frac{f(g(x+h))-f(g(x))}{g(x+h)-g(x)}\frac{g(x+h)-g(x)}{h}$

I can ask it as a question if the audience thinks it deserves one...

5:14 AM
@Bullmoose It is approximately $\frac{1}{\sqrt{x}}$
@Bullmoose as $x\to\infty$

@robjohn it's so obvious I'm doubting how I've managed to stay alive O_O

ok, thank you!

@robjohn, seriously I've been looking at this the whole day. Uh, I ought to be shot.
@robjohn in other words, thx. :)

@Bullmoose so I guess you'd say the order is $-\frac12$

@KorganRivera I am glad I am not the only one who feels like that :)
yup, thanks @robjohn

5:16 AM
@Bullmoose, lol. I feel like that every day. :)

@KorganRivera we should start a club or something

@Bullmoose, I agree. It'll be called "The Mathematicians who ought not to be"
or "The Oh Ffs Why Couldn't I Have Seen That 8 Hours Ago?!?" Club.

@KorganRivera :)

I spend way too long on the most basic, pathetic problems, then someone comes along, or I read a line somewhere, and it's revealed to me as being as lowly as it is. And without having read or heard whatever it was, I'd be stuck in this disgusting pit of not understanding. It really makes me wonder about my capabilities.

@KorganRivera Mathematics, in my opinion, is like love ... It is better to do math and get lost, than to have never done math at all

5:28 AM
I couldn't stop studying it, no matter what. I may fail a not, but sometimes I get some traction and I edge forward and it's a very good thing.

I hold it true, whate'er befall;
I feel it, when I sorrow most;
'Tis better to have done math and lost
Than never to have done math at all.

@robjohn, I changed my question, adding in what I've just learned from you. Would you mind taking a look to see if my work is correct? math.stackexchange.com/questions/96789/…
@Skullpatrol lol

@KorganRivera ;-)
@robjohn Do you think "A Mathematician's Apology" is worth reading, sir?

5:48 AM
Is there a way to stop people editing my questions? Every time I return to my own questions, someone is in the process of formatting how they like it and it's thoroughly irritating.
Would you say the derivative of f(g(x)) was f '(g(x)) or (f(g(x)))' ?

If I have an equation for perpendicular bisector of a 2 points, can I find a point on perpendicular-bisector at distance d?

Could someone verify that the work in my question is correct and then I can leave happy?
Just looking for a "yep it's correct" and then I can say "woo" and leave.
No woo for me then. Goodnight all.

6:05 AM
allright
goodnight everyone! (well, at least it's night here on the US eastern seaborder)

@Bullmoose Good night

6:21 AM
@ZhenLin This question looks to me as a typical case where the answer was yes, obviously and now it is tried to make it sensible at all cost...

6:33 AM
@tb What did you think of the "backwards epsilon" question, sir?

What do you mean?

@Skullpatrol I know that you talk about this question. I was wondering what you want to know from me.

@tb I just find it interesting that the symbol can be read left to right as well as right to left.

Hm, just got warned by Mariano. :/

6:40 AM

@Skullpatrol If it's used as $X \ni x$ then it's fine with me and a reasonable usage. On the other hand using $\ni$ in the sense of "such that" is thoroughly bad and completely unnecessary.

I remember that someone I know who uses it. I don't remember who.

@Srivatsan To be honest I don't understand the whole unnecessary braces thing some people here have going. Why bother? There's absolutely no need to remove them, it doesn't make any sense to me.
I appreciate the effort in retagging and general clean-up, though.

@tb Well, it doesn't matter; that wasn't why I edited. =)
Unless your point is that the OP chose to use it, so we should respect the OP. I don't feel strongly against it.; but I don't like it personally.
Tell me this:
Is it true that every continuous bijection from $\mathbb R^n$ to itself is actually a homeomorphism? Why?

6:51 AM
@Srivatsan Yes, but it's highly nontrivial and due to Brouwer. It's called invariance of domain: a continuous injection from $U \subset \mathbb{R}^n$ to $\mathbb{R}^n$ is open.

In general, under what broad conditions does such a thing hold? I.e., every continuous bijection $X \to X$ is a homeomorphism. I think it is true if $X$ is compact.
@tb Oh, I see.
[The OP said so...]

The compact thing is also true.
are you talking about the $f(x) - x$-thing?

There's definitely a proof somewhere in Hatcher.

