Mathematics - 2012-03-16 (page 1 of 6)

Henning Makholm

00:00

@robjohn Nope, as far as I can see. And I've been reloading pages all afternoon...

robjohn

@Skullpatrol I'm sorry, I got taken away from the site while I was downloading the video.

Henning Makholm

The last "chat message" notice in the inbox is from March 8 or earlier.

robjohn

@HenningMakholm I have sometimes lost the sound from the ping, but I think I get them in my inbox on my profile page.

Skullpatrol

@robjohn Oops I meant Kip Thorne

robjohn

@Skullpatrol I knew what you meant. I didn't even notice the typo.

Henning Makholm

00:03

@robjohn Ever since OSes began using soundcards instead of the computer's built-in speaker, my computer usage has been totally silent (except when I explicitly pick up the headphones).

Skullpatrol

@HenningMakholm So you didn't hear me greet you when you arrived in the chat room? chat.stackexchange.com/transcript/message/3840969#3840969

robjohn

@Skullpatrol Are you talking about the discussion about the "tactile", geometrical tools used by Hawking?

Skullpatrol

@robjohn Yes, losing one set of "tools" makes you develop another set.

Henning Makholm

@Skullpatrol You have a history of bombarding people who recognize you with random questions of doubtful relevance. Easier not to.

Skullpatrol

@HenningMakholm I apologize for my lack of sophistication Sir.

robjohn

00:12

@Skullpatrol I would say it encourages you to develop other tools.

Asaf Karagila

@HenningMakholm Hooray for ignore! :-D

Skullpatrol

@robjohn In my opinion, the entire video is an inspiration.

@robjohn Did you notice he has a poster of Marilyn Monroe in his office?

user19161

@skull You are back!

user19161

But still no account...

Skullpatrol

I am unaccountable...

user19161

00:24

@Skullpatrol WTF?

Skullpatrol

FYI

user19161

What is the poster doing there?

Skullpatrol

Hanging on his wall.

Bill Dubuque

@WillHunting Are you good or mean? (see above discussion for the joke)

user19161

@Skullpatrol Very good observation.

Skullpatrol

00:26

@WillHunting Thanks.

user19161

@BillDubuque I am trying to find it now.

N3buchadnezzar

Perhaps he is SD

Bill Dubuque

@WillHunting Perhaps we need a Mean Will Hunting to do some better-than-average mathematical lion hunting

user19161

@N3buchadnezzar Who is SD? You guys are all so mysterious these days...

N3buchadnezzar

SD = standard deviation, something between good and mean ^^

user19161

00:30

Whoa, all this joke is getting HEAVY!

N3buchadnezzar

Perhaps avreage would fit better.

user19161

@BillDubuque I am a bit slow when it comes to jokes as you can see. :-)

user19161

I think I have a weird sense of humour.

Skullpatrol

@BillDubuque Do you understand the Bertrand Russell quote "mathematics may be defined as the subject in which we never know what we are talking about , nor whether what we are saying is true?"

Hi @PaulSlevin

Paul Slevin

hiya

Bill Dubuque

00:34

@Skullpatrol People sometimes say that about my jokes too, which often involve too much word play!

Skullpatrol

@BillDubuque So it means mathematics involves too much word play?

user19161

@bill Do you know about the left and right arrows you can use in this room?

Bill Dubuque

@WillHunting What do you mean, good Will?

user19161

@BillDubuque Ah it seems you don't! Hover over the message you want to reply to and click the arrow on its right to reply.

user19161

Clicking on the left arrow links backwards to the message replied to.

user19161

00:37

This helps users to follow the conversation.

Bill Dubuque

Ah, I see . Haven't used chat much. Thanks for the tip.

Skullpatrol

@PaulSlevin I found a good quality link to "A Brief History of Time" if you're interested

Paul Slevin

I've bookmarked it. Thanks for that.

I am severely over my internet quota for the week though so I'll have to watch it later.

robjohn

Darn! the site used to tell when someone else answered a question. I have been working on a problem that was answered 4 hours ago.

The same thing happened to me yesterday with an even greater loss of time.

