Mathematics - 2012-01-06 (page 2 of 2)

Skullpatrol

10:00 AM

to enter a period of chaos or confusion.

Srivatsan

@robjohn Did you make this?

Skullpatrol

@robjohn I'll just have to get used to it and not understand it.

robjohn

@Srivatsan No, I grabbed it from here

t.b.

@robjohn I know what you're thinking, 'cause right now I'm thinking the same thing. Actually, I've been thinking it ever since I got here: Why oh why didn't I take the BLUE pill?

robjohn

@MartinSleziak if $x\in y\wedge y\in x$, then the chain of inclusions gets dizzying.

@tb Indeed :-) Perhaps if I realize that all of this is a computer simulation...

oh, wait...

Skullpatrol

10:12 AM

So, in mathematics, can things can belong to each other
at the same time?

robjohn

@Skullpatrol Not if you have the Axiom of Regularity as Martin points out.

Hello

@QED Hi there :-)

In mathematics, the axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo-Fraenkel set theory and was introduced by . In first-order logic the axiom reads: :\forall A (\exists B (B \in A) \Rightarrow \exists B (B \in A \land \lnot \exist C (C \in A \land C \in B))). Or in prose: :Every non-empty set A contains an element B which is disjoint from A. Two results which follow from the axiom are that "no set is an element of itself," and that "there is no infinite sequence (an) such that ai+1 is an element of ai for all i." With the axiom of dependent...

QED

Axiom of extensionality

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo-Fraenkel set theory. Formal statement In the formal language of the Zermelo-Fraenkel axioms, the axiom reads: :\forall A \, \forall B \, ( \forall C \, (C \in A \iff C \in B) \Rightarrow A = B) or in words: :Given any set A and any set B, if for every set C, C is a member of A if and only if C is a member of B, then A is equal to B. (It is not really essential that C here be a set — but in ZF, ev...

Skullpatrol

10:34 AM

"no set is an element of itself"

If x belongs to y and y belongs to x, then x belongs to itself.

You can't question an axiom called "the axiom of foundation"

I'll just have to get used to it and not understand it.

Asaf Karagila

12:19 PM

@Matt Huh?

robjohn

12:32 PM

@AsafKaragila Wha?

Asaf Karagila

12:43 PM

@robjohn Who?

robjohn

@AsafKaragila Whe? the three W's

Asaf Karagila

@robjohn Why?

robjohn

@AsafKaragila $y_0$

Martin Sleziak

Oh, now I get Matt's comment. He meant three kings.

I have to admit I am a little slow...

Asaf Karagila

I am going to make lunch. Ciao

Martin Sleziak

12:48 PM

Drei Könige in German.

Bye

robjohn

@MartinSleziak that must have been a while ago. I don't see it in my backlog.

@AsafKaragila what's for lunch?

Martin Sleziak

@robjohn See here: chat.stackexchange.com/transcript/message/2911892#2911892

Szabolcs

Hello everyone! I thought if there are any Mathematica users among you, you might be interested in this (recently very active) proposal:

Martin Sleziak

It's the one to which Asaf reacted by his Huh

Szabolcs

area51.stackexchange.com/proposals/37304/…

robjohn

12:49 PM

@MartinSleziak Okay, thanks.

Martin Sleziak

@Szabolcs It was discussed here at meta Mathematica proposal has been closed, new one started

So I guess most people know about it.

Szabolcs

Ah sorry @Martin, I didn't know about that.

Martin Sleziak

I think that perhaps SE site including more mathematical software (Sage, Maple, Matlab, Mathematica, Derive, perhaps GAP) could be better.

But not much can be done about this, since proposal on Mathematica is already going on.

QED

I'm opposed to it

Martin Sleziak

(I am not Mathematica user myself.)

QED

12:52 PM

I agree with Martin

Martin Sleziak

@Szabolcs There's no need to apologize - I think that reminding it once in a while is good thing.

Szabolcs

This reasons why we prefer a Mathematica-only site too (perhaps coexisting with a more general one if it ever laucnhes) has been discussed here: discuss.area51.stackexchange.com/questions/3766/…

Martin Sleziak

Thanks for the link @Szabolcz. It is good to know, that this was discussed. When I have more time, I'll have a closer look at it.

