Mathematics - 2013-06-11 (page 2 of 3)

Lord_Farin

11:14

@exitingcorpse Rest assured that I am not offended by your misinterpretation. It happens to me a lot, because I'm (at times vehemently) opposing the communis opinio on this matter.

Gigili

@BenjaLim: Hi, can you see deleted answers?

Umm

Peter Tamaroff

@Gigili You can do that with high rep.

Now I'm off to uni.

BenjaLim

11:35

@Gigili yea.

exitingcorpse

@Lord_Farin i'm glad you have a thick skin, it was wrong of me to be so cynical (especially when i didn't even ask you first about it).

skullpatrol

I believe "thick skins" should be required attire :-)

exitingcorpse

i worked as a cleaner in a bakery for a while, and had to do lots of washing up with my arms half buried in industrial chemicals

it made the skin on my forearms so thin that even scratching myself would cause bleeding

Lord_Farin

@exitingcorpse Sadly, the human race has as of yet been unable to stop making errors. At least, it is good to see that you display to have taken the nontrivial hurdle of being able to admit you make mistakes at times. :)

@exitingcorpse That sounds awful.

exitingcorpse

if you ever see me trying to split a bill, you'll see just how prone to errors i am!

the obvious solution would be to wear washing up gloves, but they were too short, so the water would just get in anyway

Bandeira Gustavo

11:48

@exitingcorpse Oh, you're "if you are on a mac, there's a program called 'grapher', it's perfect when you don't want to think!" guy.

exitingcorpse

hah, will this be my claim to fame

Bandeira Gustavo

@exitingcorpse Is it a metaphor? Why did you work there?

exitingcorpse

nah, it's an application bundled with os x

Bandeira Gustavo

@exitingcorpse I'm replying to another message.

exitingcorpse

oh woops

i worked there when i was in school

3 hours weekdays, 8 hours saturday woooo

Bandeira Gustavo

11:54

I have the slight impression the math students are mostly from families of good wealth and education.

exitingcorpse

i grew up on a cattle farm with separated parents, i'm the first member of my family to go to university

it varies i guess

Bandeira Gustavo

I also grew up in a farm.

exitingcorpse

in it?

Bandeira Gustavo

In and on.

You know, sometimes you just enter the house. Sometimes you get out.

exitingcorpse

haha

Bandeira Gustavo

11:56

@exitingcorpse If you're the first of the familiy to go to university, why mathematics?

exitingcorpse

i'm basically useless at everything, just slightly less useless at mathematics than other things

Bandeira Gustavo

In Brazil, Programming, medicine, law and engineering are the choices when you want to get rich.

exitingcorpse

BRIC represent represent

Bandeira Gustavo

I was thinking that if you were the first one to go to the uni, your family would force you to a "wealth generator course".

exitingcorpse

haha, i had more of a laissez-faire upbringing

they're basically just happy i'm not doing heroin

2

Bandeira Gustavo

11:59

I'm not sure, but I guess mathematicians are internacionally poor (except for finance, I guess)

@exitingcorpse XD

exitingcorpse

i don't think i've got the soul (or lack of it) for finance

Bandeira Gustavo

Same to me. I'll just work and make some investments in stocks.

Lord_Farin

@exitingcorpse Same here.

exitingcorpse

both my parents own their own houses, my dad lives off an air force disability pension, my mum still works a bit

so acquiring more capital isn't really a huge drive for them

Lord_Farin

In fact, my lack of care for money probably indicates that I'll (try to) stick to academia.

Bandeira Gustavo

12:01

@Lord_Farin I don't know if you feel the same, but the idea of working with finance seems boring.

You invent ways of making rich people richer. Meanwhile mankind is in the same putrid state it ever was.

2

exitingcorpse

i think the work can be very challenging, but the hours seem just insane to me

Lord_Farin

@exitingcorpse Good. Too many people become total jerks when it is a huge drive for them.

@BandeiraGustavo +1. :)

exitingcorpse

and of course, i have the good fortune of being australian

it's not called "the lucky country" for nothing

Bandeira Gustavo

@exitingcorpse I remember a meme.

@exitingcorpse This one.

exitingcorpse

ahahaha

our country is always at least one of: on fire, in drought, ravaged by a tropical storm

Lord_Farin

12:04

@BandeiraGustavo What about Mexico?

