Mathematics - 2014-11-14 (page 1 of 4)

Daniel Fischer

00:00

@N3buchadnezzar What's the problem?

Pedro Tamaroff

@DanielFischer Hello Daniel!

How are you? Did you hear the bad news?

Daniel Fischer

@PedroTamaroff You mean Grothendieck?

Pedro Tamaroff

Yes.

Daniel Fischer

I just read it here a couple of minutes ago.

Jasper Loy

@PedroTamaroff The good news is that Grothendieck will be reborn and contribute to math again, hopefully. What seems good may be bad, and what seems bad may be good.

robjohn

00:01

@skullpatrol They don't render in my browser, but I know that they are the three monkeys...

N3buchadnezzar

@DanielFischer The loop stops prematurely

skullpatrol

Yes @robjohn classics :-)

Jasper Loy

@robjohn I have three monkeys now: runny nose, sore throat, dry cough.

Pedro Tamaroff

@DanielFischer It is amazing how the proof of the Riemann Mapping theorem uses almost all the fundamental yet elementary facts about holomorphic functions.

N3buchadnezzar

@DanielFischer I think I figuredit out =)

Alexander Gruber

00:04

does anybody know if he wrote anything at all about his life in isolation?

Jasper Loy

@PedroTamaroff Is this your first course in complex analysis?

Pedro Tamaroff

@JasperLoy Yes.

robjohn

Ooh... the clock has flipped... I can get points again :-)

Mike Miller

I would imagine so, @Alexander, but I would also imagine it is not publicly available

Jasper Loy

@PedroTamaroff Then it must be moving very fast to cover the RMT.

Daniel Fischer

00:05

@N3buchadnezzar What was it? That range doesn't include the upper bound?

skullpatrol

Good luck @robjohn

N3buchadnezzar

@DanielFischer Well it does except for the last one

Alexander Gruber

@MikeMiller You mean in letters to his friends?

Jasper Loy

@robjohn I better put the clock back, lol.

Daniel Fischer

@N3buchadnezzar I meant range(1,3) = [1,2].

Alexander Gruber

00:06

i'll tell you one thing, i do not understand that guy's theorems. everytime his name comes up in a class I have to brace myself for some next level confusion.

N3buchadnezzar

@DanielFischer scracthes head Does it really do that?

Jasper Loy

I hope I win something big in tonight's lucky draw.

N3buchadnezzar

@JasperLoy Your momma?

Jasper Loy

@N3buchadnezzar Yes, it is my mum going to the lucky draw, not me, lol.

Daniel Fischer

@N3buchadnezzar Yes. It's the spec.

Ted Shifrin

00:07

He started off as a functional analyst, @Alex ...

N3buchadnezzar

@DanielFischer I should add a +1 then

Jasper Loy

I ordered a whole bunch of books from amazon, decided to return them before they arrived, and interestingly they all got lost by the carrier, lol.

N3buchadnezzar

@DanielFischer pastebin.com/7N2LFtZ9 Still the code seems to miss many combinations..

Alexander Gruber

@TedShifrin maybe that's why.

skullpatrol

The books about learning languages @JasperLoy?

Pedro Tamaroff

00:13

@JasperLoy I don't know if they'll get there. I am studying on my own.

Daniel Fischer

@N3buchadnezzar You mean like 3+3+3+3+3+3+3 = 21?

Pedro Tamaroff

@AlexanderGruber Look. =)

N3buchadnezzar

@DanielFischer Yeah

Daniel Fischer

@N3buchadnezzar Since you let the upper bound for the sum of the first six be S - t, which is 14, and the upper limit is excluded in range, you never get anything with g < 8.

N3buchadnezzar

@DanielFischer Well each number must be atleast 1

Daniel Fischer

00:20

@N3buchadnezzar But that only gives an upper bound on g, namely 15. The sum of the first six could be as large as (numbers-1)*(S/numbers) (18).