Szabolcs

In short (and from my personal viewpoint), the deepest reason is that the perception is that we will able to build a very functional and enthusiastic community if it's an Mma-only site. E.g. I don't think we could have attracted so many respected experts to commit if it's a general site. The there are the other simpler reasons discussed on the page I linked to

This of course sounds very subjective and it's difficult to show to someone who's not already in the StackOverflow mathematica community, but personally I think that among all other possible and discussed reasons, this is the drive behind the choice

QED

1:07 PM

why so much free support for a non-free software?

Martin Sleziak

@QED My opinion: It's good and it's widely used. (As I already mentioned, in my case this is only based on what people using Mathematica told me.)

Jonas Teuwen

@JM Do you happen to know if you have a certain drug (by that Belgian pharma company) first in oral pill form and then in oral solution if the effect can differ even if you take the same dose (the uptake might be different, for example)?

Asaf Karagila

@robjohn Shakshuka.

robjohn

@AsafKaragila You have eggs?

Asaf Karagila

@robjohn I do.

I also had ripe tomatoes which I saved aside for this lunch from a few days ago.

robjohn

1:12 PM

@AsafKaragila Then go for it :-) Sounds tasty.

Asaf Karagila

Tomatoes are cooking right now.

I'm gonna give them a few more minutes to juice-out before adding all the spices.

robjohn

@QED At least they now have a Home Version that is more reasonably priced than $1200.

QED

If it cost $1 it would still be non-free

robjohn

@QED I was not saying that it was free. Just that it is a lot more reasonable than it was 5 years ago.

Matt

@AsafKaragila 6th of January is called 3 kings day here : )

robjohn

1:20 PM

@Matt Today is also Epiphany (the end of the 12 days of Christmas).

J. M.

@JonasTeuwen The solution ought to be quicker to absorb; it does take a while for the stomach to process the binders in pills. Why do you ask?

Jonas Teuwen

Because it feels like Thor smashes my head with a hamer with the solution and in a pill form it doesn't.

robjohn

@JonasTeuwen ooh, messy hammer.

Jonas Teuwen

Yes.

J. M.

@JonasTeuwen The label mentions headaches as a side effect, no?

QED

1:23 PM

I expect to get a lot of downvotes for this discuss.area51.stackexchange.com/a/3969/50721 but I tried to explain in an impartial way

@Szabolcs

Jonas Teuwen

Well, it's not a headache, it is sleepyness.

Szabolcs

@robjohn Catholic priests go to every house here and "bless" (I don't know the proper English word) them. They write "GMB + 2012" on the door. I don't know the exact details because my family is protestant.

J. M.

@JonasTeuwen ... then I'm not quite sure why the pills and the solution behave differently in you...

Jonas Teuwen

Okay 8-).

Nobody seems to do.

I was wondering if the plasma peak could be higher because it is more easily absorbed.

J. M.

But generally: quick-acting - solution. Sustained-action - pills.

@JonasTeuwen That, too.

robjohn

1:26 PM

@JM The pills probably release more slowly into the system. Never mind :-)

J. M.

@robjohn Correct. The starch, cellulose and other binders allow for a controlled release.

Jonas Teuwen

Well, since it is a solution I can try 3/4th of the dose 8-).

J. M.

(Of course, if you really want something quick-acting, you jab a solution through a vein, under the skin, or through a major muscle.)

robjohn

@Szabolcs: was your spirographic avatar made with Mathematica?

J. M.

@JonasTeuwen You could, but you really should ask your doc first of all...

Jonas Teuwen

1:29 PM

Yeah, in the leg, through the clothes.

Sure, but she allows me to experiment a bit with it.

J. M.

Oh, so she's letting you titrate? I guess you can do bisection...

Jonas Teuwen

Yes.

Szabolcs

@robjohn it was

J. M.

@Szabolcs It's pretty. :)

robjohn

@Szabolcs I believe that @JM's fern was also done with Mathematica

@JM: am I correct?

J. M.

1:32 PM

Yes, it was. :)

robjohn

@Szabolcs I had a candy cane border around my avatar for the holidays that was rendered with Mathematica also.

J. M.

@QED: I don't think it was rude; Szabolcs is trying to wear your shoes here...

Szabolcs

@JM I wanted a fern originally, but then I came across one of your posts, so I made the wiggly round thing instead :-)

J. M.

Wait, what? I don't remember posting an answer involving Barnsley...