Bandeira Gustavo

A friend of mine told me something (don't know if he was joking), that in australia, everything is poisonous.

exitingcorpse

i remember reading an article in the economist once that said the drug cartels in mexico drop its GDP by at least 1%

Bandeira Gustavo

Even a cute little cat is poisonous in australia.

exitingcorpse

hah, a good example is mushroom hunting. apparently in australia it is very dangerous, as the mushrooms can look very much like european ones, but be poisonous

Bandeira Gustavo

@Lord_Farin I guess it's a neutral zone - Perhaps we start there, then the difficulty menu appear in front of us and when we choose, we go from Mexico to the chosen country.

exitingcorpse

12:05

our cats went extinct :( independentaustralia.net/Wordpress/wp-content/uploads/2012/04/…

Gigili

@PeterTamaroff Even a two-year old child knows that. I asked him to show me what the deleted answer is. It's not difficult to get, but neither you nor him get the point. Interesting.

Lord_Farin

@Gigili Did you run out of politeness for the day?

4

skullpatrol

:D

Bandeira Gustavo

@Lord_Farin EVEN A TWO-YEAR OLD CHILD NOTICED THAT!

XD

Gigili

@Lord_Farin I didn't @ mention you anywhere, as far as I recall. The other people are able to respond on their own.

skullpatrol

12:08

Two two-year olds who don't get the point don't add up to one four-year old who does.

Bandeira Gustavo

What about $\sqrt{-1}$-year old children?

I always forget that the plural is children.

Lord_Farin

@BandeiraGustavo How did you know that I was going to comment on that mistake? :D

skullpatrol

Are you imagining what it is like to have children?

Bandeira Gustavo

@Lord_Farin I always forget that. One day I wanted to say $\text{I'm a child}$, I said $\text{I am a children}$.

$\text{I AM A LOT OF KIDS!}$

exitingcorpse

"When my mother was pregnant with me, they did an ultrasound and found she was having twins. When they did another ultrasound a few weeks later, they discovered that I had adsorbed the other fetus. Do I regret this? No, I believe his tissue has made me stronger. I now have the strength of a grown man and a little baby."

Bandeira Gustavo

12:13

@Lord_Farin Also, first I remembered that it's wrong. When I corrected, I thougt: "I guess Farin os Skull were almost typing their corrections to that" XD

@exitingcorpse Aphex Twin?

exitingcorpse

dwight schrute

Lord_Farin

What a coincidence. Right after our dear friend @Gigili left, I incurred a downvote on one of my questions.

Bandeira Gustavo

@Lord_Farin Can I make a confesion?

(It wasn't me who downvoted, it's about another thing).

Lord_Farin

@BandeiraGustavo Naturally.

Bandeira Gustavo

@Lord_Farin I imagined this...

skullpatrol

12:20

@BandeiraGustavo How could you downvote my pal Lordy?

Lord_Farin

@BandeiraGustavo I'm afraid I don't get it.

Bandeira Gustavo

@Lord_Farin It's a meme, do you know the original one?

@Lord_Farin I imagined you saying that to Gigili. xD

Lord_Farin

@BandeiraGustavo I know barely any memes.

Bandeira Gustavo

@skullpatrol I didn't do that.

skullpatrol

(-:

Bandeira Gustavo

12:22

Yes. I said I didn't downvote him.

skullpatrol

Ok, sorry I meant gigili

@Gigili How could you downvote my pal Lordy?

Lord_Farin

Allow me to continue working on my thesis. Should anyone of you run out of ideas on what to do, join the Crusade! :)

Bye all.

skullpatrol

later

Bandeira Gustavo

@skullpatrol She'll come back, say mean words for you and your family, get pissed and then GTFO. Then Matt Nott Madd Kiddo will come and say: "Oh, another one went away because of skullpatrol, we gonna cry-ay-ay - PLIS, do something! :"(

Be careful, bro.

skullpatrol

Thanks for the heads up :-)

Bandeira Gustavo

12:31

@skullpatrol BTW, there are two links there. There's another link in the PLIS. =D

@skullpatrol This reminded me of you. "There's a serious accusation that I'm making users go away..."

skullpatrol

@BandeiraGustavo Yeah, nice double link pal :-) I'll just tell'em all you want a piece of me?