@tb I'm sure that is elementary. I am even supposed to know why that's true, but I don't recollect.

@Srivatsan show that it's a closed map (assuming that $X$ is compact Hausdorff).

6:54 AM
Hausdorff is assumed. In fact, I'll even assume it's a metric space.

Probably you just need some basic properties of homology.
Not that any of that is obvious.

@DylanMoreland yes, every basic algebraic topology text worth the name proves it. There are also proofs that avoid homological machinery (as did Brouwer's original one). I think there's one direct approach in Dieudonné's treatise of analysis.

@tb Yes, the x-f(x) question.

@Srivatsan as I said: whatever assumptions you like. Just show that $f$ maps closed sets to closed sets (because closed subspaces are compact and mapped to compact sets which in turn are closed).

@tb Oh, I see.
We want compactness on the left hand side, no? (Assuming $f : X \to Y$ instead of $X \to X$.) Since continuous functions preserve compactness.

6:58 AM
@Srivatsan That's basically the gist of it. I would definitely not appreciate it if someone removed my superfluous braces... I understand that you re-tagged and made some other minor things, which is perfectly fine with me, but again: what is the point of removing unnecessary braces? I almost always use braces out of habit, why should I bother to add them to other posts so others do that as well? I basically can't read code of the form $\frac1x$ and I find that distinctly ugly.
@Srivatsan $X$ compact and $Y$ Hausdorff is what's needed.

@tb Hm, ok. Thanks for letting me know.

@tb Does "contains as an element" = backwards epsilon, and "an element contained within" = forwards epsilon show that the "epsilon relation" is a invertable relationship?

@Srivatsan: Look at this here. In my opinion the source is a horrible mess. But obviously the OP has his own quirks of (bad IMO) taste, so I just leave it... Even though I'm very tempted to adjust the misplaced tildas and to remove about one hundred spacing thingies.

Misplaced tildes? How should they have been?

@Srivatsan $\tilde{g_1}$ versus $\tilde{g}_1$.

7:08 AM
Presumably the first is better here?

Obviously the second one is the typographically acceptable one, while semantically the first one is correct.
The first one is very bad typographically.
@Skullpatrol No, it does not mean that. At most one of the relationships $A \in B$ or $B \in A$ can hold. So if $A \in B$ holds and you want to switch the places of $A$ and $B$ you need to write something else and $B \ni A$ seems the logical thing to do.

@tb Thanks for explaining that to me ;-)

@tb Typography should follow semantics. =)

@Srivatsan I would argue that what counts is the end result. If the typographical system makes bad choices it forces me to break its semantics...

Well, I might prefer $\widetilde{g_1}$.

7:20 AM
+1ed your comment don't understand Mariano's either.
@Skullpatrol Here's an example where I sometimes use it: in topology you often have to say: "given a point $x \in X$, let $U$ be an open set containing $x$." If I need several such instances I might write: "Given $x,y,z \in X$ choose pairwise disjoint open sets $U \ni x$, $V \ni y$ and $W \ni z$" or something to that effect.

The question is extremely clear conceptually (quite surprising :-)): the OP clearly understands the two interpretations and asks which one is standard.

Teachers doing this are those responsible for the spate of $1+2/3+4$-type questions. As if ad hoc conventions are an excuse for ambiguous writing...

@tb hmm.. that's interesting, so your using the "containment" meaning of the symbol?

@Skullpatrol that and only that one.

@tb "that and only that" = thatt since "if and only if" = iff
;-)

7:26 AM
@Skullpatrol why not tthat? :) "iff" is another thing that makes me cringe.
Worse: "ssi" in French.
(for "si et seulement si").

@tb Oops ... sorry I didn't mean to make you cringe

@Skullpatrol You didn't. I understood that you were making a joke :) I don't like it when people use it in mathematical writing.

@tb This epsilon symbol can also be interpreted as "belonging to."
@tb Rather than contained.

But those are synonyms mathematically :)

@tb Would that make the "epsilon relation" is a invertable relationship?

7:32 AM
I'm not sure what this is supposed to mean.

@tb Since two things can belong to each other.
@tb Can they not?

In everyday life, yes. In mathematics no.

@tb :-(

@tb What's up?

Oh, I'm procrastinating, as usual...

7:38 AM
Procrastination is always fun.

Dangerously so...

We baked a cookie last night.

