Mathematics - 2013-05-14 (page 2 of 5)

Dominic Michaelis

10:06 AM

guys i am getting hungry

DanZimm

pizza!

MphLee

I have lunch in fact

bye

Alexander Jones

Why are high school maths teachers so bad? What do they do in their free time?

Dominic Michaelis

getting worse it is not that easy

Edwin Montufar

Are you a high school student?

Alexander Jones

10:20 AM

Yeah, final year.

Faust7

High school teacher especially in North american require very little qualifications

teachers*

Edwin Montufar

Do you have a library nearby?

Faust7

wth is a libary

Alexander Jones

If I was a high school maths teacher I would spend all my free time learning about maths and training my students to the best of my ability but I think most teachers have a very low IQ so they can't learn anything beyond high school curriculum

Edwin Montufar

A library is a place where you can check all kinds of books

Whenever I was dissatisfied with my education in school I'd go to the library or internet.

Faust7

10:23 AM

Im only half jokeing O.o n im almost a half generation older then Alexander

Edwin Montufar

One shouldn't let the quality of their school determine the quality of their education.

Alexander, what math courses have you taken thus far?

Alexander Jones

Yeah, school, school environment, parents etc. can very negatively impact one's education

I have completed high school maths, now training for IMO and studying single variable calculus, linear algebra and learning about differential equations and analysis

Faust7

Yeah i guess i was lucky my math prof had a masters degree in physics

Edwin Montufar

Well, then a library is a good place to escape. Some libraries even have sharing programs with other libraries so that you can checkout books you can't find.

Faust7

when i was in high school

Alexander Jones

10:28 AM

My teacher at school doesn't know basic maths like proving that sqrt2 is irrational or proving AM:GM inequality or any of these famous proofs. I complained so they replaced her. Luckily the new teacher is pretty good.

Faust7

those kind of things arent important

specially in high school

Alexander Jones

I am a strong believer in that 'you are who you are with' so I spend a lot of time in the library, I have heaps of books on my computer and I ask questions here :)

Well, it is part of the syllabus so they are important

Faust7

very very very very few people in a high school math class will be going to university to do math

Edwin Montufar

I finished high school having completed only algebra 2.

Alexander Jones

In 2010 they asked to compute zeta 2, I'm pretty sure 70% of teachers can't do that...

Edwin Montufar

10:31 AM

I'm studying mathematics at a university now. I didn't even know how to prove things in basic geometry.

Alexander Jones

Really? How are you finding maths at uni?

Lord_Farin

@Faust7 Sorry to drop in, but at least here in the Netherlands, the education system is so messed up that it is virtually impossible to discover that one likes mathematics by just going through the high school curriculum.

Faust7

geometry can be veyr hard if u dont use modern techniques

Edwin Montufar

I found geometry to be very intuitive once I encountered Felix Klein's method.

Faust7

as i earlier mentioned didnt find out i liked mathematics until i did sevral 3rd math class's

in university

hated the first 2 years and high school math

Alexander Jones

10:33 AM

High school maths is basically training you to do the test, not really teaching you maths

Faust7

The worst part about most 1st and second year math class's in university is that

Edwin Montufar

I started off as a computer science major, but when I got into more advanced concepts, I realized I enjoyed the mathematical aspects even more. So then I switched to maths, but it was a difficult process to gain some measure of competence with proofs.

Faust7

the course is taught in a way that is not geared towards any students enjoying it

its just like high school gear towards plug n chug an answer

Edwin Montufar

Well, even the 1st and 2nd year math's are not deep enough.

Faust7

so math students hate it

and eveyrone else hates math

Alexander Jones

10:35 AM

I decided to do engineering + maths at uni. It is a 5 year degree but there are more jobs

Faust7

eh i already have a job

i do math for fun.

Edwin Montufar

It's when you actually start learning things like analysis, abstract algebra, etc that you really begin to appreciate it.

Faust7

my first 3rd differntail equations class i really enjoyed

Alexander Jones

Many of my friends doing maths at uni say they love analysis

Edwin Montufar

Analysis is very nice, I enjoyed it thoroughly.

Faust7

10:36 AM

analysis is a very useful set of tools

Alexander Jones

Do you guys agree that algebraic geometry is very difficult? I heard that from many people.