Bandeira Gustavo

XD

skullpatrol

13:10

Hey @amWhy you want a piece of me?

amWhy

@skullpatrol What? Say again... :-)

skullpatrol

@amWhy It's a joke, just like Britney :D

amWhy

@skullpatrol hahahaha...Just played it...(the video)...

@skullpatrol (She's) a joke, yes indeed.

How are you, @skull ?

skullpatrol

@amWhy Fine thanks, how are you?

amWhy

@skullpatrol hmmmm.... Official word, I'm fine (I think?)

skullpatrol

13:24

Hey @JayeshBadwaik you want a piece of me?

exitingcorpse

whoa at this question math.stackexchange.com/questions/417439/…

robjohn

@Gigili where?

exitingcorpse

at first i was impressed that they typed it all out, until i noticed these kind of sentences "PART 3 5 X 4 = 20 MARKS IN THE SECTION, SOLVE ANY FOUR OF YOUR CHOICE 1. "

skullpatrol

Are questions like that allowed?

exitingcorpse

my guess is they've just straightup copied the pdf or whatever and pasted it into the box

amWhy

13:32

Shake head, this post, shake head again, sigh...

skullpatrol

Does that make it plagiarism?

exitingcorpse

new lows in readability wooo

skullpatrol

chat.stackexchange.com/transcript/message/9840303#9840303 @amWhy

amWhy

@skull Ahhhhh....missed it! I thought it was just me. It got an upvote?

exitingcorpse

14:23

i can't believe that until this day, i did not know the \mid command

my life has been a sham

M.B.

15:31

Uhm, if I have a surjective simplicial map between simplicial complexes i.e. every simplex in K' is the image of a simplex K under f: K -> K' for f simplicial map, is f_* surjective in homology?

(finite simplicial complexes)

exitingcorpse

if K is a disjoint union of four triangles, and K' is a tetrahedron, can't you map the triangles to the faces?

(or start with a disjoint union of subdivided simplices or whatever, i'm used to delta complexes)

basically start with a K that has trivial homology, and a K' that doesn't

M.B.

But then it wouldn't be surjective?

or, sorry.

you are correct, thanks

exitingcorpse

i'm just happy to finally be able to answer a question that's above calculus level!

M.B.

hehe.

blob

16:13

hi

Lord_Farin

@blob Hello there.

blob

hi Lord_Farin

Lord_Farin

@blob How are you doing today?

blob

Now I am studying probability calculus

and you?

@Lord_Farin

Lord_Farin

@blob Working on my thesis, as usual.

blob

16:22

@Lord_Farin what is the topic of your thesis

Lord_Farin

@blob Logic in category theory, with some applications.

blob

it seems complex

exitingcorpse

@Lord_Farin do you know any topos stuff?

Lord_Farin

@blob I guess it is. It has taken me quite a bit of time to get familiar with it.

@exitingcorpse My entire thesis revolves around them (specifically, Grothendieck topoi).

exitingcorpse

ah cool. are you familiar with Robert Goldblatt's book on it? i went to the library the other day and they didn't have the book i was after, i saw the name (i recognise it from his book on nonstandard analysis)

it's got one of the most sinfully ugly covers i've seen in maths

this is another possible contender fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-prn2/…

Lord_Farin

16:27

@exitingcorpse I have that book (presuming you mean "Topoi - the categorial analysis of logic").

exitingcorpse

yep, that's the one

BenjaLim

@exitingcorpse Hey

exitingcorpse

hi

BenjaLim

@exitingcorpse New to math.se?

M.B.

@Lord_Farin: what does "Farin" mean?

exitingcorpse

16:31

yeah, finally signed up the other day

BenjaLim

are you a grad student by any chance?

Lord_Farin

@M.B. tolkiengateway.net/wiki/Farin.

exitingcorpse

notionally, i'm here in budapest but i've had to take a break (woo mental illness)

BenjaLim

@exitingcorpse Have you had any experience with Borel weil bott? I have a question about references

exitingcorpse

ask me no questions, i'll tell no Lies

that was wittier in my head

(i don't know any lie stuff)

BenjaLim

16:34

@exitingcorpse There is something wrong with my simplicial structure of $S^1$ here: math.stackexchange.com/a/411877/38268

I don't know why I have to reverse the orientation on one of the $1$ - simplices

exitingcorpse

the mspaint diagram you mean?

amWhy

17:13

Nice post on meta, @exitingcorpse I appreciate your desire to see more gender-neutrality on main!

exitingcorpse

Thank you sir! (i kid, i kid)

it was feeling a little lonely on that thread

amWhy

@exitingcorpse Maybe I'll post an answer. I get tired of how dismissive users are about any concern to address gender/gender neutrality on the site.