Szabolcs

@JM I mean I saw that someone had this gravatar already. I might have been you, I am not exactly sure

@robjohn I like to play with graphics in Mathematica. Do you still have your Christmas gravatar somewhere? I like that there are so many "fun" features (even in early versions there was easy declarative graphics, sound generation, animation, and now we have MIDI)

robjohn

1:46 PM

@Szabolcs I have put back the Holiday avatar. If you refresh your chat window, or just look at my profile, you should see it.

It being Epiphany, I guess I can still celebrate today :-)

Szabolcs

:-)

J. M.

@Szabolcs That's one thing I liked about it. Back in the day, I was heavily using POV-Ray. It didn't take much for me to adapt to Mathematica's graphics.

Now that I think about it, I could have done a monochrome snowflake for Christmas...

QED

That's nice

robjohn

@JM buds?

J. M.

@robjohn I guess you could call them that...

robjohn

1:54 PM

@JM Or you could invert it and it looks like a snowflake.

Asaf Karagila

@Matt Ah.

J. M.

@robjohn Oh well, maybe next Christmas... :)

After seeing this, I wonder about the series $\sum\limits_{n=1}^\infty \frac{q^{n^2}}{n^z}$. It's like the unholy marriage of a Dirichlet and theta series...

QED

that function has a really cool graph

Asaf Karagila

I am starting to write my thesis.

Anyone got a LaTeX template for an M.Sc. thesis?

QED

\begin{MScThesis}

:D

J. M.

2:02 PM

@AsafKaragila Your university doesn't have one?

Asaf Karagila

Not really.

Szabolcs

@AsafKaragila I used the memoir class with a little bit of gradual customization

J. M.

@AsafKaragila Well, what did the people who graduated before you use?

Asaf Karagila

Hmmm. I'll check.

I know most people use the LEd prepared stuff. I don't like LEd.

Martin Sleziak

@AsafKaragila I really liked how this guy's [thesis(diss.fu-berlin.de/diss/servlets/MCRFileNodeServlet/…) look. He mentions in the introduction what LaTeX package he used.

For my thesis I simply used documentclass report, nothing fancy.

Asaf Karagila

2:10 PM

@MartinSleziak Is this M.Sc. or Ph.D.?

Martin Sleziak

BTW the above link is Peter Krautzberger: Idempotent Filters and Ultrafilters; the name might be familiar for people how frequent MO.

Asaf Karagila

It rings a bell.

Was Blass his external advisor or a judge?

Martin Sleziak

@AsafKaragila It's PHD thesis. But not having the source code, perhaps the most useful information from there is: The actual LATEX style is my own modification of the tufte-latex package developed at [Kle].

@AsafKaragila I'm not sure about that. Maybe both?

Asaf Karagila

Are you asking me? I surely don't know :-)

Jacopo Notarstefano

Tufte LaTeX? That sounds interesting!

Martin Sleziak

2:16 PM

Not asking. I'm guessing that this might be the case.

Asaf Karagila

2:33 PM

Hmm.

I think that I know what I am going to write in the dedication part.

$\text{"Greater than the death of flesh is the death of hope. The death of dreams."}$

Screw quotes in LaTeX.

Asaf Karagila

3:27 PM

Okay, I have the general outline for the LaTeX file.

Matt

3:43 PM

I was too quick on the trigger on this one. Is the solution to close it and then vote to reopen?

robjohn

@JM well, we know it converges for $|q|=1$, but for notthing outside that. It seems to lack all the interest of $\sum\limits_{n=1}^\infty q^{n^2}$.

@JM Oops, I thought it was $n^2$ in the denominator. Never mind.

t.b.

@Matt If people had looked at the linked thread instead of just at the title they'd have seen that the question is fully answered there.

Good morning, e'one.

@Srivatsan it works!

Morning @Srivatsan!

3:47 PM

But since we're at least four with re-open powers I'm not opposed to it.

Srivatsan

@robjohn What a relief! =)

robjohn

@Srivatsan how is the morning treating you?

J. M.

@Srivatsan Good day, all and sundry.

Srivatsan

I may not be around for long -- if my vote is needed somewhere, earlier we do it, the better.

@robjohn How do you like your morning?

robjohn

@Srivatsan over-easy.