Faust7

youd have to explain what u mean by algerbraic geometry

Alexander Jones

I haven't done it so I don't know :(

Faust7

honestly if u make it past the first 2 years of math

Lord_Farin

@AlexanderJones It requires a quite different mindset. You have to be very strong in the commutative algebra department.

Faust7

10:38 AM

everything is really easy

at least compared to before

Lord_Farin

@Faust7 So why haven't you proved the Riemann Hypothesis yet?

Faust7

not part of my class's

Edwin Montufar

Alexander, that's more specialized, once you get that deep you kinda have to decide what you want to specialize in.

Faust7

im just saying that 3rd n 4th year math class's though they can cost a hefty work load

Dominic Michaelis

@Lord_Farin yesterday a proof for the weak goldmann conjecture was uploadet to arxiv

Faust7

10:39 AM

are signifigantly easier then 1st n second year math class's

Alexander Jones

Can you guys explain to me the reimann hypothesis in one sentence? I read about it on wikipedia but it is hard to understand what it is hypothesizing

Lord_Farin

@AlexanderJones $\zeta(z) = 0 \land z \notin -2 \Bbb N \implies \operatorname{Re} z = \dfrac12$.

Faust7

have you started calculus yet?

Lord_Farin

@DominicMichaelis Link?

Gustavo Bandeira

@Lord_Farin Great! Really great.

Alexander Jones

10:40 AM

Yes, I have done a lot of calculus

Dominic Michaelis

@Lord_Farin arxiv.org/pdf/1305.2897v1.pdf

Alexander Jones

@Lord_Farin hmm that made no sense to me :(

Gustavo Bandeira

@Faust7 RH is unproved for like 200 years. xD

Edwin Montufar

Learn some complex analysis Alexander.

Gustavo Bandeira

It's a millennium problem.

Edwin Montufar

10:42 AM

Try getting Real Analysis done asap, then move onto complex analysis.

Alexander Jones

What textbooks do you recommend?

Edwin Montufar

It should make the terminology for the underlying theory of the Riemman Hyp more digestible.

Gustavo Bandeira

@Lord_Farin What's the meaning of $-2\mathbb{N}$?

Faust7

@GustavoBandeira he was being a smart ass and he knew it, comment was to emphasis the fact that hes a troll.

Lord_Farin

@DominicMichaelis Thanks. I see Mellin transforms and the like; probably better not spend my time on that right now.

Gustavo Bandeira

10:43 AM

First time I see this.

Lord_Farin

@GustavoBandeira Well it's a special form of a set-product: $aB = \{ab: b \in B\}$.

Edwin Montufar

For a beginning class in real analysis, start with Bartle and Shebert intro to Real Analysis

Alexander Jones

I am currently using Apostol but it is hard :( I will use the one you suggested

Edwin Montufar

once you're done with that, for a complex analysis course, I suggest you look at An Introduction to Complex Function Theory by Bruce Palka

Gustavo Bandeira

@AlexanderJones Try not to struggle too much - search for another books.

Lord_Farin

10:44 AM

@Dominic It's unbelievable. I just came up with a combinatorial argument for a combinatorial identity.

Edwin Montufar

As an adjunct to you studies in complex analysis, I suggest you look at Tristan Needham's Visual Complex Analysis

Gustavo Bandeira

@AlexanderJones Peter Smith wrote: "I very strongly recommend tackling an area of logic (or indeed any new area of mathematics) by reading a series of books which overlap in level (with the next one covering some of the same ground and then pushing on from the previous one), rather than trying to proceed by big leaps."

Lord_Farin

@GustavoBandeira This is very good advice.

Edwin Montufar

How good are you with proofs Alexander?

Alexander Jones

I know basic proofs, nothing advanced

Edwin Montufar

10:47 AM

Are you comfortable with logical patterns behind their reasoning?

Gustavo Bandeira

@Lord_Farin Yeah. Perceiving it helped me a lot, I was stuck in the "strugle to read the hardest book!" - I wasn't doing any progress.

Alexander Jones

@GustavoBandeira I agree with Peter Smith, thanks :)

Edwin Montufar

For example, are you comfortable with the notions of DeMorgan's Law, Contrapositive, an Indirect proofs, etc.?

Alexander Jones

Some one told me to learn proofs from Daniel Vellemann Proof book but it is a bit hard

Lord_Farin

@GustavoBandeira More so considering that books are still easy, compared to research papers.