Babak S.

@amWhy: I am too. :-(

amWhy

@BabakS. Hi, Babak!! :-)

exitingcorpse

i've seen a lot worse things in maths departments, but for this site it's the only hurdle i can think of

Babak S.

17:17

@amWhy: ;-) Hiii

somaye

hi

@BabakS. how are you?

Bandeira Gustavo

@amWhy Did you see my question?

@somaye Hello'

somaye

@BandeiraGustavo hello

@BandeiraGustavo what are you doing?

i was going out of room i come back for you

Bandeira Gustavo

@somaye well. Thinking about waking up. Bed is so confortable.

Lord_Farin

@amWhy I would like to stress that I am not dismissive of gender neutrality concerns.

somaye

17:27

@BandeiraGustavo you want to tell that you just got up?

Lord_Farin

@BandeiraGustavo Siesta?

Bandeira Gustavo

@amWhy It's a comment I posted in your answer to my question on biconditional plots.

amWhy

@BandeiraGustavo No, not yet...here? on chat?

Bandeira Gustavo

@somaye yep.

somaye

@BandeiraGustavo you are busy here

i got to go

but come back after 1 hour

Bandeira Gustavo

17:29

@Lord_Farin Kinda. :-P

@somaye oky. Ill be on ym.

amWhy

@Lord_Farin Got it. Glad to hear. The post just struck me as somewhat dismissive of the OP's concern, etc. No offense taken!!

somaye

@BandeiraGustavo ok :)

Lord_Farin

@amWhy Your last comment to my answer indicates that we think alike. Such seems to happen a lot lately. :)

@amWhy Hm, I hope you didn't read the comment from which it was distilled... // I did actually attempt (in parenthetical comments) to indicate that it is not the issue that I object to, but the method. Apparently, I didn't fully succeed.

amWhy

@Lord_Farin Yes, I do not think "imposing" reform on others is the route to go...I try to lead by example, so to speak, or comment, to bring attention to the matter when I see it, and usually, the author of a comment or answer that I address in a comment is very receptive/acknowledging.

Jayesh Badwaik

@BandeiraGustavo You CAN do good things in finance. But then, very few people do it, so there's that.

amWhy

17:39

..I do wonder, though, for those who are dismissive of the issue, of addressing such a user, say it happens to be "Bruce Manford" that is dismissive. countering with something like "When Bruce stated____________she meant...", or "Bruce's comment upsets me: her use of _________________" :)

exitingcorpse

that's a pretty interesting idea @amWhy

amWhy

@BandeiraGustavo Replied. Let me know if my reply makes sense.

Bandeira Gustavo

@Jayesh But those who do good things in finance become poorer than mathematicians, isn't it?

Jayesh Badwaik

@BandeiraGustavo Not necessarily... You can earn well...

amWhy

@exitingcorpse "turn the tables, so to speak"

Bandeira Gustavo

17:42

@amWhy Yep.

Jayesh Badwaik

@Lord_Farin :-)

Lord_Farin

@JayeshBadwaik :)

Bandeira Gustavo

@Lord_Farin childs!

Jayesh Badwaik

@amWhy I am not very sure. Recently, I have read books by many authors who by default use "she" instead of "he" and I have never even noticed it. And if you were to pass a directive saying that, in case the gender is not known, by default use "she", I would not care. And yes, edits only on gender neutrality shift focus away from more important edits as Lord Farin said. And there is already too much information to be processed on MSE.

Bandeira Gustavo

@amWhy do you remember that there was one guy who answered about a mac app called grapher? He's here in the chat, it's @exitingcorpse

Lord_Farin

17:46

@JayeshBadwaik I think the "she" default is pedantic and liable to hypocrisy.

exitingcorpse

such a directive would be fine! it's more about "not seeing yourself" in the things you read

Jayesh Badwaik

@exitingcorpse I do not understand... "Not seeing yourself"? But then that is how sometimes you visualize your reading. You put yourself in the shoes of people who post the question and then imagine how you would solve it.

exitingcorpse

well, an analogous example (text: books :: actors : movies) is the general male dominance in films. you might like to read about the bechdel test, for instance

Bandeira Gustavo

@Jayesh What if they're not using shoes? This is a deep question.