What a waste of energy. A single cookie...
:)
But that was probably the humor of it.

7:41 AM
It's the size of a plate.

Oh, you mean by accident?
Dough too liquid?

No... the dough was kinda sticky and we grew tired of working with it so we just made it into one huge cookie.

I see :) Nice!

Yeah, I've eaten the first bite now. It's pretty good.

Oh, that's what all those $\color{lightgrey}{\text{(removed)}}$ were about?

7:44 AM
That too.

It kind of looks dangerously sweet, that cookie...

Hah, yeah. I took a recipe from my mom and just cut all the amounts in half. But I put regular amount of sugar so I had to use a spoon to take out half a cup of sugar from the top of the pile... I probably missed a bit.

@tb In mathematics, each negative number can be said to be the opposite of (or paired with) each positive number. Thus they are opposites of each other and therefore belong to each other as opposites, true?

Hm. Looks like a play of words to me...
@AsafKaragila I see.

@tb Plus, almost all the recipes I've seen are about the same.
The difference in the amount of flour, eggs, sugar... are very minor.

7:48 AM
Yes, it reminds me of what we call "chrömli" hereabouts.
(depending on the precise location in Switzerland, of course)

@Skullpatrol And the opposite of zero is itself!?! Bam! Math crushed by a simple argument.

@tb Of course :-)

@tb How about a "number" and a "point" they certainly belong to each other.

@Srivatsan I changed backlog to transcript.

7:51 AM
@tb Even a number paired with a point?

Sorry, you lost me

@tb Where did I lose you?

@Skullpatrol here, at the latest.

@tb a "number" and a "point"

Repeating "a 'number' and a 'point'" doesn't help me following the point you're making.

7:55 AM
The coordinate of a point is a number and the graph of a number is a point.
@tb The point I'm trying to make is that in math there are many things that "belong to" each other.

You're still playing with words. When I made my comment I was talking about the \in/\ni relation where this simply is not the case.

hi $\forall$

@tb I considered that. When I asked here no one responded.

@AsafKaragila I overlooked that.

I mean, I am the king but you still have to vote for me... :-)

8:01 AM
@tb Yes, I agree with that if the symbol is only interpreted as "containment"
@tb But if the symbol is interpreted as "belonging to" then things change, right?

@tb Either way, I've added the sixth rule. I consider adding $\vdots$ and then $\omega$-th rule $\textbf{ALL GLORY TO THE HYPNOTOAD}$.

@AsafKaragila Thanks.

@Srivatsan No problems.
I wonder who downvoted that. I wonder if that someone who's using the chat at all...
Either way, I have to go meet my advisor. Ciao.

Conventions are nice so long as nobody uses them.

@Srivatsan I have tagging related question.
According to this answer at meta I thought that is going to be eradicated.
I propose to delete the tag. It has 4 upvotes.
But recently I noticed your edit: math.stackexchange.com/posts/67032/revisions

8:10 AM
@Srivatsan How does "And the opposite of zero is itself!?! Bam!" crush Math?

@Skullpatrol Doesn't it? I was hoping it would.

@Srivatsan Crushed math would be mash :-)

@MartinSleziak I'm not really sure why I added it :-)

@Srivatsan So we are still planning to get rid of the tag, correct?

@MartinSleziak Good question. =) I think so.
I was confused between inverse and inversion. What is the difference between the two tags?

8:16 AM
Ok. I just wanted to be sure, so I asked here.
BTW I've noticed that has about 10 questions less every day, which is mostly thanks to you, I guess. Thanks for your work!
@Srivatsan IIRC several questions from have been moved to .

@MartinSleziak You're welcome. I will slow down my pace though (see here).
[inversion] is empty?

A quick good morning to everyone.

Good morning, Matt.
@MartinSleziak Oh right. I am slowly recollecting.
Someone expressed an opinion somewhere that [inverse] seems ok as a tag. Willie maybe?

@Srivatsan Yes, I've got even private message from a mod about that when I started retagging algebra. That was the reason for this comment.

Oh and happy 3-Asaf's Day to everyone!

8:20 AM
@Srivatsan Yes. This was Willie's comment to that question: _I don't see the problem: deep below the surface they are all the same thing. I am however in favour of a tag wiki that briefly mentions inversion as an abstract concept and asks the user to specify the regime where the idea is used in the question. _
Morning Matt.