Edwin Montufar

10:48 AM

If you found that hard, then I have some suggestions for you.

Alexander Jones

I haven't done any of those :( What are your suggestions?

Gustavo Bandeira

@AlexanderJones I really loved this book‌.

Look the quote from the author in the website.

Faust7

Anyone have that webcomic picture witht eh graph of understanding of 1+1?

Edwin Montufar

Let's start with the following books: Intro to Inequalities by Beckenbach and Bellman, a Primer of Abstract Mathematics by Robert B Ash, and Mathematical Thinking by Douglas West

Dominic Michaelis

@Lord_Farin yeah it seems to be not that trivial

Faust7

10:52 AM

looks like a double bell curve its got a funny comment at the lowest point "define 1?" with a picture of a guy with a phd?

Alexander Jones

@EdwinMontufar Thank you, I will look for these books on the internet.

Lord_Farin

@DominicMichaelis No surprise of course; otherwise it would have been solved long ago.

Edwin Montufar

The inequalities book will help you tackle some fundamental concepts in real analysis.

Alexander Jones

Nice talking to you guys, I will go do some studying now :)

Lord_Farin

@AlexanderJones Bye, good luck!

Edwin Montufar

10:55 AM

@Alexander Jones Good luck.

Faust7

@AlexanderJones http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

imho is a great intro to Analysis textbook and its a free pdf

Edwin Montufar

@Faust7 that book looks really good. Reminds me a bit of Bartle and Sherbert's book, but it has more topics.

Faust7

I had never taken analysis before n that was recommended to me by a prof at my uni.
Sadly its out of print spent an hour on a crappy mac at the local print shop trying to crop and print the pdf. Something about math i just can't handle it as a pdf =(

Edwin Montufar

Same here, too much eyestrain.

Plus I like to write on margin spaces

Faust7

specially in a class like analysis!

Lord_Farin

11:03 AM

@EdwinMontufar Interesting; I never do that.

Edwin Montufar

@Lord_Farin, do what?

Lord_Farin

@EdwinMontufar Write in margin spaces (or generally, in a book). Unless it is to indicate a typo/mistake.

Edwin Montufar

Well sometimes the authors leave out details on purpose, so I just fill them in.

Faust7

so i just realised the taylor expansion (1-x)^{-1} = 1+ x +x^{2}+.... actually comes from the geometric series...

(1-r)^{-1}

Lord_Farin

@EdwinMontufar An admirable practice; in hindsight I think I could've learned some things faster if I had done that as well.

But usually I just try to formulate the argument in my head, or when that does not work, write it out on some paper. Or sometimes I just take it for granted when it is a minor point.

Faust7

11:06 AM

Thats why i alwasy keep my math textbooks, they are better then the original assumeing you can read my shitty wok writeing

Edwin Montufar

For example some authors put (Why?) besides some of their statements, and so I put the answers in the margins. Of course there's also the occasional typo. Or sometimes I even generalize concepts in the margin space.

Faust7

Cept this Calculus textbook im going to burn it as soon as i get home today after my test.

Lord_Farin

@EdwinMontufar Are you hoping to have your own "Fermat moment" one day? :)

@Faust7 If you keep it, the only thing that really matters is that you yourself retain the ability to read your writing (sometimes when I read old notes from lectures I attended I'm struggling to decrypt the ubiquitous abbreviations :)).

Edwin Montufar

@Lord_Farin, well the problem with Fermat is that he didn't have enough space in the margins to put proofs for some of his theorems ;)

Lord_Farin

@Faust7 You have a test today?

Edwin Montufar

11:10 AM

@Lord_Farin, sometimes if the book is too involved, I dedicate a notepad or journal to it.

Lord_Farin

@EdwinMontufar I'm impressed. I'm usually too lazy for that kind of stuff.

Faust7

@Lord_Farin honestly i can't usually read my notes or problem sets i have started to just type them out in latex my marker appreciate it and both of us can read it.
Yes i have a test i was hospitalized during finals and missed a few exams i need a 3rd calculus course to be properly registered in Analysis. also I like Fermats little theorem more then his last one =)

Gustavo Bandeira

@Lord_Farin I'm reading an introduction to category theory. =)

Lord_Farin

@Faust7 The LaTeX skill is indeed a very useful one. Good luck with your exam!

@GustavoBandeira Which one?