They could be using this, for example.

@exitingcorpse Uh, male dominator! Whip me please.

Will Jagy

18:16

@BabakS., in case you are still here, does it seem possible to post in Farsi here on Chat, or at least mix English and farsi? I have seen other languages/alphabets here, some going right to left...

0x4A4D

18:29

@amWhy "contaminatorics" - so that's why I sometimes feel dirty after counting money...

Will Jagy

@somaye, if you return this evening, could you please see whether you are able to type anything here in Chat in the Persian alphabet?

Bandeira Gustavo

@WillJagy Charlie says hello.

Will Jagy

18:44

@BandeiraGustavo, Say hello to Charlie. She has my email address, but not everyone likes email.

anon

so, charlie left chat?

somaye

سلام

همگی خوب هستید؟

خوشحال هستید؟

Will Jagy

@somaye excellent! And these are real phrases in Persian and make sense and all?

somaye

yes

بله

Will Jagy

@somaye, very good, that gives some extra options.

somaye

18:50

@WillJagy :)

Will Jagy

@somaye, alright, I think two of them have question marks.

amWhy

@0x4A4D When did you change gravatars and your user?

somaye

@WillJagy همگی خوب هستید =are you fine ?

@WillJagy خوشحال هستید؟=are you happy?

0x4A4D

@amWhy A few weeks ago, in that other site I hang around in. Since I need that to be my main account for modly purposes... here we are.

amWhy

I've seen you, but didn't "make the connection" ... but noted I hadn't seen J.M. for awhile...So good, now I can get A.J.M. back? ;-)

Will Jagy

18:58

@somaye, I get it, the second and third lines. Easy answers, I am fine but not usually happy. The fine part will be tested this week, twice a year I get checked for too much cholesterol and the possibility of diabetes. So, this week I go to the place and they take a little blood, send that to a medical/chemistry laboratory. Then on June 19 I see my medical doctor and she tells me how i am doing.

0x4A4D

@amWhy Well, I still have that name in math's main site, but don't let me stop ya. :)

Will Jagy

@anon, Charlie told me in general terms that she was fed up with Chat. She does not seem to like email either, just individual chat features as part of Facebook or Gmail or the like.

somaye

@WillJagy then it means that you must care more about what you eating

amWhy

@0x4A4D Just kidding...I've grown attached to "amWhy" ;-)

Will Jagy

@somaye, well, yes. The first tests, in 2007, were very bad. Then I completely changed my diet, on advice from a friend who is a gastroenterologist. I think the thing that helps the most is the fish oil pills. I take five pills each morning, each 1100mg (big), providing 300 mg EPA and 200 mg DHA. I also take three pills of flaxseed oil, each providing 540 mg of ALA. These are the three important "Omega-3" fatty acids that Americans do not get enough of.

Omega-3 fatty acid

Omega-3 fatty acids (also called ω−3 fatty acids or n−3 fatty acids) refers to a group of three fats called ALA (found in plant oils), EPA, and DHA (both commonly found in marine oils). Common sources of animal omega–3 EPA and DHA fatty acids include fish oils, algal oil, egg oil, squid oils, krill oil and some plant oils contain the omega 3 ALA fatty acid such as seabuckthorn seed and berry oils, flaxseed oil, Sacha Inchi oil, Echium oil, and hemp oil. Omega-3 fatty acids are vital for normal metabolism but some of the potential health benefits of supplementation are controversial. Omeg...

somaye

19:10

@WillJagy you are better now :) i is too hard for me that i do not eat some think

as candy and oil food

you do it!

