Mathematics - 2013-01-26 (page 1 of 2)

Apparently, a new user thought I "copied" his/her answer, and I guess flagged a moderator. I tried to appease him/her by deleting my answer; it wasn't anything noteworthy to bother keeping...

user19161

@amWhy Ah, but what happened to make him think it was copying?

user19161

Is the question asking about 1+1=2?

user19161

There are not many ways one can say that 1+1=2.

amWhy

They were both similar...yeah, it was that sort of question; obvious approach...I was thinking of deleting my answer anyway, since my post followed his/hers, in timing.

robjohn

1:07 AM

@amWhy It has happened to me, too. I usually do the same thing (delete mine)

amWhy

@robjohn Certainly - nothing to fret about...:-)

@JasonBourne 2 = 1 + 1

user19161

If they are sufficiently distinct keep them.

user19161

If they are too similar, delete them.

amWhy

@JasonBourne Yup...

robjohn

parktime... bbl

user19161

1:09 AM

@robjohn Have fun with doggie!

Alexander Gruber

yo i got a question about probability.

say i'm trying to estimate the probability that the product of two invertible matrices with finite order has finite order

with entries in {-1, 0, 1}

never mind actually.

BenjaLim

3:11 AM

@MarianoSuárez-Alvarez Hey

Is there a typo here?

0

Q: Typo in Marcus' $\textit{Number Fields}$?

I am doing Problem 5.10 of Marcus where it is given that $m$ is a square-free negative integer and that $\mathcal{O}_K$ is a PID where $K = \Bbb{Q}(\sqrt{m})$. Now in part (b) of this problem he asks: 5.10 (b): Suppose $p$ is an odd prime such that $m < 4p$. Show that $m$ is a non-s...

anon

mfw MO comments have no edit window

BenjaLim

3:57 AM

@Sanchez hey

anon

@OldJohn I posted a p-adic question on MO you may have interest in.

BenjaLim

@anon Man I can't believe

students nowadays just want to study advanced stuff very quickly

without the basics

anon

ain't-nobody-got-time.jpeg

BenjaLim

@anon huh?

Sanchez

@BenjaLim, hey

BenjaLim

4:16 AM

@Sanchez hey

@Sanchez I can't believe my friends who have just taken a basic course in group theory

very very basic

want to learn category theory :D :D

For me, if you don't even understand the what the universal property of the quotient is

You are not fit to learn just yet what a derived functor is.

@WillJagy yo

Will Jagy

Alright, yo. We'll go with that

BenjaLim

@WillJagy I wonder why students nowadays are so impatient

Of course everyone wants to be Gordon Ramsay

but who can be one without first learning how to peel and slice a cucumber?

Will Jagy

By and large, I think it is the effect of computers, calculators, and so on. They give support to anyone who feels it is not necessary to understand anything, or remember much either.

BenjaLim

I agree.

@WillJagy If I see a student who hasn't even internalised the definition of a ring, that person is definitely not ready to learn about the Yoneda Lemma.

Will Jagy

Well, there you go. There was a little while after World War II when science and mathematics were important in the US. But most of the population still didn't care. Now, computers have made significant inroads into mathematics education, so even the tiny population who would be doing mathematics are affected to some extent.

well, night

Crazy Buddy

4:35 AM

Hi guys...

I require some help regarding the TeX

how to use teX for equations...

like say - you wanna show that this expression is eqn. (1)

Any help..?

someone here alive..? :P

Sanchez

@CrazyBuddy, use eqnarray?

or just \label, actually

Crazy Buddy

a sample maybe good..?

coz I require it over Physics.SE ;-)

I'll see...

Sanchez

@CrazyBuddy, hmm, it doesn't seem to work here. What about just manually add (1), (2), (3)?

Crazy Buddy

I tried that... - manual adding is a bit nasty ;-)

Crazy Buddy

4:57 AM

never mind...

Anyway, thanks for responding.. Sanchez ;-)

eephyne

7:07 AM

hi everyone

could someone light me on this

i try to make logarithmic spiral

and following the formulas i found on wikipedia (or wolframalpha)

$user image$

but r = a *exp(b*T) work

does i misunderstood the first formula ?

Gustavo Bandeira

7:24 AM

@eephyne I guess it's better to ask in the main.

robjohn

@mick used is the opposite of left

@mick and right is the opposite of wrong

eephyne

I was thinking that was a little to "light" to be q main question

too*

robjohn

@CrazyBuddy You can use \tag{1}

@CrazyBuddy or \label and \ref

Crazy Buddy

@robjohn Yeah... I saw that already ;P

Anyway, thanks John :-)

Ohh... Rob John...

robjohn

@CrazyBuddy sorry, I just saw \label I missed the rest

Crazy Buddy

7:31 AM

No worries... I'm happy that some guys noticed it :P

Matt N.

