Mathematics - 2013-02-11 (page 4 of 5)

user19161

8:00 PM

Bijective means injective and surjective.

Jenna Magic

just from f(0) = f(1)?

user19161

Understand the definition of injective and surjective to tell.

user19161

That is your homework @jenna.

Jenna Magic

I understand the case

user19161

So can you tell me what is one-one then?

Jenna Magic

8:01 PM

where f(0) =/= f(1)

0x90

let's say I have S = {1,2,3,4,5,6,7,89,88,321,3} and $\lambda(S)$ is the maximal length of the consecutive subsequences of S. so in this example $\lambda(S) = 7$

Jenna Magic

each integer has it's own value

when plugged into f(x)

right?

user19161

That is not too clear.

Jenna Magic

since there are 2 y values for both x values of 0 and 1

it is not one to one

user19161

That is not too clear: 2 y values?

Jenna Magic

8:02 PM

i mean

the same y value*

user19161

It is important to write clearly in mathematics.

Jenna Magic

Since there are the same y value for 2 x values of 0 and 1, then it is not one to one

user19161

Can you tell me why it is not onto then?

Jenna Magic

Not sure about that one

Help me on that one? xD

user19161

That is your homework, first understand onto.

Jenna Magic

8:03 PM

that's why i'm here =(

user58512

I already told you

user19161

Ah, so what is onto?

user19161

You must tell us what you know, otherwise we know not what you know.

skullpatrol

@Charlie You have to kiss alot of frogs to find a prince goes well with this

user58512

@JennaMagic, look your classmate math.stackexchange.com/questions/300512/…

user19161

8:06 PM

@user58512 HAHAHAHAHA

Ed Gorcenski

@JennaMagic An onto function is like making a very nice piece of toast with jam. Your knife (the function) covers the entire slice of toast (the target set) with jam, and then it is tasty.

2

Jenna Magic

Lol

Thanks guys

Ed Gorcenski

A non-onto function is like a very badly prepared slice of toast. Some parts have no jam, and you bite into them, and it is dry and unappealing.

2

Jenna Magic

Interesting

Last question

answers.yahoo.com/question/index?qid=20111201133128AAAzlim

Is that correct?

skullpatrol

Ya hooooooooooooo

user17753

8:11 PM

Hey guys, is there a better way to express the set of natural numbers up to n. For example something like this: {1,2,3, ..., n} but without the ...?

user58512

@user17753, [n]

user19161

@user58512 It is not clear what that means.

user58512

it means the set of natural numbers up to n

user19161

It can mean other things.

user19161

I don't consider it standard notation.

Ed Gorcenski

8:13 PM

You could do $\Bbb N_n$

user19161

If you are writing your own text, define your notation.

skullpatrol

@user17753 What's wrong with {1,2,3, ..., n}?

user19161

Why do you want to use this, and where?

user19161

Context matters.

user19161

@user58512 Even natural numbers can include 0 or exclude 0.

user17753

8:14 PM

Sorry I mean positive integers, not natural numbers.

skullpatrol

@Chris'ssisterandpals you have pals now?

Chris's sister and pals

@skullpatroll: hi. I usually have as anybody has. :-)

Sister here :D

user58512

@Chris'ssisterandpals, I don't understand why you love integrals but don't learn complex analysis

user19161

@user58512 Because she is in high school.

user58512

?

Chris's sister and pals

8:17 PM

@user58512: I also love complex analysis, but I cannot learn all immediately. I love them all :)

user17753

Basically I wanted to express the set of positive integers starting from 1 to n, in order. Just didn't know if there was a succinct way to do that. I have seen [n] used in some texts, but I didn't think it was standard.

user58512

@Chris'ssisterandpals, do you have any thought on it? math.stackexchange.com/questions/300187/discontinuous-integral

@user17753, "in order"?