Will Jagy

@somaye, you are young, so your doctors are not going to pressure you too much, yet. After age 50 they get very aggressive. It is better to eat actual fish, but I really, really, really hate that fishy taste. So, I take the pills instead. I had difficulty digesting the pills, it took more than three years to gradually increase the dosage to the current level.

somaye

@WillJagy i must teach you how i cook fish then you will like it

Will Jagy

@somaye, I am a poor cook. You will need to visit California and cook it for me.

somaye

@WillJagy Ok But i am a good teacher you can learn

:)

Will Jagy

@somaye, alright, but a recipe is a long thing for a Chat window. Maybe you could write a (short) lesson and email me that. I do not promise to put in much effort, though. My mother sometimes cooked swordfish I never liked it.

somaye

19:19

@WillJagy :) i still am eating my mom food

but i like cooking

Will Jagy

@somaye is your mother a good cook?

somaye

but i 'll send for you

@WillJagy She is great

for cooking

@WillJagy some fish food and some persain food

good/

Will Jagy

@somaye, John Wordsworth, who was called Old John before, has been putting pictures of barbecue on Facebook, Persian style, on an outdoor babecue (fire) grill. I will try to copy the names of the dishes
John: I now follow the Iranians when it comes to barbecuing food. I reckon they have several thousand years experience
John: Planning a barbecue tonight ... with kabob koobideh and shish tawook - hope it all works out well!

somaye

@WillJagy fesenjun do you hear it's name?

fesenjun is very compelete food

Will Jagy

@somaye probably this: en.wikipedia.org/wiki/Fesenj%C4%81n

somaye

19:31

@WillJagy yes i like it too much

Will Jagy

@somaye, I will see if I can find it somewhere. Meanwhile, Charlie is on email complaining that I take too long to answer, which is why she prefers chat. i am trying to explain that sometimes i do not really want to explain why there is a delay, at least not publically. So it seems better to me to use a facility where such explanantions are not necessary. I will be back in ten minutes or so...

Ethan

19:50

@WillJagy what type of logic deals with like variables in proposition

Like statements of the form $x$ has $y$ cars today

somaye

20:02

@WillJagy i got sleep now

@WillJagy and @BandeiraGustavo and other friends good night:)

Will Jagy

@somaye good night

Bandeira Gustavo

@somaye im gonna eat brb

exitingcorpse

20:36

@amWhy 77 is not a prime

or err, it's only a grothendieck prime

amWhy

I was thinking of G being abelian (jumped to that conclusion), so $\gcd(7, 11) = 1$: therefore G is cyclic...flip flopped assumptions!

exitingcorpse

@amwhy hah wow so reading comprehension is not really My Thing

sorry about that

amWhy

@exitingcorpse Don't worry...I've been second-guessing myself a lot lately, and certainly did when I read your comment, so rushed to delete my answer...all is good...I'd rather be corrected "wrongly" than not corrected, when I'm wrong!

exitingcorpse

even the best make mistakes, i made a mistake, therefore i am the best

let's not think too critically about that sentence

Dohleman

Preparing for my last math test ever to be taken (unless I declare a math minor...)! How exciting! It's at 8:00AM tomorrow morning.

DanZimm

20:55

is anyone thats good at topology around?

Julian Kuelshammer

@DanZimm depends on the level

DanZimm

@JulianKuelshammer how come $\{0\}$ is open?

Julian Kuelshammer

open is a relative thing, open in which ambient space

DanZimm

open to $\mathbb{R}^n$, sorry

John Wordsworth

Hmm - which topology on $\mathbb{R}^n$ are we talking about?

DanZimm

21:02

from what I understand, it isn't open (I'm using the 'normal') topology

@JohnWordsworth heh got to it before I got to type enter. The family of all open intervals

Julian Kuelshammer

in the standard topology it is a non-open closed set

DanZimm

@JulianKuelshammer ok just making sure

can someone explain to me this then? math.stackexchange.com/questions/417851/…

John Wordsworth

@DanZimm But you need to be a bit careful: the family of all open intervals is not a topology - but it does generate a topology

DanZimm

@JohnWordsworth ah ok, the topology is the pair of the family and the space itself, right?

John Wordsworth

a topology is really a collection of sets - the open sets

Julian Kuelshammer

21:05

@DanZimm in this case you are not talking about $\mathbb{R}^n$ as ambient space, but about $X$ equipped with the subspace topology from $\mathbb{R}^n$.