(Note that if numbers doesn't divide S, it's more complicated.)

N3buchadnezzar

@DanielFischer I think I figured it out

@DanielFischer pastebin.com/pqd63iu4 This seems to get all the cases.

robjohn

00:54

@Chris'ssis: I am mired in Si and Ci functions. I think I need a different approach, so I am putting this to rest for a while.

Studentmath

\o

skullpatrol

o/

Studentmath

How are you @Skull?

Anyone remembers a bit from logic course? I am stuck on some simple exercise

skullpatrol

Fine thanks. How are you pal @Studentmath ?

Studentmath

Fine, a tad exhausted but fine :)

Kaj Hansen

01:09

Grothendieck died today :O

skullpatrol

Yep, we heard :'(

He was 86.

Alizter

Sleep? Never heard of it.

evinda

Hey!!! Is every ideal $I=<f(x)>$ a principal ideal?

Alizter

Oh wrong princaple

evinda

@KajHansen And if it is irreducible?

Kaj Hansen

01:17

Oh wait.

I was thinking maximal ideal >_<

Yes, it is principal @evinda.

By definition, any ideal generated by a single element is principal.

Alizter

"princ"

evinda

@KajHansen Even if it is not irreducible?

Alizter

single

Kaj Hansen

That is correct @evinda.

Alizter

@evinda What is your definition of principle ideal?

Kaj Hansen

01:19

Moreover, in polynomial rings over a field are principal ideal domains (all ideals are principal).

evinda

@Alizter There is no definition in my notes :/

Alizter

@evinda That is not too good :P

evinda

@Alizter Could you give me a definition?

Alizter

sure

Fernando Martin

for polynomial rings in one variable

skullpatrol

01:21

Drum roll....

Kaj Hansen

The definition I use is as follows:

A principal ideal is an ideal $I \subset R$ that is generated by a single element $a \in R$. Notation-wise, a principal ideal is any ideal that can be written as $<a>$.

Alizter

Or an integral domain where all ideals are principal

oh wait

evinda

@KajHansen @Alizter Could you also maybe at the following exercise?

Notice that in $\mathbb{C}[X,Y,Z]$:
$$V(Y-X^2,Z-X^3)=\{ (t,t^2,t^3)/ t \in \mathbb{C}\}$$

In addition, show that:

$$I(V(Y-X^2,Z-X^3))=<Y-X^2,-X^3>$$

Finally, prove that the ideal $<Y-X^2,Z-X^3>$ is a prime ideal of $\mathbb{C}[X,Y,Z]$. Conclude that the algebraic set $V(Y-X^2,Z-X^3)$ is irreducible.

Could we show like that, that in $\mathbb{C}[X,Y,Z]$:
$$V(Y-X^2,Z-X^3)=\{ (t,t^2,t^3)/ t \in \mathbb{C}\}$$
?

$$V(Y-X^2, Z-X^3)=\{(a,b,c) \in \mathbb{C}^3 | b-a^2=0, c-a^3=0 \Rightarrow b=a^2, c=a^3\}=\{(t, t^2, t^3)| t \…

Alizter

that is PID

A principal ideal is an ideal that has multiplicative absorption.

Kaj Hansen

How can you tell so quickly @Alizter?

Alizter

01:23

a screw it

I am too tired

skullpatrol

Try sleep.

Ever heard of it ^_^ @Alizter

Kevin Driscoll

@RobJohn I found that my divergent integral indeed should be regularized by the surrounding structure of the problem, and comparing some numerical results it seems like just subtracting the offending divergent piece is the right thing to do. Now I'm trying to prove it though and I have no idea how to make progress.

evinda

@Alizter Were you referring to the exercise I asked? :/

Alizter

@evinda No. I can't think straight.

I need to finish my physics coursework by tomorrow

All the hardness tests look the same to me.

don't tell semiclassical.

Kevin Driscoll

@Alizter Hardness tests?