Edwin Montufar

@Lord_Farin it's always good for me to keep records. I typeset a lot of my journals in latex to store the info electronically. I use a program called Lyx to typeset rapidly, almost like a word processor.

Gustavo Bandeira

11:14 AM

@Lord_Farin An Introduction to Category Theory: Harold Simmons

Lord_Farin

@GustavoBandeira Nice.

Gustavo Bandeira

@Lord_Farin What book did you used?

Edwin Montufar

@Lord_Farin, the only problem with typesetting my work is that implementing diagrams can be rather tedious.

Faust7

I Found a "Fermat Prime" while taking a 1st year math class i didn't know the theorem at the time but i was using a combination of mod and different base number systems and came to the conclusion the number i had was prime. ( turns out it was just very likely prime) but my prof was nice enough to explain the theorem to me =)

Lord_Farin

@EdwinMontufar I tried Lyx, but nowadays I just use WinEdt. For diagrams I use TikZ.

Gustavo Bandeira

11:17 AM

I feel me attracted by some mathematical ideas. As I'm a noob, I have no idea of what most of them are. Category theory, topology, automata, etc.

Edwin Montufar

@Lord_Farin Yeah, I've messed around with Tikz, the syntax is quirky, but it has good output.

Lord_Farin

@GustavoBandeira To get started I used CWM by Mac Lane and Category Theory by Awodey.

Gustavo Bandeira

Yeah. I've heard about these ones.

Lord_Farin

@EdwinMontufar The syntax of all diagram typesetting mechanisms I've used cq. seen so far is quirky.

Edwin Montufar

@Lord_Farin Asymptote is pretty straightforward actually, though it could use more documentation.

Faust7

11:19 AM

if you got the coin fork out the dough for a laptop/tablet hybrid i got one with a 8.5x11.5 inch screen it takes some training the software but it can read any of your writeing and you can add vocab like the intergral sign with bounds and get the program to export your writing directly to latex

Edwin Montufar

@Lord_Farin the syntax in Aysmptote bears some semblance to C++.

Lord_Farin

@EdwinMontufar I've done my fair share of programming, so it wasn't too hard to get used to TikZ (I mostly use the tikzcd environment which is relatively accessible compared to the full-fledged version).

Faust7

Oh also im sure most of you have a program for type setting in latex? the program im using to make pdfs to send my hw assignments in is really annoying what do you guys use?

Lord_Farin

@Faust7 In set theory, we have things like this. I'm happy with the \aleph command :).

@Faust7 I use WinEdt.

Gustavo Bandeira

Dude. In the future I'll build aquariums again. Look at this

Edwin Montufar

11:22 AM

@Faust7, I'm a big fan of Lyx. It's a word processor like environment that uses latex to typeset your documents.

Gustavo Bandeira

Damn beautiful.

Faust7

ill check out both

Edwin Montufar

If you don't want to worry too much about your latex code, then I suggest you go with lyx. It simplifies a lot of latex functionality and has autocompletion.

Lord_Farin

@Faust7 For your demands, Lyx is probably a good place to start. Once you get to need a lot of custom macros, a text-based editor like WinEdt (there are more good options, just do a web search) can become preferable.

Gustavo Bandeira

@Lord_Farin I'll give it a try. I loved TeXworks.

Faust7

11:25 AM

Im using Texworks

i dont liek that you need \\ to put a spcae between a line it formats everything veyr oddly

like worse then my typeing

it also compiles randomly and doesnt properly dump temp after each compile

Lord_Farin

@Faust7 It retains the auxiliary files to speed up future compilations.

Gustavo Bandeira

@Faust7 But have you searched for solutions?

Faust7

im more of an intuitive software user

Edwin Montufar

so go with Lyx

Gustavo Bandeira

Yeah. Just as I guessed. :P

Faust7

11:29 AM

i work in the tech field, if i cant mess with it some way i find logical to get what i want

then i dislike it =)

but i did like read most of the option links u can click on but god knows i didnt open a help file

This book i have listed a formula for calculating surface integrals but i think its just a change of varibles written out funny

Edwin Montufar

dropbox.com/s/rsq7dt83d5nfd3o/Assignment11.pdf Here's an example of some of my output with lyx

Faust7

$\int \int_{S} F \cdot n dA= \int \int_{w} F(G(u,v) \cdot (dG_{u} X dG_{v}) du dv$

Edwin Montufar

Lyx is pretty flexible with formatting so it'll make things pretty easy for you.