DanZimm

@JulianKuelshammer ah ok!

makes sense now

John Wordsworth

the family of open intervals is not a topology since the union of 2 intervals is not always an interval

DanZimm

@JohnWordsworth ok, I'm sorry, a bit new to topology and the such, haven't read up on the rigorous definitions of a topological space

John Wordsworth

@DanZimm No problem. But I would suggest that a rigorous definition is probably a good place to start

DanZimm

@JohnWordsworth yea, all the knowledge I know is from the basic topology chapter in baby rudin

it introduces metric spaces and the such

John Wordsworth

21:08

That is probably rigorous enough :)

DanZimm

@JohnWordsworth he doesn't mention a topological space anywhere in that chapter

so my knowledge is simply from the inter webs at this point

John Wordsworth

Ah - I see - I am not very familiar with baby Rudin, but I reckon you could master the essentials of a rigorous definition for topological spaces in half an hour from an introduction to topology.
I mananged to do so - and I am not a a topologist (just use it sometimes)

DanZimm

@JulianKuelshammer so we are considering $\{0\}$ open with respect to $X$ in that case? or am I still misunderstanding and I need to go read more? :P

exitingcorpse

formally, it's with respect to X and its induced topology

DanZimm

ok

exitingcorpse

21:13

i think the two most basic notions to get acclimated with is "sets are not doors" (they can be both open and closed) and the definition (or characterisation, depending on your axiomitisation) of continuity in terms of "closeness"

DanZimm

@exitingcorpse I've never heard the second thing you said

exitingcorpse

basically there's a version of the definition (equivalent, of course) of a topological space in terms of a "closure operator"

then a continuous function, in this formalism, says "a continuous map maps close points to close points"

nerdy

Does anyone have a clue about linear function of more than 1 variable ?

For example, take f(x,y)

what does linearity mean for f ?

Can i only talk, f is linear regarding some variable ? Or can i talk f is generally linear in that case ?

exitingcorpse

the usual definition takes as a basic concept "open sets", and says that "the preimage of an open set is open". a lot of people get confused why it isn't the other way around

@nerdy you can talk about both. f(x,y) would have the form f(x,y) = ax + by, where a and b are constants

nerdy

in that case f would be linear for what variables ?

for both x and y ?

exitingcorpse

21:18

well, if it just says "linear" then what i've written would probably be the usual interpretation

"linear in x" would mean something like f(x,y) = ax + g(y), where g is some other function

nerdy

could it be

a(y)x + g(y)

like, f(x,y) = y²x + 3y

linear for x

exitingcorpse

woops, yep

nerdy

then, how would we test it ?

i mean, f(x,y) is linear for x if

f(c1x1 + c2x2,y) = c1f(x1,y) + c2f(x2,y) ?

maybe ?

but then a(y)x + g(y) wouldnt satisfy it

anorton

I just need 3 more rep to cap today! :) (this will be my first time to cap, if I do so!)

(In other news, so much for trying to quit the site.)

nerdy

f(c1x1 + c2x2,y) = f(c1x1,y) + f(c2x2,y) would'nt satisfy it as well

exitingcorpse

21:22

urgh, i am clearly very drunk, sorry

nerdy

exitingcorpse, the problem is that my differnetial equastion book

exitingcorpse

drop the g(y) and it's fine

nerdy

is saying the same thing

i know

my diff equation book says

exitingcorpse

which particular book is it?

nerdy

generally a differential equation can be written as

f(y(n),y(n-1),...,y',y,t1,t2,...,tn) = 0

if y is the dependent variable

t is the independent variable

and y(n) is the nth derivative of y

then he goes saying

we say that this differential equation is linear iff

it is linear for y(n),y(n-1),...y',y

then it would have the form

f(y(n),y(n-1),...,y',y,t1,t2,...,tn) = a(t)y(n) + b(t)y(n-1) + ... + c(t)y' + d(t)y + e(t)

which is similar to what we were discussing

but then f wouldnt be linear for y(n),y(n-1),...,y',y

wierd.

i think i'm gonna post in Main

exitingcorpse

21:25

hang on

if you don't have the e(t), it's fine right?

no e(t) means you call it homogenous (linear)

with the e(t), it's inhomogenous

kind of like the difference between solving Ax = 0 and Ax = b

nerdy

my main problem is, he says that f is linear for y(n),y(n-1),...,y',y if
f(y(n),y(n-1),...,y',y,t1,t2,...,tn) = a(t)y(n) + b(t)y(n-1) + ... + c(t)y' + d(t)y + e(t)

is that a correct statement ?

exitingcorpse

yes, that's the terminology

the main important part ist he stuff in front of the y and its derivatives

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$Mathematics$ Mathematics