Skullpatrol

@robjohn Maybe yours is a better answer ;-)

robjohn

00:45

@Skullpatrol In both cases, they were about equivalent.

Bill Dubuque

@robjohn I've seen some slow answer notifications, but 4 hours takes the cake. Which question?

robjohn

this one. Luckily, I checked before I posted.

Bill Dubuque

@robjohn I wonder if the fact that it has a bounty somehow affects the answer notifications...

robjohn

It might. I don't see why, but I don't see why not :-)

I have to take the dog for a walk. I will be back later.

Skullpatrol

@robjohn Happy walking...

@BillDubuque Are you willing to give me a serious answer to what the Bertrand Russell quote "mathematics may be defined as the subject in which we never know what we are talking about , nor whether what we are saying is true" means to a mathematician?

Paul Slevin

00:58

well everything we say relies on abunch of axioms which you can never prove

robjohn

I did the integration without W|A, so maybe I will post when I return from the park.

ttfn

Bill Dubuque

@Skullpatrol I'm not a philosopher, so I can't speak on BR's philosophical viewpoints. But presumably, at the crudest level, it refers to the hypothetico-deductive nature of mathematical reasoning.

Skullpatrol

Thanks @PaulSlevin @BillDubuque

That's what I thought it meant, but I needed a second or third learned opinion.

Bill Dubuque

Whitehead's remark may have been in reply to Hilbert's famous remark that 'one must be able to say "tables, chairs,
beer-mugs" each time in place of "points, lines, planes"'

Skullpatrol

@BillDubuque Didn't Euclid say that a "point" is that which has no part?

Bill Dubuque

01:11

@Skullpatrol See this encylopedia article on Whitehead for more.

Skullpatrol

@BillDubuque Thanks for the article

Here is where I found the quote.

At the bottom of the page.

Bill Dubuque

@Skullpatrol The point is there is on absolute universe where truth is decided, e.g. there is Euclidean or non-Euclidean geometry, Cantorian or non-Cantorian set theory, continuum hypothesis true or not? etc. Everything is hypothetico-deductive: if these axioms holds true then these theorems are consequences.

Skullpatrol

01:28

@BillDubuque Unlike your jokes where people never know what you are talking about, nor whether what you are saying is true ;-)

Bill Dubuque

@Skullpatrol Some said the same about infinitesimals before Abe Robinson.

Skullpatrol

@BillDubuque Seriously though: we never know what we are talking about because our propositions are stated as true for anything, nor whether what we are saying is true because the propositions are accepted as true.

Skullpatrol

02:28

. When a branch of mathematics is treated as a logical
system, it consists of four ingredients: undefined terms, defined terms, postulates and propositions. As
it is not possible to define everything, some terms in the system are undefined. For instance, in
geometry the concepts of point, line and plane are not defined. However defined terms are stated in
terms of the undefined ones. Thus, we don’t know what we’re talking about. Next, the system is based
on certain assumptions called postulates or axioms from which the theorems and propositions are

Skullpatrol

03:06

WHITEHEAD, A. N.
Universal Algebra (Cambridge, 1898), p. 12.

DEFINITIONS AND OBJECTS OF MATHEMATICS 7

127. Pure mathematics consists entirely of such assevera-
tions as that, if such and such a proposition is true of anything,
then such and such another proposition is true of that thing.
It is essential not to discuss whether the first proposition is
really true, and not to mention what the anything is of which
it is supposed to be true. ... If our hypothesis is about
anything and not about some one or more particular things, then

user19161

@Skullpatrol LOL

user19161

Wait, I just learnt about Kannapan's departure.

user19161

That means he will not be here when I reveal my secrets in a couple of years! Oh no!

Profile to be deleted.

@WillHunting I have changed my mind. : )

user19161

@Profiletobedeleted Hehe, good good.

user19161

03:16

@Profiletobedeleted By the way it is terribly hard to delete one's account here. One must email the SE team and edit one's about me to say "please delete me". Then after a few days of waiting when the SE team is sure you are not being rash they will do it for you!

Profile to be deleted.