Jayesh Badwaik

@EdwinMontufar Graphs are with TikZ? Or Pstricks?

Faust7

Cause isnt that formula just a change of varibles on F and then a new normal vertor n_{1} that is normal to the change of varibles?

Edwin Montufar

11:37 AM

@JayeshBadwaik those are with Tikz

Faust7

i downloaded it and installed both will play with them tonight after my exam

Edwin Montufar

@Faust7 look up a lyx tutorial on you tube to get an idea of what the workflow is like

Faust7

Sankyuu =)

Edwin Montufar

Good luck with the exam Faust. I'm out fellas, have a good one.

Lord_Farin

@EdwinMontufar Bye!

Faust7

11:47 AM

its should be ok, studied like a slave for it and had 96%+ going in =)

Gustavo Bandeira

@Lord_Farin What do you use to read PDF's?

I loved STDU Viewer. It's the only one that really stores the page I'm in.

Lord_Farin

@GustavoBandeira I generally just use Adobe XI Pro; for previewing my TeX documents I use SumatraPDF (because that one is designed to work well with WinEdt).

Babak S.

@Faust7: Have a look at your question. I made it better in looking. :)

Faust7

lol yes you did =)

that "formula" has been driving me nutz where it comes from

its just writen down in my textbook as this exists use it if u want

Lord_Farin

12:12 PM

I'll be off to useful things. Bye all.

Gustavo Bandeira

@Lord_Farin See ya

Vrouvrou

1:08 PM

hello

robjohn

@Vrouvrou howdy

pourjour

supposing $\displaystyle F_n(x)=\int_0^x t^ne^{-t}\,dt$ using induction how to prove that the limit exist when x tends to $+\infty$?

Faust7

Q: i got a limit that defined to be 0 but as the derivative of my function aprochs this value from 0+ or 0- there is no neighborhood of 0+ that is strictly positive or strictly negative. how do i use that to violate conntinuity

i know that if i have some point x and x>0 then there exists a nieghbourhood of x that is stricly positive this is true for all x>0 but is violateing that suffient to say i am discontinous at my limit?

my confusion arises from if you take the actuall limit point ie x=0 then there is no neighbourhood of this point what my criteria above is satified can argue that 0+ or 0- are a limit and show they are diffrent then 0 to show im not continous?

Lord_Farin

@Faust7 It seems that the continuous function $f(x) = x \sin \frac1x$ provides a counterexample to your assertion.

OTOH it is necessary for the limit still to exist, given your condition, that the function value at zero is zero.

Faust7

1:26 PM

not sure thats a counter example |Sin(1/x)| \leq 1 so you have lim x /to 0 of x*1

if you lose that x bound though

sin (1/x) x\to 0

defin f(0) =0

then f is discontinous at x=0

maybe im nutz

Lord_Farin

Yes $\sin \frac1x$ cannot be continuously extended to $x = 0$. But that's exactly my point.

$x \sin \frac1x$ changes it sign infinitely often when approaching $0$, but it still is continuous at $x = 0$.

Faust7

so it you look at 0+ of sin(1/x) there is no neighborhood of 0+ s.t everything in that interval is postive

no matter how small you make that interval

that violates being continous somehow more directly because the definition of a point be continous is that that interval must exist or you have a limit point

Lord_Farin

What is your definition of "continuous", then? $\epsilon$-$\delta$?

Faust7

no nothing that strong

but normally when u have a limit point at 0

Lord_Farin

(By the way, on the right you see a link "$\LaTeX$ rendering in chat" which may help you reading my messages, and possibly format your own.)

Faust7

1:35 PM

i dunno i just seems to have it drilled into my mind that there must exist a neighbourhood of every positive/negative point that is stricly positive or negative in order for something to be continous

perhaps im out to luch

Lord_Farin

@Faust7 As I said, you are correct as long as the function value at the limit point is nonzero. In that case, if e.g. $f(x_0) = a, |a| > 0$, taking a suitable $\delta$ for $\epsilon = \frac a 2$ will provide you with the desired neighbourhood.

Faust7

but o+ >0 by cant i make the argument about 0+ sinc eits not a limit point and no such neighbourhood exists as x \to 0?

even if my function did take the value 0?