Chris's sister and pals

@user58512: at a first sight, no. I could ask some ppl that know complex analysis. If I find an answer about it I'll let you know. :)

skullpatrol

Basically I wanted to express the set of positive integers starting from 1 to n, in $\Huge\text{order}$. Just didn't know if there was a succinct way to do that. I have seen [n] used in some texts, but I didn't think it was standard.

user17753

In other words, the first n elements of the positive integers.

user58512

8:20 PM

@Chris'ssisterandpals, no its ok just wondered if there was anything immediate

You know what I am thinking this is related to fourier analysis

skullpatrol

@user17753 {1,2,3, ..., n} is the standard way.

user19161

Like I said, just define your notation if you are writing your own stuff.

user17753

OK thanks guys

skullpatrol

np

user19161

skullie is talking like a prof today. =)

skullpatrol

8:27 PM

Bow wow

or

Woof woof

=)

user19161

How long must one wait to accept an answer?

user58512

100 years

user19161

HAHAHAHA, you are very funny today.

user19161

I think one has to wait 9000 years.

user17753

15 minutes IIRC

user19161

8:36 PM

3

Q: Proving my legit set is real

Thanks guys for all the wonderful help!

user19161

@jenna WTF are you doing?

user19161

This is considered vandalism. One must not edit out the question like that.

user19161

Konig Asaf has rolled back.

user58512

apparently my problem is an easy exercise in contour integration.. but I do not know how to do it :(

skullpatrol

@JacobBlack Don't call him Konig!

user19161

8:39 PM

@user58512 Sometimes, one just needs to be acquainted with the right technique.

user19161

@skullpatrol How about King or Queen?

user58512

it seems like all I got out of my complex analysis class was the idea of a holomorphic function, no skills

skullpatrol

@JacobBlack I'll accept "Queen"

user19161

@user58512 Did you take complex analysis in your bachelor degree?

user58512

yes

user19161

8:41 PM

Was it done properly with proofs?

user58512

yes

Old John

@user58512 What kind of skills do you need from complex analysis? - there are some excellent books that would help

user19161

Interesting that even Cambridge offers two complex analysis courses in the second year, one with more proofs than the other.

Michael Greinecker

@skullpatrol Will your strange obsession with Asaf ever end?

3

user19161

One is called Complex Analysis and the other Complex Methods.

user58512

8:42 PM

@OldJohn, well I got Ahlfors which I really like - but I can't study it methodically now, I just reference it

user19161

@MichaelGreinecker Rather, conflict.

Old John

@user58512 Yeah - Ahlfors is excellent - but not a book you can read quickly

Michael Greinecker

@Jacob Seems a bit too one-sided for a conflict.

user19161

@user58512 That is the classic text. But there are equally good ones that are cheaper unless you got the international edition.

user58512

i really wish i could hit pause, and study mathematics properly -t hen go back to this ridiculous thing i am in the middle of

skullpatrol

8:43 PM

@MichaelGreinecker @JacobBlack Neither of you were here.

user19161

@user58512 It is too late to back out now right?

user19161

@skullpatrol Well, I am not saying the conflict should end.

user58512

yeah, I tried to quit last term too and it was too late

Michael Greinecker

@skullpatrol And?

skullpatrol

nvm

user19161

8:44 PM

@user58512 OK, so now just finish up the year, and move on from there, this time making a careful decision.

user58512

@OldJohn, you may n ot be interested but I finally found why zeta has infinitely many zeros - it is quite nice math.stackexchange.com/a/300337/58512

user19161

@user58512 The problem with many undergrad courses is that they don't prepare students adequately for a career in mathematics.

user19161

By the time one realises this, one has finished the degree.

user19161

So I always tell high school students to choose their university carefully.

user58512

@JacobBlack, yes I could be really well prepared if I knew what I should have been doing instead of wasting my time with 4 years of easy boring classes but thinking this makes me upset so I just try to push on

user19161

8:48 PM

Come on guys. Is there a need to flag skullie when he said "Queen"?

TRiG

@JacobBlack No.

Old John

@user58512 Interesting - looks similar to the proof I saw in Bateman and Diamond - I think all proofs rely on some kind of factorisation of complex functions

Michael Greinecker

@JacobBlack How can one see chat flags?

user19161

@MichaelGreinecker When you have 10k SE wide you see flags in chat.

user58512

@OldJohn, I think the same idea can be proved in a couple different ways. The biggest change in the details is whether we use order or Jensens formula - and Jensen is quite mysterious to me even after studying the proof.

Michael Greinecker

8:51 PM

@JacobBlack Where? I do have 10K in MSE.