@WillHunting Oh, I see. Do you know how to delete some of id's I use for logging in.

user19161

@Profiletobedeleted What do you mean?

Profile to be deleted.

@WillHunting I use email-1 and email-2 for logging into Math.SE and TeX.SE. I have used both these emails at both the places. Now, I'd no more want to use email-2. What should I do?

Skullpatrol

@WillHunting I have something to add to your LOL

user19161

@Profiletobedeleted OK from experience and common sense, I say this. Go to your google accounts for example and delete the site from there. Also go to your SE account and delete the email you use to log in, then log in with the email you want and this new email will auto appear in the field.

Profile to be deleted.

03:21

@WillHunting How would I do it on Google?

user19161

@Profiletobedeleted Revoke authorisation from one of the pages there? I never tried it. You check it out.

Profile to be deleted.

@WillHunting I find this relevant but cannot find such an option anywhere.

10

Q: Cannot remove logins anymore?

I just noticed that the login portion of my StackOverflow profile is different than it was back when I joined the site. It now lists some email addresses, and indicates I can sign in with any Google, Facebook, Yahoo or Stack Exchange account that lists the specified email addresses. Then it also...

user19161

@Profiletobedeleted By the way I CANNOT delete my youtube account unless I delete my google account!

Profile to be deleted.

Oh, I know. Google sucks when it comes to the way they handle User preferences over their accounts.

@WillHunting Can you tell me how do I get the pop up window shown there in that answer?

Skullpatrol

@BillDubuque I found the missing part of the quotation in the original.

user19161

03:26

@Profiletobedeleted Oh things have changed! That is new to me too!

Profile to be deleted.

:-)

Skullpatrol

@BillDubuque "Mathematics uses a notion which is not a constituent of the
propositions which it considers namely, the notion of truth."

David Wheeler

03:45

informally, mathematicians use "true" as a short-cut for: "consistent with wide-spread assumptions". this is by deliberate analogy with using deductive reasoning to add not-yet directly experienced facts to previously experienced facts.

Rajesh D

Hi @David @Skull

Skullpatrol

Hi @RajeshD

Rajesh D

What is that

ok

Skullpatrol

@DavidWheeler How does a mathematician "experience a fact"

David Wheeler

well not just mathematicians, i daresay...you go outside, it's raining....you get wet. these things are not surprising.

some of these types of deductions are used when children play games....even though a certain event has not happened yet, they know that the rules of the game make the event inevitable.

Skullpatrol

04:04

@DavidWheeler If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics.

David Wheeler

well, i suppose that depends on what you mean by "particular thing"

math uses logical formal systems, but it would be selling it short to regard it as a grand unified formal system itself

Skullpatrol

Particular = Specific

David Wheeler

well, for example, certainly statements about integers constitute mathematics. so the question is: are integers "specific enough"?

many mathematical statements are very narrow in scope

Skullpatrol

1=1 is a narrow mathematical statement

David Wheeler

but, you see, there are very few consistent statements you can make that apply to all things equally well

Skullpatrol

04:13

Is infinity=infinity a mathematical statement?

David Wheeler

in logic, you have the notion of a tautology, something that is "true no matter what" (note the quotes, there are certain caveats).

but tautologies are not, by and large, the focus of logical investigation. they are the sort of thing which does not generate much excitement.

Skullpatrol

Again we come back to "true" (no matter what)

David Wheeler

perhaps the greatest achievement of mathematics, is the conscious replacement of equality with equivalent

Skullpatrol

Is that the same as the conscious replacement of same with similar?

David Wheeler

on a certain level, the only thing you can say about an object using a strict definition of equality is something along the lines of: an object is itself (and only itself).

yes, similarity is a type of equivalence (given certain conditions).

Skullpatrol

04:18

Is infinity itself?

David Wheeler

the important thing about going from the "everyday" idea of similarity, to a "mathematical" one, is by being quite explicit about one's criterion for similarity.

i do not like to make sweeping statements about infinity....there are too many different hats worn on that head.