7:48 AM

Morning everyone.

@robjohn Looks like I missed you yesterday. And I didn't get pinged, either, I only saw you replied because other messages pinged me and I clicked.

knocker

Hello everyone..

Matt N.

Hello.

knocker

I need help to brush up my maths..
specifically Linear recurrence relations

can somebody point me to good online material..

1st question.. is ther way or formula to find nth fibonisis number..? i mean when n is very large..

2nd how that is derived from f(n)=f(n-1)+f(n-2)

Matt N.

@knocker You could look at page 8. (bottom of)

bbl

knocker

Thanks man

robjohn

8:03 AM

@MattN. hmm... how are you now?

@knocker $\displaystyle F_n=\frac{\left(\frac{1+\sqrt5}{2}\right)^n-\left(\frac{1-\sqrt5}{2}\right)^n}{\sqrt5}$

BenjaLim

@robjohn hi

robjohn

@BenjaLim hey there...

BenjaLim

@robjohn It's australia day today

robjohn

@BenjaLim what about Australia does that celebrate?

the date commemorates the arrival of the First Fleet at Sydney Cove, New South Wales in 1788 and the proclamation at that time of British sovereignty over the eastern seaboard of Australia (then known as New Holland)

BenjaLim

8:18 AM

@robjohn Sometimes the celebration of australia day causes a lot of pain

last year the prime minister was swarmed by some demonstrators

@robjohn Not sure if the natives in america

@robjohn Sorry for deleting these I don't want to say anything politically incorrect in an online chatroom.

robjohn

:7843010 There is never an end to such upset. Things get less inflamed, but they are not happy.

BenjaLim

@robjohn They say there are three things one should never discuss: sex, politics and religiion

robjohn

@BenjaLim yes. However, I don't think we've said anything controversial. Just factual so far.

BenjaLim

@robjohn But some people in australia are really really sensitive about this stuff

robjohn

:7843017 Now, that would be controversial...

BenjaLim

8:25 AM

@robjohn that's why I deleted it

Jonas Teuwen

Here they combine the three in one discussion.

David Wheeler

8:36 AM

@BenjaLim if i can't discuss sex, politics, or religion...then what are we going to talk about? ...math?!?

BenjaLim

yes

David Wheeler

let's try combining the subjects in pairs: do you think god is a mathematician? are the integers "hot"? are you going to vote algebraicially next election?

BenjaLim

no the integers are not hot

whether god is a mathematician depends on your definition @DavidWheeler

David Wheeler

my view on international policy: taking Obama mod 3, we see he is not prime. QED.

which definition: "god" or "mathematician"?

BenjaLim

mathematician and god

btw @DavidWheeler

the definition of god

is not a well - defined definition

David Wheeler

8:42 AM

well people certainly argue about its definition a lot.

the english word has a root meaning of something akin to "ultimate super-moral entity of goodness"...the existence of which is the contention of goedel's "proof of god"

BenjaLim

@DavidWheeler what are you up to now

David Wheeler

people being what they are, tend to anthropomorphize concepts....leading the the quaint image of '"some bearderd guy on a big chair in the clouds"

at this very moment i am in the process of trying to finish the repairs on my computer.

this video game i played burned up my old graphics card, so i got a new one, and a bigger PS

this ancient piece of 20-th century technology has a "grandmother board" at this point :(

trying to tickle better performance out of antiquated architecture is almost beyond my limits of technical comprehension of electrically thingymabobs

robjohn

9:00 AM

@BenjaLim well, perhaps the first 68 integers are not...

David Wheeler

@robjohn roflmaopmpzomgha!

robjohn

@DavidWheeler that's what I get for coming into a conversation late. :-)

err... joining

@robjohn: hi

@Ilya hey there :-)

howdy

9:11 AM

@Ilya anything exciting going on today?

Ilya

mmm

working on Saturday. exciting?

robjohn

@Ilya on Saturday?

Ilya

yes

robjohn

@Ilya do you work on holidays as well?

Ilya

depends

robjohn

9:15 AM

@Ilya time to heat water for tea...

Ilya

@robjohn: just do it! don't mind circumstances )

how is the weather?

robjohn

@Ilya It is raining this weekend... but the storm is not as bad as predicted

Ilya

@robjohn that's nice

robjohn

@Ilya I'd like the rain. We really need it.

Ilya

you don't seem to have is often there, do you?

robjohn

9:21 AM

@Ilya Perhaps you didn't notice when you were here, but we are very dry here.

@Ilya not as much as other places.