Old John

@user58512 order - as in order of an entire function?

user58512

yeah

user19161

@MichaelGreinecker It means you missed it.

user19161

You can only see it when it first appears.

Michael Greinecker

@JacobBlack Thanx.

user19161

8:51 PM

After it has been dealt with it disappears.

user19161

You can click valid, invalid, unsure.

Michael Greinecker

i c i c

user19161

I usually click invalid, unless the sentence is "all ABCs are XYZs"

Michael Greinecker

All ABCs are XYCs!!

user19161

Flag!

skullpatrol

8:54 PM

done

user58512

Jensens formula seems impossibly powerful and the proof is just a basic deduction

I can't beleive it

hi

hi

hi

how are u folks?

8:56 PM

Fine and dandy.

user19161

Hey @trig LOL at your last ping to me in the other room.

Old John

@user58512 Hmm - not sure I would regard Jensen's formula as any more powerful than the factorisation needed for the proof

skullpatrol

@pourjour fine.... you?

pourjour

@skullpatrol pretty good

@GraceNote great

Charlie

@skullpatrol :/

@pourjour How are you Soufy?

user19161

8:57 PM

Guys, I think I will never fall in love with anyone again.

pourjour

:8070417I feel good and u?

Charlie

@pourjour good

Old John

Need to pick people up from airport - back later

skullpatrol

@JacobBlack again?

user19161

@skullpatrol Nah, just a casual statement.

Charlie

8:58 PM

@JacobBlack hmmm

pourjour

can somebody plz remind of the how we can find the principal angle

for example $\cos(250\pi)$

user19161

I see that Henning's quote of mine gets 3 stars while the original gets 2 stars, sad panda...

3

Charlie

Panda sad

pourjour

nobody

??

user58512

@pourjour, cos(250pi) = cos(0)

pourjour

9:01 PM

@user58512 can u remind of the manner

Charlie

@skullpatrol anda again and again

pourjour

like using inequality

user58512

because cos(x) = cos(x + 2pi)

and 2|250

skullpatrol

@Charlie Do you like this?

Ed Gorcenski

@JacobBlack I have now given Henning's quote a fourth star, out of spite!

Charlie

9:02 PM

@skullpatrol oh, of course!

Ed Gorcenski

(not really -- I am not spiteful)

user19161

@EdGorcenski Now I must flag you.

Ed Gorcenski

:(

Charlie

@skullpatrol what would youi like to do before dying, Skull?

user58512

i want to compute the integral $$\frac{1}{2 \pi i} \int_{c - iT}^{c + iT} y^s \frac{ds}{s}$$ any hints? I asked about this on the site too

for y=1 it's easy to evaluate, I need to do 0 < y < 1 or y > 1 (and c > 0)

user19161

9:07 PM

@user58512 No answers yet?

user58512

I tried to change it to the integral around a circle minus the residue but then I get e^{T e^{i\theta} \log y} in the integrand which looks really awful

no answer but someone commented a book which has it

user19161

@JennaMagic You have not accepted my answer...

Ed Gorcenski

have you tried parameterizing the curve as $s(t) = c+ti$, $t \in [-T,T]$, then using that $\int_C f\ ds = \int_{-T}^T f(s(t)) ds/dt dt$?

skullpatrol

@Charlie Tough question :-\

@Charlie Do you wanna start a rating system on songs from 1 to 10?

user58512

@EdGorcenski, yeah I tried that thismorning and it didn'twork but let me try again now

Charlie

9:09 PM

Not even everyone is obligated to accept your answers, @jacob , get over it

@skullpatrol yes!

user19161

@skullpatrol Most of Mariah's songs are at 10.

skullpatrol

@JacobBlack Do you think she is a 10?

Ed Gorcenski

so in this case $ds/dt = i$, so you would get $\frac{1}{2\pi i} \int_{-T}^T \frac{y^{c+it}}{c+it} i\ dt = \frac{1}{2\pi} \int_{-T}^T \frac{y^{c+it}}{c+it}\ dt$

Charlie

Mariah screams too much while singing

user58512

now i change the denominator to c^2 + t^2 and split the integral into real and imaginary parts?

user19161

9:11 PM

@skullpatrol Yes, I am absolutely in love with Mariah.