Lord_Farin

The notation $\lim\limits_{x\to 0^+} f(x)$ means that the limit is taken as "approaching from the right".

See e.g. here.

Faust7

sorry im not entirely following but 0+ is \delta >0 so why is there no neighbourhood about 0+ say \delta /2 thats stricly positive?

MJD

@robjohn In this month of moderators losing their heads, burning out, and resigning, it took me a while to remember which moderator has not done that. I think it's to your credit that I couldn't remember at first who the remaining moderator was, and I would like to thank you for your hard work.

Faust7

1:43 PM

hmm ok well imt rying to prove that $\sin (x^{-1})$ where f(0)=0 lim x \to 0) does not exist and i can't use any epislon's or deltas how would i do this?

Lord_Farin

@Faust7 If $f$ were continuous, then for any sequence $x_n$ with $\lim\limits_{n\to\infty} x_n = 0$ one would have $\lim\limits_{n\to\infty} f(x_n) = f(\lim\limits_{n\to\infty}x_n) = f(0)=0$.

So all you need to do is conjure up a suitable sequence such that $\lim\limits_{n\to\infty} f(x_n) \ne 0$.

Faust7

O.o

Lord_Farin

I apologise if I'm being too formal about it. But it has been a long time since I dealt with limits in an intuitive way.

Faust7

haha =)

Lord_Farin

But you could e.g. take $x_n = ((n+\frac12)\pi)^{-1}$.

Faust7

1:52 PM

its there some way i can bound sin(1/x) by something that converges to 0 from above?

Lord_Farin

@Faust7 No, because the sequence I just gave provides points $x$ where $\sin(1/x) = 1$ arbitrarily close to $0$.

Faust7

oh im a moron nvm

last stupid question sin( \pi n) = -sin (n) ?

Lord_Farin

@Faust7 $\sin \pi n = 0$.

And $\sin -x = -\sin x$.

Faust7

sorry not where n \ \mathbb N but n \in \mathbb R ?

Lord_Farin

In that case nothing can be said.

Dominic Michaelis

2:01 PM

@Lord_Farin well $\sin(\pi x)\in \mathbb{R}$ for $x \in \mathbb{R}$ :D

Lord_Farin

@DominicMichaelis Thank you, Captain Obvious...

Faust7

rofl

Dominic Michaelis

@Lord_Farin i lost 3 of 4 points in a complex analysis exam cause i didn't proof that $\sin(i)\neq 0$ ...

Faust7

that blows

Lord_Farin

@DominicMichaelis ... I say, trial by fire.

Faust7

2:04 PM

thats ok i lost 0.5 marks on 2 questions my exam was out of 40 and marker wrote 31/40 on the front of my test

took my prof 10 minutes to figure out what my grade was supposed to be and to this day i havent any idea how he added the numbers together to get 31

as no combination of number gave an 8 =\

Lord_Farin

Couldn't you appeal or otherwise request justification for your mark?

Dominic Michaelis

Don't you know 40-2 * 0.5=31 because **** you ? :D

Faust7

lol my prof eventually gave me 39/40

its just there no logcical way he could of added or subtracted the numbers i had on my paper to get 31

Lord_Farin

@Faust7 We conclude that mathematicians aren't necessarily adepts at basic arithmetic :).

Dominic Michaelis

well the heuristic is clear

Faust7

2:09 PM

my prof really didnt like that grad student though =P

Dominic Michaelis

you don't have 40 points but that lose that much hence your points are 3x

because 2*0.5=1 it is 31

Faust7

shoulda had 40 on that test but i used a method we allegedly didnt learn to solve one of the problems =\

but honestly who use a liaponov function to show that you have a limit cycle? poincare bendixion is clearly the most logical method.

does calculus ever get easier? it seems to take me 3-5x as long to get calculus concepts as well any other area of math?

Dominic Michaelis

@faust7 Show wheter $$\sum_{k=1}^\infty \left( \frac{(\sin(k)+2)^k}{3^k}\right)$$ converges

Lord_Farin

@DominicMichaelis $k = n$?

Dominic Michaelis

oh right

Faust7

2:18 PM

(sin (n) +2 )^{n}< 3^{n} call it L< 3^{n} thus let r= \frac { L}{3^k} thus |r|<1 for all k hence it converges.

Lord_Farin

@Faust7 It gets easier. But it requires a lot of practice.

There is no $L$ that works for all $n$.