Alizter

01:30

@KevinDriscoll For materials.

Kevin Driscoll

@ALizter Yes, where are you learning about that?

evinda

Have somebody an idea if that's what I have tried is right and how I can show that I is a prime ideal?

Alizter

@KevinDriscoll erm school?

Kevin Driscoll

Ya but what subject?

Alizter

physics?

Kevin Driscoll

01:31

UUUUUUGH. That hurts my soul, @Alizter

Alizter

@KevinDriscoll Why?

They are all "Stick diamond pointy thing in material"

tbf most datas use brinell and convert.

Kevin Driscoll

@Alizter There are so many more important things to learn in physics class. Hardness tests sounds like the ultimate waste of time

You are in secondary school, right?

Alizter

@KevinDriscoll Oh no. You will hate the physics we are supposed to learn. I can't even understand how they made it so boring.

The most complicated thing is solving linear ODEs

Kevin Driscoll

@ALizter Well in secondary school you sweep most of the calculus under the rug because even the students who've taken the calculus course aren't very good yet.

Alizter

@KevinDriscoll On the other side of my physics course we have spent forever on waves.

Kevin Driscoll

01:35

But yes id its things like this that you're expected ot learn I would hate it..... There's no better way to make physics seem like a terrible subject than to turn it into just memorizing a bunch of formulas and experimental techniques

Alizter

We are doing the rayleigh thingy?

With apertures and stuff.

Kevin Driscoll

The Rayleigh criterion?

Alizter

Reasonably interesting

@KevinDriscoll yes.

I am actually finding chemistry a lot more fun though.

Kevin Driscoll

MEH it's slightly more fundamental. Wave emchanics is fine. Rayleigh criterion is just sort of arbitrary.

Alizter

I hope that I will not need a second redbull tonight

Kevin Driscoll

01:38

In our 1st semester freshman physics class we spend all of our time on 3 main principles. Newton's 2nd law for translation. Newton's 2nd law for rotation. Work-energy theorem.

You know, like actual fundamental physics.

Alizter

@KevinDriscoll We have done more mechanics in maths.

Which I find really fun.

We are doing moments now.

All very basic.

I think the hardest it will ever get is some fluid mechanicsy type thing.

Kevin Driscoll

Moments like moment of inertia? Or moments like moments of proability distributions?

Alizter

torque?

Kevin Driscoll

OK moment of intertia then

Im sure you wont do any kind of serious fluid dynamics because even professional physicists can't do it. But you could do some hydrostatics and laminar flow, perhaps.

Alizter

@KevinDriscoll I did not want to say inertia because I have not seen the word come up yet.

skullpatrol

01:41

Do you do any relativity?

Kevin Driscoll

@Skullpatrol It's in our introductory textbook but we sorta ignore it usually. SOMETIMES at the end we do some conservation of energy problems involving radioactive decay

skullpatrol

Hmm...

Alizter

@KevinDriscoll LOL. I looked at it again and I had read it wrong the first time. It was just displacement with water current effects.

Kevin Driscoll

@ALizter Ah yes. WE do those sorts of problems as a way of getting more work with vectors.

Alizter

Second order vector DE are the "hardest" topic.

Kevin Driscoll

01:45

I would say difficulty is not the most important thing. It's about accurately communicating what physics is about and giving students some insight into what it means to think like a physicist.

Alizter

hardnesstesters.com/…

they look very similar

Kevin Driscoll

I think economics is really the model we should follow. My experience is that most introductory economics teachers understand that the goal is tohelp students learn to think like an exonomist

Alizter

@KevinDriscoll I hated economics.

Kevin Driscoll

@Alizter Engineering at best......

Alizter

It was really essay oriented.

Kevin Driscoll

01:46

Lots of people don't like economics.

Ya they shy away from the math even more than physics

Alizter

And memorising of reasons for inflation etc...

The hardest maths we did was percentage calculations.