Skullpatrol

@DavidWheeler In this Bertrand Russell quote: "The whole of Mathematics consists in the organization of a series of aids to the imagination in the process of reasoning." He seems to be advocating memorization.

David Wheeler

Bertrand Russell is a well-respected philosopher and mathematician. but, again, i'd like to point out that there is not general agreement, even amongst mathematicians, as to what mathematics is, and is not.

Skullpatrol

@DavidWheeler What would you say mathematics is?

David Wheeler

people think about things, sometimes even very precisely and formally, that would not (without a very elastic notion of what mathematics is) be called by most people, mathematics.

i am not the most qualified person to answer that....but to me, mathematics is a process of making correspondences, a kind of "partial function" from data to structure

Skullpatrol

04:42

@DavidWheeler The above quote "The whole of Mathematics consists in the organization of a series of aids to the imagination in the process of reasoning." is not Russell but was said by WHITEHEAD, A. N.

David Wheeler

those are thought-provoking comments, but i would argue that taking them at face value misses the point.

Skullpatrol

mathematics may be defined as the science of successive substitutions of simpler concepts for more complex. . . . WHITE, WILLIAM F.

David Wheeler

that's not entirely accurate, either. often the direction goes the other way...for example, we start with natural numbers, then integers, build the field of fractions, and uses equivalence classes of rational cauchy sequences to create real numbers

by the time we consider real-valued functions of a real variable, we're a long way from an inductive construction of natural numbers based on the distinction between the empty set and a singleton set

Skullpatrol

04:58

@DavidWheeler It has been a pleasure chatting with you, thank you for your attention.

Benjamin Lim

06:42

Hey guys anyone know how to label a commutative diagram?

Daniil

Are you using TikZ/pgf?

Benjamin Lim

No

I'm using xy

xy matrix

$\begin{xy} \xymatrix@1{
0 \ar[r] & \ker(f') \ar[r]^{\bar{u}} \ar[d] & \ker(f) \ar[r]^{\bar{v}} \ar[d] & \ker(f'') \ar[d] \\
0 \ar[r] & M' \ar[r]^u \ar[d]^ {f'} & M \ar[r]^v \ar[d]^f &M''\ar[r] \ar[d]^{f''} &0 \\
0 \ar[r] & N' \ar[r]^{u'} \ar[d] & N \ar[r]^{v'} \ar[d] &N''\ar[r] \ar[d] &0 \\
& \coker(f') \ar[r] & \coker(f) \ar[r] & \coker(f'') \ar[r] & 0 }\end{xy}$

crap no commutative diagrams in chat???????????????????????????????

t.b.

what's the problem?

@BenjaminLim nope, no commutative diagrams at all

Benjamin Lim

How do I label a commutative diagram? Like I want to label it say "figure 1"

Daniil

Ah

@BenjaminLim you use \begin{figure} ... \end{figure}

\begin{figure}[h]
\input{eltokens1.tex}
\caption{$NPN_3$}
\label{fig:tokens1}
\end{figure}

Benjamin Lim

06:45

But now the commutative diagram is in [ \begin{xy} ... \end{xy} ]

Daniil

\caption is your label and label is a reference (so you can use \ref{fig:tokens1} later in the text)

Benjamin Lim

how to put a figure in there?

Daniil

@BenjaminLim pastebin.tlhiv.org/Tv0FqFx7

Also: en.wikibooks.org/wiki/LaTeX/Floats,_Figures_and_Captions

Benjamin Lim

@tb If you have an exact sequence that is too long

And you want to make it into two rows

xy gives me funny errors

\xymatrix{ 0 \ar[r] & \ker(f')\ar[r]^{\bar{u}} & \ker(f) \ar[r]^{\bar{v}} & \ker(f'') \ar[r]^d & \coker(f) \ar[r]^{\overline{u'}} & \coker(f') \ar[r]^{\overline{v'}} & \coker(f'') }

How do I split this up?

I want to do after \ker(f'') \ar[r]^d, put a \\ here to start a new line

but then errors are coming in

@Daniil thanks

Daniil

I haven't use xy tho, so I am not sure

t.b.