Orange Harvester

@skullpatrol 1-10 is too complex. Rating should be 0-1, and then recorded over time. So, a software should list of some songs that you have heard at random times and then make you choose which ones you like, after which there should be a weighted average determining the number between 0-1 that will be then multiplied by 10 on the fly to give the rating of the song.

Ed Gorcenski

Or, convert $\frac{1}{c+it}$ to the form $a(t)+ib(t)$,which is effectively the same

user58512

ok

Charlie

Let's make it, @skullpatrol !!!

Ed Gorcenski

Then you're left with integrating an exponential.

Orange Harvester

9:13 PM

@skullpatrol Other method is what my music player does, it records which songs have been played how many times, but more importantly, it records when a song has been skipped/queued/played manually (instead of being played normally by the playlist). And then, depending on that, assigns rating to that song. It is a very awesome system.

user58512

the real part tends to zero

so im left with $$i \frac{y^c}{2 \pi} \int_{-T}^T \frac{t y^{it} dt}{c^2+t^2}$$

I can'tdo it

Ed Gorcenski

Not sure if it's the right path. Worth a shot.

user58512

ok , thanks you

robjohn

I am not seeing messages being posted in the chat page title. Is it just that quiet here?

user58512

@robjohn, i don't understand your comment

user19161

9:24 PM

Let's close the comment as not a real comment.

user58512

lol

user19161

Oh I think I get it.

user19161

Maybe he means the tab in your browser.

user58512

just curious, are the zeros of zeta all multiplcity zero?

user19161

I forgot all my complex analysis.

robjohn

9:26 PM

@user58512 Usually, I see the number of chat messages since I had the window front in the eindow title

Orange Harvester

@robjohn I am seeing those messages alright.

user19161

Hey @eric what made you choose "ke"?

Eric

@JacobBlack My name is eric, which in chinese is 埃里克

Charlie

@Argon HIIIIIIII!

;)

Argon

@Charlie Hi Marilia!

user19161

9:28 PM

@Eric Yes, I suspected.

Eric

@JacobBlack my Chinese friends would call me "克克"

user19161

@Eric Are you Chinese?

Eric

No

@JacobBlack But my wife is chinese, and i lived in china for about 8months

and i still have a lot of Chinese friends i keep in contact with

Charlie

@Argon you don't post Aaron's integral no more?

Eric

@JacobBlack Why do you ask?

user19161

9:30 PM

@Eric Just for fun. All my questions are for fun.

Eric

ok

Argon

@Charlie Hmmm... I forgot from school and exams and stuff. I will find one!

Charlie

@Argon yay!

user58512

i want to stay up late studyin but then I would miss class in the morning

Argon

Argon's Integral of the Day: $$\int_{-\infty}^\infty \frac{\arctan\left(e^{-x}\right)}{\cosh^{2q}(px)}\, dx
=\frac{\pi^{3/2}}{4p}\, \frac{\Gamma(q)}{\Gamma \left(q+\frac12\right)}\qquad p,q>0$$

2

Orange Harvester

9:33 PM

@user58512 when do you normally sleep?

Charlie

@Argon YAY!

Argon

@Charlie YAY!

Orange Harvester

@Argon where do you find such integrals?

Charlie

@OrangeHarvester From his brain

user19161

@OrangeHarvester He has a beautiful mind...

Orange Harvester

9:34 PM

sheesh, now ever jacob and charlie are trolling me. :P

Argon

@OrangeHarvester Usually from de.wikibooks.org/wiki/…

@Charlie @JacobBlack Ha, I wish I was so smart

user19161

@Argon You read German?

Charlie

@Argon wish granted

Argon

@JacobBlack Nope, but I am fluent in reading integrals! XD

@Charlie Hahahahah

Orange Harvester

@Argon cool collection.

Argon

9:36 PM

@OrangeHarvester They have a bunch of really nice ones, some have proofs too

Charlie

@Argon :D

Orange Harvester

@Argon who needs the proofs!!! :P

Argon

Hahahaha!

Charlie

@OrangeHarvester the judge

user19161

@cha Hi.