Kevin Driscoll

Well that's unfortunate. If you understand the principles of economics there should be no need for memorization

Alizter

I am still surprised that Mathematical Chemistry is not a big thing.

Kevin Driscoll

It is at the university level, but htey call it Physical Chemistry

Guest

Given a compact topological space $(X,\mathcal{A})$, let $C(X)$ denote the space of continuous complex-valued functions defined on $X$, that is, $C(X):=\{f:X\to\mathbb{C}|f\text{ is continuous}\}$. Define $+:C(X)\times C(X)\to C(X)$ by $(f+g)(x):=f(x)+g(x)$ for all $x\in X$. How does one show that $+$ is well-defined, that is, that $f+g\in C(X)$? Surely it must be simple. I know $f^{-1}(V),g^{-1}(V)\in \mathcal{A}$ for all open sets $V\in \mathbb{C}$ and want to show the same for $(f+g)^{-1}(V)$

Alizter

01:49

@KevinDriscoll Silly naming.

Zach Saucier

Good evening, guys

skullpatrol

There is also Chemical Physics.

Alizter

Astronuclearthermophysics

as avengers would say

skullpatrol

Hello :-)

Kevin Driscoll

Indeed, but in chemical physics and physical chemistry basically all serious work is numerical

Alizter

01:50

@KevinDriscoll I would love just to model chemistry.

Perfect periodic table

bounded PDF's for electron orbits

topologically logical molecules

Zach Saucier

can someone check my work real fast? The answer is correct, but I don't know if it's by coincidence or not

$\mathbf{F} = -x^2y \textbf{i} + xy^2 \textbf{j}$, find $ \displaystyle\mathop{\oint}_C \mathbf{F} \cdot \textbf{n} ~\mathrm{ds}$. My thoughts: $\int_{0}^{2pi} -(\cos{t})^2\sin{t} + \cos{t}(sin{t})^2 = 0$

Kevin Driscoll

@Zach what is C?

Alizter

or n?

Zach Saucier

oh, right

Alizter

or s?

Zach Saucier

01:52

@KevinDriscoll $C : \textbf{r}(t) = (1 \cos t) \textbf{i} + (1 \sin t) \textbf{j}, ~ 0 \leq t \leq 2 \pi$

Kevin Driscoll

@Alizter n is the unit normal to C, ds is the line element of C

Mike Miller

@Guest The composition of continuous functions is continuous. The summation map $\Bbb C \times \Bbb C$ is continuous, and $f$ and $g$ are continuous, so their sum is continuous.

Alizter

Ok. Stuff I do not know.

runs

trips over rock and cries

then falls asleep

Zach Saucier

@Alizter o/ sleep well

skullpatrol

That wasn't a rock that was me :p

Alizter

01:53

@ZachSaucier No sleep well. Coursework 24 hrs before the deadline does not create itself.

user105491

Allegedly (see Wikipedia), Grothendieck died today. Anyone know if it's true?

Studentmath

Is there any nice way to prove that if $(\phi)\square (\phi)$ is a sentence, so is $\phi$?

Alizter

\boxed?

or \square?

Kevin Driscoll

@Zach What did you calculate $\hat{n}$ to be?

user105491

@Alizter - my thoughts precisely

Studentmath

01:55

@Alizter thanks!

Square stands for any two-way connection.. for example V

Alizter

@Studentmath What happens when it is not a sentence. What does this make $\phi$?

or something like that

Mike Miller

The sources are obituaries in a pair of French newspapers, @Sanath, Le Monde and Liberation. It's up to you to decide whether or not to trust them.

Zach Saucier

@KevinDriscoll My understanding was that I was supposed to put it in the form $Pdx + Qdy$, so I didn't have an n directly

Alizter

@MikeMiller Nobel again?

Kevin Driscoll

@Zach Oh, green's theorem>

user105491

01:56

@MikeMiller I don't know; what do you believe?