06:52

@TheChaz speaking of the devil and such things... I'm sure you'll like this: math.stackexchange.com/questions/120434/searching-for-formulas errrr... this

Benjamin Lim

@tb Do you wear glasses?

All this texing is making my eyes go

Daniil

I use Emacs for my TeXing, it's quite all right.

t.b.

@BenjaminLim No, I don't.

Benjamin Lim

Oh man

my power now is like 800

Matt N.

Morning.

t.b.

07:00

I have no idea what this could possibly mean. My power now is like 22.

Morning, Matt

Benjamin Lim

haha theo without my glasses I am like blind

Matt N.

And I'm just blind. But I wouldn't wear glasses : )

Maybe not entirely blind.

I was exaggerating. But here they want to make you wear glasses as soon as your eye sight isn't 100 % on both eyes.

@BenjaminLim What's your correction?

Benjamin Lim

800

astig 125

Daniil

I think glasses are kinda cute

t.b.

@Ben: What units do you use? It can't be dioptres.

Benjamin Lim

07:03

+8 dioptres then

Matt N.

Holy monkeys.

Benjamin Lim

why??

Matt N.

I have -0.25 on one eye and they want to make me wear glasses.

: D

Benjamin Lim

@MattN

Matt N.

@BenjaminLim Yes?

Benjamin Lim

07:06

Matt N.

@Daniil I think so too. I might try some time in the near future. I just think they're really uncomfortable.

Daniil

@BenjaminLim 8)

Benjamin Lim

That's an idea of how thick my glasses are

Matt N.

: )

Daniil

@MattN I'd imagine, maybe that's why so many people wear lenses.

Matt N.

07:08

@Daniil I guess. But that's not more comfortable.

t.b.

@MattN You're going to get used to it pretty quickly. With such a minor correction it might be quite irritating because the tiniest piece of dust on them will bother you...

Benjamin Lim

@MattN Wanna talk on skype?

Matt N.

@BenjaminLim Why? Do you have anything personal you'd like to discuss? I only just got up and unless there is something bothering you and you need someone to talk about I'd rather not.

Benjamin Lim

Ok no worries.

Kannappan has not been online today. Otherwise I would have talked to him.

Matt N.

So there is nothing bothering you?

Benjamin Lim

07:11

rien du tout.

Matt N.

Good : )

t.b.

I'm glad he changed his mind about leaving the site...

Benjamin Lim

@tb Qu'est-ce qui se passe?

Matt N.

Has he?

t.b.

@MattN apparently

Matt N.

07:12

@BenjaminLim Qu'est-ce que c'est que ça avec *le French all the time? : D

t.b.

'sch halt sone spliin

Benjamin Lim

@MattN Je peux parler 4 langues et un dialecte :D

Matt N.

@tb I know I've heard Swiss people use that word but I don't actually know what it means.

Benjamin Lim

What language is that???

Matt N.

@BenjaminLim Cool! Aussie, Mandarin, French, and then German maybe and Cantonese? Or something like that? Or what's the dialect?

@BenjaminLim It's Peasant.

Benjamin Lim

07:15

Aussie

French

Mandarin

Indonesian

Matt N.

Oh!

t.b.

@BenjaminLim Tu sais parler...

Benjamin Lim

@tb I forgot that savoir + verb = know how to (verb)

Matt N.

Mandarin is pretty cool.

I assume you can read and write as well.

Benjamin Lim

@MattN en.wikipedia.org/wiki/Hokkien

t.b.

07:16

@BenjaminLim while pouvoir + verb = be (physically) able to

Benjamin Lim

No my mandarin is very bad.

@tb I remember the french people always saying je peux parler....

Matt N.

I've not heard any French people in 15 years.

Benjamin Lim

@MattN Tu as quel âge?

Matt N.

In fact more, since my second French teacher in high school wasn't French and had a foreign accent.

Benjamin Lim

@MattN Are you serious with AM or what?

Very soon you will be in deep water

Matt N.

07:19

I don't have a choice.

t.b.

@MattN Idiosyncrasy

Benjamin Lim

What is this?