Ilya

@robjohn well, it was foggy

Garbage Collector

Hi folks, I have a question about mathematical writing.

robjohn

@Ilya That's true. I forgot that that day was uncharacteristic.

@GarbageCollector Ooh... math. What are you doing here?

@GarbageCollector what's your question?

Garbage Collector

If we have to write algebraic operation steps, which one we have to use aligned in displayed mode or align*?

\documentclass{article}
\usepackage{amsmath}

\begin{document}
The following calculation is a trivial example
\[
\begin{aligned}
a(x+b)^2 - ab^2 &= a(x^2 + 2bx + b^2) - ab^2\\
&= ax^2 + 2abx + ab^2 - ab^2\\
&= ax^2 + 2abx
\end{aligned}
\]

The following calculation is a trivial example
\begin{align*}
a(x+b)^2 - ab^2 &= a(x^2 + 2bx + b^2) - ab^2\\
&= ax^2 + 2abx + ab^2 - ab^2\\
&= ax^2 + 2abx
\end{align*}

\end{document}

I am really confused.

I need conventionally adopted (by professional mathematicians) rules. :-)

robjohn

@GarbageCollector here is something worth a look

Garbage Collector

9:30 AM

@robjohn OK. Thanks. I am reading...

Old John

@anon That looks interesting. I have found the tree idea for visualising p-adic distances really useful for $\mathbb{Z}_p$ and $\mathbb{Q}_p$, but my intuition for $C_p$ and $\Omega_p$ is really poor - so far so at the moment I don't have any ideas about differences for algebraic or transcendental elements . I find it curious that even on MO, p-adics questions don't seem to generate a lot of views.

robjohn

@OldJohn I think that part of the reason is that on sci.math, there used to be a lot of cranks posting questions about p-adics.

@GarbageCollector I don't think that either has been generally deprecated. Use whatever works best for you.

Old John

@robjohn Ah - That is interesting. I never looked at sci.math, but heard there used to be a lot of argumentative stuff on there. We seem to be able to keep the cranks under control quite well on MSE :)

robjohn

@OldJohn This is part of the reason I moved here from sci.math. I have never looked back.

Sanchez

@robjohn, how would you compare sci.math to here, or other math forums (say AoPS)? I heard about sci.math a long time ago but never really participate there.

Old John

9:38 AM

@robjohn I reckon that here, the nonsense seems to be limited to the chatroom, and away from the main site :)

robjohn

@Sanchez It was very good when I was working at Apple (early to mid 90s), but after 2000 or so, it started a slow decline.

@OldJohn yes, the chatroom, while supposedly an interactive math forum, does play an important role of defusing the need to act out.

Sanchez

@robjohn, was it similar to mathoverflow now?

robjohn

@Sanchez well, it was open to any level of question, so in that respect it was more like MSE... sci.math.research was more for advanced questions and discussions.

Sanchez

I see.

Ilya

9:57 AM

@robjohn: do you have an access to Math Sci Net?

robjohn

@Ilya I have never tried.

Ilya

I need to find a bibtex entry for one book from a reliable source

robjohn

@Ilya for what?

Ilya

Lindvall, Lectures on coupling method

robjohn

@Ilya didn't find anything. Is everything spelled properly?

Ilya

10:02 AM

maybe on THE coupling method

only

like here

robjohn

I found the proper title...

@book {MR1180522,
AUTHOR = {Lindvall, Torgny},
TITLE = {Lectures on the coupling method},
SERIES = {Wiley Series in Probability and Mathematical Statistics:
Probability and Mathematical Statistics},
NOTE = {A Wiley-Interscience Publication},
PUBLISHER = {John Wiley \& Sons Inc.},
ADDRESS = {New York},
YEAR = {1992},
PAGES = {xiv+257},
ISBN = {0-471-54025-0},
MRCLASS = {60-01 (60J10 60K05 60K35)},
MRNUMBER = {1180522 (94c:60002)},
MRREVIEWER = {Uwe R{\"o}sler},
}

Ilya

thanks!

Jonas Teuwen

10:23 AM

Coupling??

We do decoupling.

Is Ilya our inverse?

@Ilya Are you in your office?

Ilya

no, fortunately I'm at least working from home

crafting a report for Frank

Jonas Teuwen

Good.

Happy to hear that Frank is of any help.

user19161

10:52 AM

OK, the new way of changing your picture now is working perfectly, no need to use gravatar anymore.

Novice

11:46 AM

@JasonBourne Hush.

Mats Granvik

12:39 PM

x
x*x
x*x*x
x*x*x*x
x*x*x*x*x

x^1 + x^2 + x^3 + x^4 + x^5+...