Zach Saucier

@KevinDriscoll ya :)

Studentmath

Well, obviously it makes the whole thing not a sentence, but the way of proving why is a bit annoying. I thought about considering all the ways to 'divide' the whole thing so it is a statement and show each is impossible.

But that could be a bit exhausting

Mike Miller

I don't see any reason to disbelieve them. MathOverflow seems to believe them.

Alizter

@MikeMiller If MO does then i am sold.

Guest

@MikeMiller What do you mean by "summation map $\mathbb{C}\times\mathbb{C}$"?

user105491

01:58

@Mike I agree with @Alitzer

Kevin Driscoll

@Zach you still ahve to calculate what n is though, don't you? HOw else do you know what goes in front of $dx$ and what in front of $dy$?

user105491

It truly is the loss of a great mathematician

evinda

@MikeMiller Could you also maybe at the following exercise?

Notice that in $\mathbb{C}[X,Y,Z]$:
$$V(Y-X^2,Z-X^3)=\{ (t,t^2,t^3)/ t \in \mathbb{C}\}$$

In addition, show that:

$$I(V(Y-X^2,Z-X^3))=<Y-X^2,-X^3>$$

Finally, prove that the ideal $<Y-X^2,Z-X^3>$ is a prime ideal of $\mathbb{C}[X,Y,Z]$. Conclude that the algebraic set $V(Y-X^2,Z-X^3)$ is irreducible.

Could we show like that, that in $\mathbb{C}[X,Y,Z]$:
$$V(Y-X^2,Z-X^3)=\{ (t,t^2,t^3)/ t \in \mathbb{C}\}$$
?

$$V(Y-X^2, Z-X^3)=\{(a,b,c) \in \mathbb{C}^3 | b-a^2=0, c-a^3=0 \Rightarrow b=a^2, c=a^3\}=\{(t, t^2, t^3)| t \in \math…

Zach Saucier

@KevinDriscoll I suppose I did it wrong then :P I just plugged in cos(t) for x and sin(t) for y

Mike Miller

@Guest $(z_1,z_2)\mapsto z_1+z_2$

Kevin Driscoll

01:59

@Zach Ya I suspected as much, that is part of what you need to do, but you still have to calculate n and take the dot product

Zach Saucier

kk

Kevin Driscoll

@Zach I think you will find that your vector field is divergence-free $\nabla \cdot F = 0$ which is why the answer is 0

Zach Saucier

@KevinDriscoll Can't I just find $nds$? Not just n?

Kevin Driscoll

@Zach how do you propose to do that?

Zach Saucier

isn't $nds$ just the normal? So $nds = (dy, −dx)$ ?

I suppose it wouldn't work because it's dotted

Kevin Driscoll

02:06

@Zach Normal to what, though?

Zach Saucier

to the function they give us for F I thought

Kevin Driscoll

@Zach Ah no, the normal is the unit normal vector of the curve $C$

Zach Saucier

I see

that helps my understanding

Guest

@MikeMiller Ok thanks. So if I get it right, if we define $+:\mathbb{C}\times\mathbb{C}\to\mathbb{C}:(z_1,z_2)\to z_1+z_2$ and $h:X\to\mathbb{C}\times\mathbb{C}:x\to (f(x),g(x))$ then $+\circ h=f+g$. I can show that if $h_1:X\to Y$ and $h_2:Y\to Z$ are continuous then $h_2\circ h_1$ is continuous. Also the topology on $\mathbb{C}\times\mathbb{C}$ is just the cartesian product of open sets of $\mathbb{C}$ (since we have a direct product of a finite number of topological spaces there is no choice).

Kevin Driscoll

@Zach Yes, think about the plain-English meaning of the integral you wrote. If n is a vector normal to the field $F$ at point $(x,y)$ then the dot product always gives 0 ebcause you're dotting a vector into a vector normal to it!