Charlie

9:40 PM

@JacobBlack I'm here for so long....

user19161

@Charlie I am always here...

user19161

Wow, why don't people upvote lhf answers?

user19161

I am not talking about my own, but others'.

user19161

Come on guys, be more generous.

user19161

If the answer is correct, I upvote it, no matter how simple the question is.

user58512

9:45 PM

is there a computing project which searches for Siegel zeros?

let's disprove GRH.

user19161

Does your course now mention RH @user58512?

user58512

no

user19161

If you ever apply for a PhD program, I suggest you restudy everything fundamental.

user19161

Sounds like your undergrad wasn't a good preparation.

user58512

yes

user19161

9:49 PM

Mine was pretty bad too.

user19161

I was very excited during my first math lecture.

user19161

After the first year or so, I realized how terrible the courses were.

Jimmy Hoffa

If I took 1 class a semester every semester, how long would it take me to get a BS in general math, anybody got a guess? I tried looking it up and find all these numbers about credit-hours and things but can't come up with the translation...

(how many years that is)

any guesses?

user19161

@JimmyHoffa Haha, it depends on where you are!

Jimmy Hoffa

US

user19161

9:53 PM

Same answer.

Ed Gorcenski

@JimmyHoffa A while

Jimmy Hoffa

Would it vary by years?

user19161

It depends on the exact university dude.

Ed Gorcenski

The reason being, most US universities typically require many general education requirements

user19161

Every university is so different.

user19161

9:54 PM

This question is really not answerable.

Jimmy Hoffa

Balls

Orange Harvester

@Charlie the judge only needs the evidence.

Ed Gorcenski

Among schools that use a semester system, there are two main credit schemes: 3x5 and 4x4. In a 3x5 system a class is 3 credits, and a full-time student typically takes 5 courses per semester (at least in the first couple of years)

Jimmy Hoffa

like 10-15 years would be good guess?

Ed Gorcenski

In a 4x4 system, the student takes 4 classes per semester, at four credits each

user19161

9:56 PM

@JimmyHoffa They might not allow you to take that long.

Ed Gorcenski

So, assuming the more common 3x5, it would take you 5 years per semester -- multiply by 8 semesters

That's 40 years.

user19161

@JimmyHoffa Like I said, you should find out if you really want to know the answer by looking it up.

Jimmy Hoffa

40 years or semesters?

user19161

41 secs ago, by Jacob Black

@JimmyHoffa They might not allow you to take that long.

Ed Gorcenski

er, 40 semesters

so 20 years

Jimmy Hoffa

9:56 PM

There's only 2 semesters a year?

Ed Gorcenski

At a typical university, yes.

Fall and Spring

user58512

this book doesn'thave anything on Siegel zeros...

user19161

@jimmy Are you asking a serious question?

Ed Gorcenski

Many universities offer a very limited selection of courses during the summer.

user58512

that's weird

user19161

9:57 PM

Because I am giving you a serious answer.

Jimmy Hoffa

@JacobBlack generally yes, I did honestly spend about 20 minutes trying to find this info on my own but all the info I found presumed I knew a lot about college which having never gone I know dick

Ed Gorcenski

Some universities work on a trimester system: fall, winter, and spring trimesters, with a limited summer work.

*a limited summer work period

user19161

@JimmyHoffa US universities either have two or three periods a year. One usually takes 4, 5, or 6 courses a period.

user19161

One usually graduates in 3 or 4 or 5 years.

Ed Gorcenski

But by and large, the vast majority of universities work on 3 credit courses, two semesters per year.

user58512

9:58 PM

lol I just found on google, ABC implies no Siegel zeros

Orange Harvester

I am not sure colleges allow just one course per semester to register unless there is a specific medical case, that too for a particular semester. In my uni, you had to register for minimum 15 hours of credit to attend a semester.

Ed Gorcenski

This amounts to 15 credits per semester, so a total of about 110-120 credits are required to graduate

Jimmy Hoffa

@OrangeHarvester what are those of us with families who are working supposed to do then?

Ed Gorcenski

At my university, 124 credits were required, with classes typically being 4 credits.

Jimmy Hoffa

Just be relegated to fake-school at the Phoenix?

Ed Gorcenski

9:59 PM

@JimmyHoffa Community College can get you through the first two years quickly

Transcript for

$Mathematics$ Mathematics