Srivatsan

3:49 PM

Did you think about the sequence question at all? Did I mention that I'm timing you? =) [just kidding, of course.]

J. M.

Paramedics needed.

robjohn

@Srivatsan Oh, well... I did not have too much of a chance while I was driving my son around, and then I got into writing up an answer I had been working on.

Srivatsan

@robjohn - which answer?

Matt

@tb So how is that potential flu of yours doing?

t.b.

@Matt okay, it's quite certainly not a flu :) Thanks for asking

Matt

3:54 PM

@Srivatsan Actually, what were you testing up there? : )

Srivatsan

@Matt If I can chat. Long story, don't ask. =)

Matt

I won't then : )

QED

what are the chat issues?

Srivatsan

Short version: my laptop is falling apart; it's giving me weird problems.

QED

I was blocked from chat for some time

Srivatsan

3:55 PM

@QED What's "blocked" mean?

QED

it says "only users with more than 10 reputation can chat"

Matt

I don't like it when people want "X for dummies".

Srivatsan

@QED We should celebrate once you get there. =)

QED

:)

@Matt, yeah - it's actually a reasonable question but that title makes me wince

Srivatsan

But seriously: it is not the case that you are logged out and hence can't chat, right?

Dylan Moreland

3:58 PM

@Matt Ultra dummies.

Matt

@DylanMoreland ...or "X for ultra dummies".

Srivatsan

Isn't that what Dylan said too?

t.b.

I'm quite surprised at some of the questions Kevin Buzzard is asking. Isn't he supposed to be a number theorist?

Dylan Moreland

He's a very good one.

Srivatsan

@tb Maybe teaching a class?

"This is a purely recreational question -- I came up with it when setting an undergraduate example sheet."

robjohn

4:02 PM

@Srivatsan this one

Srivatsan

@robjohn Oh nice. What's the idea?

robjohn

@Srivatsan I'm approaching it by computing an asymptotic expansion.

I'm just being over-careful about the details :-)

Srivatsan

@robjohn Hm, right.

Dylan Moreland

I think it's refreshing that Buzzard asks such things.

Srivatsan

@DylanMoreland Which questions are you guys talking about? The new one?

I mean: to me, it reads like any other technical question. I am puzzled by your comments. =)

QED

4:06 PM

> Proving you can't make $2011$ out of $1,2,3,4$: nice twist on the usual

that was a good one

Srivatsan

@QED Oh, that one. That is different, yes.

Dylan Moreland

All of them, really. They're not exceptional among questions here (maybe in that they're well written) but for me it's that one of the best number theorists in the world is poking around and asking about simple things.

t.b.

@Srivatsan What Dylan said :)

Srivatsan

@DylanMoreland I am pleased he even uses SE for asking questions -- simple things or otherwise.

=)

Dylan Moreland

Plus he's an interesting character.

I mean

Spot Kevin Buzzard.

t.b.

4:12 PM

Hint: yellow boots

Srivatsan

I hope that is not photoshopped...

@tb Oh yes, he is different. I was thinking the joke would be that Kevin Buzzard is not in the group, but is looking out from the window.

It's probably I just don't know enough about him.

Asking myself: Who is Kevin Boots? =)

Asaf Karagila

Who's in the wheelchair?

Dylan Moreland

Robert Coleman.

Asaf Karagila

Looks like a bunch of mathematicians and a hippie.

I'm off now. Ciao.

Srivatsan

@robjohn Question: does the upper limit on the integral matter? Will the behavior of the integral change if I change the $\sqrt{6}$ to (say) 1?

robjohn

4:24 PM

@Srivatsan Nope.

Srivatsan

@robjohn In fact, if I understand right, only the interval $[0, O(\frac{1}{\sqrt{n}})]$ is significant...

@tb: In this question, your comment is now gone, making the subsequent comments are orphaned.

robjohn

@Srivatsan It should not shrink that fast with $n$. That would have impact on the result.

J. M.

@Srivatsan That's a really annoying feature of the software...

Srivatsan

@robjohn Oh right. I meant: $[0, \psi(n)]$ where $\frac{1}{n} = o(\psi(n))$.

Or in other words, by taking a bigger and bigger constant in the "O", we can approach the value of $1$, but the limit will be strictly bigger...

Nah forget it. I am finding it difficult to word it properly...

@JM Yes. But this is the first time I am noticing a problem.