@MartinSleziak That was why I changed my mind in between. =)

Ok. I'll better keep my hands from . (I was tempted to remove tag, but it seems that this was not agreed in that thread.)

Is anyone of you having some 3-@Asaf cake, or is this only for German speaking countries? : )

@MartinSleziak Exactly. If you notice the meta post, I suggest removing inversion, whereas JM suggests doing something with [inverse], but he explicitly says he is not suggesting deleting the tag.

Bbl.

8:24 AM
@MartinSleziak Sprry, I got the two mixed up once again.
I can't believe this =)

Ok, I checked the history of edits now.

I'm not really sure, but I have not made any [inverse] edits recently. We have only removed [inversion], and moved many of them to [inversive-geometry] -- that is good.

@MartinSleziak How about High-school-Algebra and Middle-school-Algebra tags to go along with abstract-algebra and algebra-precalculus tags?

@Skullpatrol I think they fall under algebra-precalculus fine. If we tried to create tags tailored to school system of some country, probably users from different countries with different school would not agree.
Just check how different meaning can real analysis have: see this conversation.

I have a problem distinguishing between $5^{th}$ Grade Algebra and $6^{th}$ Grade Algebra...

8:31 AM
@robjohn I agree.
@MartinSleziak But there is a difference between Pre-Algebra, High-school-Algebra, and algebra-precalculus, in my opinion.

@robjohn congrats for the golden one!

@tb Thanks. It was such an uphill climb! :-D

It's by far the easiest one to get...

@Skullpatrol I don't really know the western school system, so I'm definitely not the man to discuss this.

@robjohn What do I say? You have lost some perspective there. =)

8:37 AM
@Srivatsan It was a joke, but it seems to have been taken seriously by at least one, it seems :-)

@MartinSleziak What school system are you familiar with?

@robjohn [So was my comment...]

@Skullpatrol Well, I only studied her in Slovakia.

@Srivatsan I know, but I took too long to type my reply.

@MartinSleziak There is no such thing as Pre-Algebra there?

8:40 AM
@Skullpatrol Wikipedia says that: "Pre-Algebra is a common name for a course in middle school mathematics. In the United States,"
So it seems that it's specific to the USA.

@Skullpatrol Perhaps we are dividing things too finely here. I think the difference between High School Algebra and College Algebra is clear; they are two different subjects. Perhaps I am missing something here.

Oh, my: is it just me or is this basically unparsable?
looking at the source gives some ideas on the intentions :)

the latter I am afraid :D

@tb There are brain-dumps and brain-farts, I think that is clearly the latter.

8:43 AM
@robjohn yep.

@tb I think that the best thing would be to keep the original version of the post and then add an LaTeXed version. And ask OP to confirm, whether it is what he meant. (And to learn using math here.)
Is there a volunteer to do this? (It would be waste of the time if several people would try to edit it at once.)

Anyone tell me: should I cut this answer in two pieces? The part up to "At the moment" is basically my clear yes as an answer, the rest are some thoughts for considerations to be made.
@MartinSleziak I won't do it.

@tb Ok, I will try to.

@robjohn I agree, the difference between High School Algebra and College Algebra is clear; they are two different subjects, but algebra-precalculus is a separate tag and I am only suggesting an algebra-high-school tag?

@Skullpatrol what is the difference?

8:47 AM
@robjohn " Algebra-precalculus" is more geared to the algebraic methods found in Calculus.
@robjohn While "algebra-high-school " would cover things like linear algebra etc.

@Skullpatrol Linear algebra is covered in High School there? Maybe some matrices are introduced here, but not anything I'd call Linear Algebra.

@robjohn " Algebra-precalculus" is to Calculus what "High-school-prelinear- algebra" is to Linear Algebra
@robjohn Would you agree with this classification, sir?

@Skullpatrol I think we are micromanaging things here.

@robjohn Me too, let the kids be kids!!!

@MartinSleziak thanks for this, but the edited version still doesn't make much sense to me, especially its relation to the question...

8:59 AM
@tb I tried to follow the original as closely as I could. The purpose was to improve readability, not change (improve) the meaning.

@MartinSleziak there was a meaning?

@MartinSleziak Of course :)

If there is something meaningful in this answer and someone is going to try to understand it, I think there is a better chance with LaTeXed version.

@tb BTW thank you for making me explain myself to you ;-)

@MartinSleziak :-) I agree.