Frank Science

12:51 PM

Must a convex mapping be continuous on a convex set?

Novice

I receive parental pressure. My parents keep reminding me the sad truth that I am not so great at mathematics. They threaten that they'd cut my internet off if I don't qualify for the Brilliant.org camp. How do I cope with the pressure?

Frank Science

What's your degree?

Novice

@FrankScience I don't know how to describe it exactly.

Frank Science

Ugh, that seems a problem set, and I think there's no serious problem if they cut off the Internet without which you can still study mathematics well.

Good luck.

Matt N.

1:09 PM

@robjohn Ok-ish, thank you. Slept with my neck twisted so that now I have a pain in the neck and a headache. What about you?

robjohn

@MattN. Doing okay. There have been few questions that I've gotten to fast enough to answer. Too many flags keeping me busy.

Theorem

1:22 PM

Hi everyone

user19161

@robjohn You should renounce your mod status then and answer questions instead!

robjohn

1:48 PM

@JasonBourne answers are important, but the maintenance of the rest of the site is also.

@Novice why are your parents so determined that you go to brilliant.org camp?

Garbage Collector

How can I explain 0.9999... = 1?

robjohn

@GarbageCollector ask what the difference of the two is.

kahen

If they were different, there'd be a number between them...

robjohn

@GarbageCollector if the difference is $0$, they are the same.

Garbage Collector

@robjohn I don't know.

robjohn

1:52 PM

$1-.9999=1/10^4$

$1-.99999999=1/10^8$

Garbage Collector

@robjohn But ... represents infinitely repeated.

kahen

Certainly we must have $0.999\ldots \leq 1$. Now, what happens if we add any $\epsilon > 0$ to $0.999\ldots$? We get something greater than $1$, so we must actually have equality in the inequality we started with. This is a standard technique for showing that two real numbers $a$ and $b$ are equal. if $|a-b| < \epsilon$ for all $\epsilon > 0$, then $a=b$.

robjohn

for any positive difference, $\Delta$, you can find an $n$ so that $1/10^n\lt\Delta$

Garbage Collector

I have no idea how to explain it to my friends without using calculus.

robjohn

@GarbageCollector they have to understand limits... without limits .99999... doesn't make sense

Garbage Collector

1:56 PM

@robjohn The book exercise just says: find 0.99999... in rational form. One method use the idea x=0.9999... and then 10x=9.9999.... You know the remaining.

kahen

One could also argue that $$0.999\ldots = \frac{9}{10} \sum_{n=0}^\infty \left(\frac{1}{10}\right)^n$$ and then use the formula for summing a geometric series. But that's just hiding what's really going on.

robjohn

@kahen All of these arguments require knowledge of limits.

Novice

2:17 PM

@robjohn That is because they are parents. :-)

The wittiest answer ever seen.

3

BenjaLim

I hope I don't get downvoted on MO.....

arber

4:03 PM

hello to all

amWhy

4:16 PM

@arber hello! Just happened by...

I'm having a slow day :-(

Mats Granvik

0
1-1
1+1-2
1+1+1-3

Jonas Teuwen

5:00 PM

Hello. I am the book of all answers.

Jonas Teuwen

5:29 PM

@MichaelGreinecker Did Ilya delete his question?

Ilya

5:46 PM

Shall I expect Ethan to delete his question as well?

Jonas Teuwen

@Ilya Did you delete your question?

Ilya

@JonasTeuwen no,why?

Jonas Teuwen

I try to find the one with the kernels.

What do you have to do when you think your neighbor is a homosexual?

Mariano Suárez-Alvarez

nothing

unless you are interested in him of course

Ilya

@JonasTeuwen depends on your preferences

oh, Mariano was first :)

Jonas Teuwen

5:52 PM

Shall I go bring him some nuts and chips?

He was licking his lips when I was standing in the elevator with him.

While looking at me!

Looked kind of creepy and cool at the same time.

Ilya

@JonasTeuwen just lips? huh!

Mariano Suárez-Alvarez

are you that surprised someone might find you atractive?

Ilya

am I correct, your tone suggests you think Jonas is attractive? @Mariano

Orange Harvester

suppose I have a boolean function $f$ which takes in some set $A$ and spits out a boolean value. And I have a set $A$ such that $f(X)= \text{true}$ for all $X \subseteq A$. Is there some formal term which will describe the relationship between A and $f$.

Mariano Suárez-Alvarez

not my type, really :D

Ilya

5:56 PM

and finally, somebody is in favor of 4's

@OrangeHarvester here $f(X)$ is the image of $X$, so simply $f(A) = \text{true}$?

Transcript for

$Mathematics$ Mathematics