@robjohn Anyway, thanks for the clarification.

t.b.

5:03 PM

Anyone opposed to getting rid of this: volume-of-rotation?

J. M.

That should definitely be deleted.

I need my shut-eye, so: I'm off, and see y'all later.

t.b.

ha!

Daniil

6:07 PM

Hi, everyone.

@robjohn got a new fancy userpic upgrade!

QED

hi

Daniil

Yes.

Matt

6:33 PM

But half of the answer to this is here.

Asaf Karagila

7:10 PM

So. What's up?

QED

Hi

Daniil

I learned about well-founded and dense linear orders today.

QED

cool

Asaf Karagila

7:30 PM

@Daniil Congratulations.

I had set up the main .tex file for the thesis.

Asaf Karagila

7:44 PM

@tb I think I'll write another description of the Borel hierarchy :-D

Daniil

Asaf, do you have a blog?

Nikhil Bellarykar

hi $\forall$

Daniil

Hello, @NikhilBellarykar

Nikhil Bellarykar

wassup @Daniil

Asaf Karagila

8:03 PM

@Daniil No. I did have a passing thought once to start one.

Nikhil Bellarykar

8:15 PM

@all I have a question

Bullmoose

@robjohn, are you around?

Matt

8:55 PM

Hello there.

Namaste, Nikhil! : )

Nikhil Bellarykar

Namaste Matt :)

wassup

Asaf Karagila

Nametasting?

Nikhil Bellarykar

or namestating?

yes

Matt

@NikhilBellarykar Not much, I'm done in for today. What's up in Nepal? Must be cold there right now. Do you have snow?

Asaf Karagila

Do you ever not have snow?

Nikhil Bellarykar

8:58 PM

hey I am not from Nepal but India :)

and that too from Maharashtra, where it never snows :)

Matt

Darn, I thought you said you were from Nepal! Sorry for mixing you up with someone else. : S

Asaf Karagila

@Matt FreakEnum/Mr. Anubis

Nikhil Bellarykar

k no problems..I was gonna ask what made you think I am from Nepal :P

Matt

FreakEnum! Of course! I'll blame my confusion on the name change.

Thanks, Asaf!

Nikhil Bellarykar

ohkk

btw where are you from @Matt?

Matt

9:00 PM

The good thing about having early onset of Alzheimer's is that you can watch the same movie again and not have a clue what's going to happen next. : )

Nikhil Bellarykar

cool...Bollywood's fav destination :)

Matt

: )

Thank you, Asaf!

: )

Nikhil Bellarykar

gotcha Asaf :D

what time is it there @Matt?

Matt

10 pm!

Nikhil Bellarykar

2:30 am here

Asaf Karagila

9:03 PM

23:30 here.

Nikhil Bellarykar

howz d weather @ ur respective locations?

Asaf Karagila

@Nikhil: cf. Rule 6 in the Chat Rules.

Matt

Cold right now. Around 2 degrees.

Asaf Karagila

Around 9 degrees Celsius.

Nikhil Bellarykar

@AsafKaragila what if l33t spik is intelligible?

Asaf Karagila

9:06 PM

@NikhilBellarykar We don't care.

Matt

@AsafKaragila What? I thought it was always around 20 degrees there!

Nikhil Bellarykar

Here it is arnd 25-30 degree selsius

@AsafKaragila okay

Asaf Karagila

@Matt Nah. During this time of year it's about 10-20 during the day and 0-10 during the night. Depending on the time, wind and the whatnots.

Matt

Hello Srivatsan!

Nikhil Bellarykar

I dont know where the cold has gone

Srivatsan

9:07 PM

hi

Nikhil Bellarykar

hi Srivatsan

Srivatsan

Nikhil: If you read my comments, I would like to delete them from the page. =) Off-topic...

Nikhil Bellarykar

yes sure :)

Srivatsan

You should also perhaps delete one of your comment referring to accepting answers.

Nikhil Bellarykar

I will also delete my responses :P

Srivatsan

9:09 PM

Just one of them...

Nikhil Bellarykar

ya that only :D

Srivatsan

OK, got to go. =) See you guys later.

Nikhil Bellarykar

seri, cya later

Matt

@Srivatsan Byee.

Asaf Karagila

Anyone knows how to make a symbols index in latex?