Zach Saucier

02:10

mmhm

Mike Miller

Yeah, @Guest.

Guest

02:33

It has been proved in my Functional Analysis course that $(\mathcal{B}(E),\|\cdot\|_{\infty})$ is a Banach space, where $E$ "is a set", $\mathcal{B}(E):=\{f:E\to\mathbb{C}|\sup_E f<\infty\}$ and $\|f\|_{\infty}:=\sup_E f$. However the proof begins with: Let $(f_n)_{n\geq1}$ be a Cauchy sequence in $\mathcal{B}(E)$. I wonder if the case $E=\emptyset$ vacuously gives a Banach space?

Jose Antonio

Hi. someone could help me is measure theory I only want to check if what I get is correct. This exercise says: let $f_n = 1_{[0,n]}/n^2$ a family of function. Is there a Lebesgue integrable function which dominates the $f_n$. I think that $g(x)= 1_{[0,1)}(x)+ 1/{\lfloor x \rfloor} 1_{[1,\infty)}$ is the function.

evinda

We have the homomorhism $\phi: \mathbb{C}[x,y] \to \mathbb{C}$ with $\phi(z)=z, \forall z \in \mathbb{C}, \phi(x)=1, \phi(y)=0$. I have shown that for $p(x,y)=a_0+\sum_{k,\lambda=1}^m a_{k \lambda} (x-1)^k y^{\lambda}$, we have $\phi(p(x,y))=a_0 \in \mathbb{C}$. How can I find the kernel of $\phi$ ?

Mike Miller

03:01

@Guest A vector space has an identity element.

Guest

@MikeMiller Well if $E=\emptyset$ then $\mathcal{B}(E)$ contains the so-called "empty function", which acts as an identity element? But if $E=\emptyset$ then I think the norm $\|\cdot\|_{\infty}$ is not well-defined since the $\sup$ is taken over an empty set...

Mike Miller

I misread your comment. I would probably agree that $\mathcal B(\varnothing)$ is a Banach space, though I guess you would have to define the norm specially in this case...

Jose Antonio

03:50

I think the $g$ I choose is correct, $g$ is measurable as is in $ (-\infty, 0)$, $ [0,1)$ and in the each interval $[n,n+1)$ with the relative sigma algebra.

Also dominates the function $f_n$ for each $n$, and its integral is $1+\sum_n 1/n^2<\infty$

I'd appreciate if someone could say me if all these is correct and I don't make a stupid mistake. Thanks.

Nick

$$\boxed{ \boxed{\boxed{\boxed{\boxed{\text{R.I.P Grothendieck}}}}}}$$

It is better to have a good category with bad objects than a bad category with good objects.

To Grothendieck, a problem was not truly solved until it was viewed from the "right" general perspective, from which it could be solved effortlessly, from which it became in a sense obvious, from which it fits naturally into a larger conceptual framework. As Grothendieck himself explained, rather poetically:

"The ... analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more ﬂexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!

A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, …

Jose Antonio

04:06

Someone? please I believe is correct but I prefer if someone could check what I have so far.

DemCodeLines

04:17

How would I do this? Integral (sec^3 x dx)?

0

Q: The proper and easiest way of doing an integral with derivative?

I have this integral: $\int{sec^3x dx}$ I don't understand how I would solve this. Google and YouTube videos don't help me understand much, other than just giving the answer. Is it possible to explain step-by-step how this would be solved, assuming that this is the first time I'm seeing it?

Jose Antonio

05:05

Here is what I have so far. Let $f_n=1_{[0,n]}$ and $g(x)= 1_{[0,1)}(x)+ 1/{\lfloor x \rfloor} 1_{[1,\infty)}$. To show that $g $dominates each $f_n$ we have to show that $f_n\le g$ and $g$ is absolutely integrable. That $f_n\le g$ is easy considering each of the possibilities for $x\in \bf{R}$. On the other hand, $g$ is measurable since is measurable in $(-\infty, 0), [0,1)$ and $[n,n+1$ for each $n\in \bf{N}$ therefore is measurable in $\bf{R}$ given that is in the partition defined above.