Faust7

L is just defined to be < 3^{n}

im relabeling sin(n)+2 < 3^{n}

then i can make it into a geometric series

where r<1

Charlie

@Lord_F hies

Faust7

its just hard to write it without picking a letter to deifn it

Dominic Michaelis

nope you can't

Lord_Farin

2:20 PM

@Faust7 For all $\epsilon > 0$, there is are infinitely many $n$ such that $|\sin(n)-1| < \epsilon$. (You did notice the power $k$ in the numerator?)

@Charlie Hello there.

Charlie

@Lord_Farin how are you doing?

Lord_Farin

@Charlie Quite fine, but busy.

@dominic hello

|sin (n)| /leq 1

@charlie hi

2:21 PM

@Lord_Farin oh!

Faust7

so why cant i say sin (n) +2 \leq 3?

Dominic Michaelis

you can say $\leq$

but $\sum 1 $ doesn't converge

Charlie

@DominicMichaelis :D

Lord_Farin

@Faust7 You can, but you can't say it is below $3-\epsilon$ for all $n$.

@DominicMichaelis I could imagine that it still converges... But it requires careful analysis.

Faust7

oh your right there are values where my r=1

Dominic Michaelis

2:23 PM

@faust7 not $r=1$ but arbitrary near at 1.

@Lord_Farin yeah it converges indeed.

Faust7

wellt here exists n s.t sin(n) =1

Dominic Michaelis

nope because $n\in \mathbb{N}$

Faust7

so there exist n s.t r=1

oh i didnt realise n \in N

Dominic Michaelis

we sum over it ;)

Faust7

then my r should still work no?

r<1 in my messed up geometric series?

i guess the ratio test might be a better choice

it will deal with the situation better

Dominic Michaelis

2:25 PM

no they all fail

even thought $\sin(n)< 1$ for all $n \in \mathbb{N}$ we find a subsequence converging to 1

Faust7

no the ratio teest will let u bound 0\geq |sin(n)| and |sin(n+1)\ <1 which will elave u with 1/3 <1 so it converges

Dominic Michaelis

you missed a +2 there

Faust7

the +2 will be on the top and the bottom

Lord_Farin

Yes, and $\dfrac{7+2}{3+2} = \dfrac 7 3$. Or not.

Faust7

so they cancel out

Dominic Michaelis

2:29 PM

@Lord seems legit ;)

Lord_Farin

@DominicMichaelis It will probably be reasonably easy to prove $0 = 1$ from there.

robjohn

@MJD Thanks, but Mariano, mixedmath, and Willie Wong will be hanging on, too.

pourjour

@Charlie Hi

Faust7

define it like this (sin(n+1)+2)^{n+1} *3^{n} / 3^{n+1} * (sin(n)+2)^{n}

dam that gives you 1 as well

i know it converges

how do you show it?

robjohn

@Faust7 there is no $r$ that works.

Faust7

2:33 PM

yeah i have figured that out

Charlie

@pourjour hi Soufian, how are you?

pourjour

@Charlie fine thanks and you?

Lord_Farin

@Faust7 You will probably have to use some intricate argument estimating how many $n$ have $\sin(n)$ close to $1$, and show that there are "few enough" of them.

Charlie

@pourjour I'm fine.

pourjour

@Charlie we started leaning organic chemistry (acid carboxylic ....)

MJD

2:50 PM

@robjohn Right, thanks for the reminder! The best moderators are the ones you can forget about.

3

robjohn

3:12 PM

@Faust7 You do? Heuristically, it would seem to diverge.

Suppose that $y=\sin(k)$ the sum for the geometric series with ratio $\frac{2+y}{3}$ is $\frac3{1-y}$. The probability of getting a sin equal to $y$ is $\frac{\mathrm{d}y}{\pi\sqrt{1-y^2}}$. Since $\int_{-1}^1\frac3{1-y}\frac{\mathrm{d}y}{\pi\sqrt{1-y^2}}$ diverges, I would expect the series to diverge.

@Lord_Farin Ah, I just saw your comment. See my last comment to Faust7 :-)

Matt N.

3:34 PM

Meh. Wrote a really stupid bug into my code as a consequence of auto completion. Then spent 6 hours trying to find it. This is why I hate writing code.

@JonasTeuwen Ayt?

Heh : )

Charlie

@pourjour that's cute :)