Nikhil Bellarykar

9:11 PM

not me

Matt

What exactly does it mean? Like a table containing all the symbols?

Nikhil Bellarykar

thought so

Asaf Karagila

Yeah. You can see those in books.

Matt

Is it not just a table?

Asaf Karagila

Yes, but you generate it automatically.

I hope.

Matt

9:13 PM

That's what I meant with the question above. So you want it auto-generated.

Asaf Karagila

Obviously, or I wouldn't have asked :-)

Martin Sleziak

@AsafKaragila Asaf I can give you my source code to show how I did it. (Of course I do not claim that it is the best way to do.)

Matt

@AsafKaragila : )

Asaf Karagila

I'll check tex.SE first

Martin Sleziak

You can check the end result here: thales.doa.fmph.uniba.sk/sleziak/papers/dizer/dizer2pdf_st.pdf

ok

Asaf Karagila

9:19 PM

Hmmm... there is a package {glossaries}

Jonas Teuwen

Is going to the opera in Syndey worth the (high) price? :-).

Asaf Karagila

Only if you're high. rimshot

Nikhil Bellarykar

Tchaikovsky rocks indeed!

anon

9:35 PM

How it is that five people came to upvote this question of mine is beyond me. I just got the fifth recently.

Nikhil Bellarykar

you think that is strange? take a look at this.

http://math.stackexchange.com/questions/96079/3k-1-can-never-be-a-power-of-4/96081#96081

the fact that such a 1-liner got 16 upvotes is strange, to say the least

Martin Sleziak

The more people understand the area, the greater is the chance of getting upvotes.

Nikhil Bellarykar

seems like math.SE's version of facebook like

Martin Sleziak

Also first answer is more probable to get upvotes.

anon

That sounds like an apt description, Nikhil

Nikhil Bellarykar

9:41 PM

thanks anon :)

@MartinSleziak true

Matt

@NikhilBellarykar Because it's a good answer. : ) + 1

Nikhil Bellarykar

Thanks Matt :)

MaX

Die anybody know this one:

_, T, T, F, F,
S, S, E, N, T,
E, T, T, F, F,
S, S, E, N, T

what is the missing letter?

Matt

E?

MaX

It's not E

Nikhil Bellarykar

9:45 PM

E?

Asaf Karagila

T

MaX

A friend send me as a teaser,

why asaf ?

Nikhil Bellarykar

may well be a teaser literally if the answer ain't E

Asaf Karagila

@MaX Why not? It's a finite thing, we can always create enough superficial demands for it to be anything.

MaX

lol :D

anon

9:48 PM

Alright, what comes next in this sequence: 7, 4, 5, 4, 2, 4, [ ]

42

3?

It must be 42

A friend gave me that in middle school and laughed when I couldn't get it for a day straight. Unfortunately, the pattern isn't even mathematical...

Nikhil Bellarykar

fan of Hitchhikers guide to galaxy @MaX ? ;)

MaX

9:49 PM

lol

Yes, and SPOJ too

try out SPOJ TEST

Nikhil Bellarykar

gimme link or sumthn

anon

|Alright|=7, |what|=4, |comes|=5, |next|=4, |in|=2, |this|=4

Nikhil Bellarykar

wow

It takes a Rajnikanth to figure it out :D

MaX

lol, Rajnikanth don't do such menial things :P

anon

mse is offline?

Matt

9:55 PM

Looks like it.

Asaf Karagila

Good. I'll return to my writing.

Alex Becker

Darn it. I was just commenting too.

anon

same here

Asaf Karagila

Same on which account?

anon

just commenting

(or should I just respond "Yes"?)

brb, library computer death and resurrection

For a second there I thought I couldn't log back in b/c MSE was offline.

MaX

10:05 PM

btw the answer of my question is O

|O|ne, |T|wo, |T|hree, |F|our ...

anon

what the hell?

drats, it's similar to my question...

Matt

@anon : D

MaX

Abstract duplicate ?

anon

Maybe we should rename "one" to begin with an "e" so as to preserve symmetry. I'm sure mathematicians will go for it with that rationale.

MaX

haha, nicely said :D

Matt

10:09 PM

Gotta go, bye folks!

anon

later

MaX

bye Matt

Nikhil Bellarykar

10:22 PM

MaX indeed :D

Transcript for

$Mathematics$ Mathematics