Matt N.

@tb That doesn't make sense.

Benjamin Lim

@MattN Do AM or die mirin'

t.b.

@MattN Yes, seriously. Yes it does.

Matt N.

07:22

@tb Want to be booked in for an argument, or what?

Benjamin Lim

@MattN facebook.com/pages/Get-Ripped-or-Die-Mirin/246326825398172

Matt N.

@BenjaminLim I choose mirin.

Benjamin Lim

Do AM or die mirin'

t.b.

@MattN No, I'm here for a hammer treatment.

Matt N.

@tb I see. You want to get hammered...

t.b.

07:24

waaah!

Matt N.

@BenjaminLim I don't get it.

Benjamin Lim

@MattN I mean do AM or die admiring others do it.

Matt N.

: )

@tb Is your bathroom fixed?

@BenjaminLim I thought I could choose mirin.

t.b.

@MattN no, they didn't have a shade that fits... It's gonna be very comfy with naked neon light in my bathroom.

Benjamin Lim

No @MattN Mirin' = admiring

Matt N.

07:26

I know : )

Benjamin Lim

It's a quote from body builders: Get ripped or die mirin'.

Matt N.

Do you do body building?

Benjamin Lim

@MattN From the picture above what do you think?

t.b.

There are two things in basic math education that I'll never understand: what's the difference between induction and complete induction and what's the difference between a proof by contradiction and a proof by contrapositive? </rant>

Benjamin Lim

@tb Hey if we have a map $u': N' \rightarrow N$

Matt N.

07:29

@BenjaminLim Well hard to tell probably not. : )

Benjamin Lim

How do we get the induced map $\overline{u'} : \operatorname{Coker}(f') \rightarrow \operatorname{Coker}(f)$?

@MattN Nope. No time for that.

Matt N.

@tb Proof by contradiction is if you want to prove A implies B then you assume A and not B and make a contradiction. Contrapositive is if you want to prove A implies B you show not B implies not A.

t.b.

@BenjaminLim the map $N' \to N \to \operatorname{Coker}{(f)}$ is zero, hence it factors over the cokernel of $f'$.

@MattN which is the same thing, isn't it?

Daniil

I think I should go to classes and eat in the uni's cafeteria

Matt N.

@tb I'm not sure. I don't see how there is any contradiction involved in a proof by contraposition.

t.b.

07:32

@MattN You show that you can't have A if you have not B, so you'll arrive at a contradiction.

Matt N.

But seeing as you've probably been thinking about this for 20 years you probably know better.

@tb I don't see how showing that something can't be is a contradiction.

t.b.

No, it's just a silly distinction that I find utterly confusing and unhelpful. It doesn't matter where you get the contradiction...

Benjamin Lim

@tb How is the map zero we are quotiening out by image of $f$

anon

Maybe proofs by contradiction prove that a statement is true by assuming otherwise and deriving a contradiction, and proofs by contraposition prove a statement is false by proving the negation of a logical consequence of it?

t.b.

@MattN You want to conclude that A implies B after all

@BenjaminLim sorry I should have started at $M'$.

Matt N.

07:35

@tb Or not B implies not A. Without contradiction.

anon

I think we're confusing the desire to utilize implications to prove or disprove statements with desiring to prove the implications themselves.

t.b.

@MattN but you can't do that without using that not(not A) <-> A

anon

Eh, nevermind.

Matt N.

What anon said.

Benjamin Lim

@tb So you mean that the map $M' \rightarrow N \rightarrow \operatorname{coker} (f)$ is zero?

Matt N.

07:38

Is it just me or is this site down: amazon.co.uk

Benjamin Lim

it's working

Matt N.

Thanks.

Benjamin Lim

im going for dinner. WIll be back

t.b.

@MattN It works for me, but apparently there's some trouble: downforeveryoneorjustme.com/http://www.amazon.co.uk

@BenjaminLim got it?

(and yes)

Benjamin Lim

no

Matt N.

07:41

@tb Thanks. That link doesn't work either. Looks like the internet is down. : )

Hi Kannappan.