9:02 AM
@robjohn I only tried to rewrite formulas. I was not able to decipher anything from ASCII-art. If you guys are able to read mathematics in ASCII, I sincerely admire you. I am able to read some short formula, but not such a long post.
If I had to choose whether read some math in ASCII art or in Russian language, I would go for Russian. Despite my problems with reading Cyrillic.

@MartinSleziak I just looked at the source so that I could see all of it in a monofont. I see that it does actually make some sense.

But the OP started to edit his answer after my modification already. Even if the only useful thing is going to be that he learns basics of math markup, it was worth the trouble.

@MartinSleziak It certainly gets munged by the processing on the main site.
@MartinSleziak Indeed!
@MartinSleziak I have written a lot of ASCII-art math. A lot of my sci.math posts contain some

@robjohn Well at sci.math you don't have much choice. (I wish google groups added an option to use mathjax; it's about time. Not for sci.math; but in some google groups I used to communicate with my students or my colleagues, it would be helpful.)

@MartinSleziak Most attempts at TeXification were severely frowned upon on sci.math.

9:12 AM
BTW if you display main site and the question, reputation for Mathlover is shown differently: i.stack.imgur.com/9pG7W.png and i.stack.imgur.com/J9qOP.png

@robjohn Did you see the conversation t.b. and I had about the "backwards epsilon?"

You can notice from the view counts that both screenshots were taken approximately at the same time.

Probably some caching problem.

It worked this way a minute ago, I guess it still does.

@Skullpatrol I saw some of the discussion. What was the main point?
@tb have I opened Pandora's box here?

9:16 AM
@robjohn If the symbol is interpreted as meaning "belonging to" it has a very nice symmetric property of two things belonging to each other.

@Skullpatrol It's two symbols: epsilon and reverse epsilon. =)

However $\ni$ is not a backwards epsilon, although it looks a bit like one.

@robjohn Just like $\in$ is not really epsilon, no?

@Srivatsan yes! $\in$xactly!
Does that mean inexactly?

@Srivatsan Yes, they are two separate but reciprocally related symbols, in that if two things are paired with each other in such a way that they belong to each other, these two symbols become interchangeable.

9:26 AM
@Skullpatrol Things don't belong to each other. Either one thing belongs to the other or it contains the other (or neither case happens).

@Srivatsan :-(

@Skullpatrol The symbols < and > provide a simpler, easier to understand example of whatever you are trying to explain.

@Srivatsan Do siblings belong to each other?

@Skullpatrol LOL. That question was very funny... =)

@Skullpatrol Siblings = {John, Mary}; John $\in$ Siblings; Mary $\in$ Siblings. But John $\notin$ Mary, Mary $\notin$ John

9:32 AM
@MartinSleziak Two brothers belong to each other as bothers. One brother has a brother and the other brother has a brother, they belong to each other as brothers.

Then you're not speaking about relation $\in$ but about relation "being a brother".

@MartinSleziak The relationship "being a brother" doesn't mean anything unless you have a brother and your brother has you as a brother.

hi \forall

@Skullpatrol Empty relation is a relation, too.

@MartinSleziak ain't got no latex support, so dollars or rupees, its the same :D

9:37 AM
@MartinSleziak having is a relationship of expressing possession, true?
just like "belonging to"

@Skullpatrol I am not longer sure what we're talking about. This conversation does not seem to lead anywhere, so I suggest we quit.

@Srivatsan historically it is.

@robjohn Can you see that the forward or reverse "epsilon" can be used to express "belonging to" or "possessing" for things that are paired with each other?

@Skullpatrol what is there to see? that is what $\in$ and $\ni$ mean. They are not epsilons.

9:42 AM
@tb You're welcome. Just to confirm - poster is pinged even whet it's CW right? (So you get a ping from my comment even though I did not use @t.b. there.)

@MartinSleziak yes. I was pinged.

Norm d'Algebra

@robjohn You then sir, are the only one who understands that things can belong to each other in math.
At the same time.

Belong to each other? you mean $x\in y\wedge y\in x$? I wasn't necessarily saying that.

@robjohn Yes, that is what I mean: x belongs to y and y belongs to x.

9:47 AM
$x\in y \land y\in x$ cannot happen, if you have Axiom of Regularity in your axiomatic system.

@MartinSleziak exactly why I wasn't saying that. It leads down the rabbit hole :-)