Now let $F_N(x)=1/{\lfloor x \rfloor} 1_{[0,N+1)}(x)$ then is not difficult to show that $0\le F_N \uparrow 1/{\lfloor x \rfloor} 1_{[1,\infty)} $ and using the monotone convergence thm we have that $$\int 1/{\lfloor x \rfloor} 1_{[1,\infty)} = \lim_N \int \sum_N 1/N^2 1_{[N,N+1)}= \sum_n 1/n^2< \infty$$ so by linearity of the integral $\int g = 1+ \sum_n 1/n^2<\infty$ which shows that $g$ is absolutely integrable and $g$ dominates $f_n$ as claimed.

I believe the above is correct but I'd appreciate the opinions of others and also any suggestions. Thanks in advance.

Mike Miller

@JoseAntonio You've been asking about this for most of the day now; I certainly can't comment, and it looks like nobody else can. I think you should post it on main!

Nick

@DemCodeLines Just do $\int \sec x \sec^2 x \mathrm dx$ using byparts.

$$\int \sec^3 x \, \mathrm dx = \frac{1}{2}\sec x\tan x + \ln \sqrt{\sec x + \tan x} + \mathcal C$$

@JoseAntonio Post it on the main site. Your concern is worthy of it. The worst come worst situation is that you are absolutely right and no one has anything more to add.

Jose Antonio

05:37

@NIck, @MikeMiller Thanks for the advice. I already posted

Nick

@JoseAntonio My prayers are with you =) Godspeed, man.

Nick

06:11

Curses!! Class XII students will not be eligible to appear for RMO/pre-RMO from 2014 onwards.

Well, there's go my dream of ever having a chance to get to the IMO,

Mhh, maybe it's better not to have a chance than to have a chance and fail =)

skullpatrol

You can still try.

Nick

@skullpatrol I can still try the out the papers unofficially for my own personal satisfaction, you mean :D Ofcourse I'd do that.

skullpatrol

Yep, make it your own personal Olympics ;-)

Jasper Loy

@robjohn You should be sleeping, lol.

Nick

@skullpatrol hugs that's a wonderful idea (sometimes we all need someone who can reaffirm our ideas inorder for us to act based on it. Thanks for being that someone)

skullpatrol

06:27

Anytime pal :D

Nick

Don't l.o.l. in the middle of the night.
For it might give someone a fright.
Especially when they turn on the light
and see you @Jasper; a blinding blue sight!

@skullpatrol Even at say, 5:30 AM on May 11, 2020 ?

skullpatrol

Sure.

Nick

@skullpatrol You are way too free if you can schedule things that far away on your calender.

skullpatrol

Have you ever heard the song Born Free?

daOnlyBG

07:06

hello

skullpatrol

07:25

Hi

en.m.wikipedia.org/wiki/Born_Free_(Matt_Monro_song)

Vrouvrou

07:45

Hello

skullpatrol

Hi

skullpatrol

08:47

►

2014 Iguala mass kidnapping

On September 26, 2014, 43 students from the Raúl Isidro Burgos Rural Teachers' College of Ayotzinapa went missing in Iguala, Guerrero, Mexico. According to official reports, they had travelled to Iguala that day to hold a protest against what they considered to be discriminatory hiring and funding practices by the Mexican government. During the journey local police intercepted them and a confrontation ensued. Details of what happened during and after the clash remain unclear, but the official investigation concluded that once the students were in custody, they were handed over to the local Guerreros...

Vrouvrou

09:07

who can help me on homotopy equivalence ?

user2179021

hi

Vrouvrou

if someone have an idea :math.stackexchange.com/questions/1019919/… thank you in advance

user2179021

you already got an answer and helpful comments!

evinda