Benjamin Lim

@tb Ok yeah if you go via $M$ then yes the map $M' \rightarrow M \rightarrow N \rightarrow \operatorname{coker} (f)$ is zero

t.b.

@BenjaminLim Go $M ' \to M \to N \to \operatorname{Coker}{f}$. Note that $M \to N \to \operatorname{Coker}{f}$ is already zero.

@MattN strange. Works for me...

Benjamin Lim

So how does this induce a map from one cokernel into another?

oh wait

t.b.

@BenjaminLim by definition of the cokernel of $f':M'\to N'$. If you have a map $g: N' \to X$ such that $gf' = 0$ then $g$ factors over the cokernel of $f'$.

Matt N.

@tb I suspect something to do with name servers.

Benjamin Lim

07:46

@tb Do you mean to say that anything in the cokernel of $f'$ we pull it into $N'$, map it to $N$ and then into the cokernel of $f$?

t.b.

@BenjaminLim Now take as $g$ the map $N' \to N \to \operatorname{Coker}{(f)}$ note that $gf'$ is the same as $M' \to M \to N \to \operatorname{Coker}{(f)}$ which is zero.

Benjamin Lim

Yeah one way you went right down down and the other down right down

t.b.

@BenjaminLim The cokernel of $f'$ is given by the canonical projection $N \to N/\operatorname{Im}(f')$. In order for $g:N \to X$ to factor over this, it needs to annihilate the image of $f$, which is the same as saying that the composition $gf' = 0$.

Kannappan Sampath

Hi all of you!

t.b.

@BenjaminLim exactly. And because you have a commutative square $M'MN'N$ those two maps are the same...

Matt N.

07:49

Hi again.

t.b.

@KannappanSampath Hi!

Benjamin Lim

@KannappanSampath What on earth was all the drama?

Kannappan Sampath

I had the monkeys again. : ( They visit me frequently.

Benjamin Lim

@tb So the map $\overline{u'}$ works by first taking $x$ in the cokernel of $f'$, looking at it's preimage in $N'$, mapping to N and then to cokernel of $f$.

Matt N.

@KannappanSampath Get a dog big enough to eat them. (Like e.g. an alsatian or Rottweiler) Problem solved.

Kannappan Sampath

07:51

@BenjaminLim Well, It was so much of a trauma and I think my dropping in here the second time made all the change in my decision. Several of you talked me in.

Benjamin Lim

@KannappanSampath What was a trauma?

Kannappan Sampath

@BenjaminLim Well, someone randomly downvotes saying I wrote down the full answer to a HW problem while there is another one that is right up there that derives from the hint and completes the problem.

Benjamin Lim

@KannappanSampath Have you seen this? meta.math.stackexchange.com/questions/3574/…

t.b.

@BenjaminLim I'd rather say by $[x] \mapsto [u'(x)]$ where $[x] = x + \operatorname{Im}{f'}$ and $[u'(x)] = u'(x) + \operatorname{Im}{f'}$. But yes choose one pre-image, map it with $u'$ and go to the quotient.

Kannappan Sampath

And, that guy leaves a note. You write answers and I'd downvote leaving some or the other comment. Why should I write it then?

t.b.

07:53

@BenjaminLim you ran into a troll...

(sorry, not Kannappan, I haven't seen what happened to you).

Benjamin Lim

@tb "It can't be problem for mathematician"

Kannappan Sampath

Well, it was almost a similar case here.

Matt N.

But it does look like a problem with mathematician...

Kannappan Sampath

There were three different occasions in which the same user downvoted with the same comment.

(Three With me.)

Benjamin Lim

@KannappanSampath Come on man. You need to be psychologically tough in your life.

"He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred. - Dhammapada 3

t.b.

07:58

@KannappanSampath so, file him under eejit. As far as I can tell he qualifies.

Matt N.

@KannappanSampath Who? If they down vote out of spite you can start a meta thread or talk to the mods.

Kannappan Sampath

I find it difficult to take. There has been exactly one instance my answer was downvoted with a very genuine reason it was wrong.

Transcript for

$Mathematics$ Mathematics