12:11 AM
@AlessandroCodenotti Will I do?
@Thorgott if you can define a meromorphic 1-form, just take the dual notion.

Hello
@TedShifrin you are here from a week ago :)

@TedShifrin This answer reads like a joke, outside of the fact that it's also a perfectly sensible answer.

I only know an insensible way of defining meromorphic 1-form, no good ones, that's why I need to learn the bundle perspective

2 hours later…
2:10 AM
@WhiteForce I am?
@Thorgott You can talk about a 1-dimensional complex manifold and a local holomorphic chart/coordinate $z$.

2:45 AM
@WhiteForce He was not here last night, so I disagree

3 hours later…
5:48 AM
Guys , when yesterday I posted a question of modulus function
then , when question says mod of -5
why is it always 5. In the examples I gave , I also found negative value of x
Like mod of 2x-3 = 9 has values of x = 6 and -3

@Physicsismylife I've never heard of saying mod a negative. The negative makes no difference. Mod $5$, $2x-3=9$ means $x=6$ which is the same as $x=1$ mod $5$. Where did you get $-3$? That isn't right.

@Physicsismylife $|x|=\left\{\begin{array}{rl}x&\text{if }x\ge0\\-x&\text{if }x\lt0\end{array}\right.$
so $|x|\ge0$
the case when $|x|=-x$ does not mean that $|x|\lt0$.

Where did absolute value come from, @robjohn?
Oh, I was doing mod 5 arithmetic.

Yeah, they mean $|x|$ when they say "mod"

Yeah, I think you're right.
But what is "the mod of $2x-3=9$"?

6:01 AM
2x-3 = 9 and 2x-9 = -9

$|2x-3|=9$

Oh, $|2x-3|=9$ is the question?

I saw this on YouTube that we write It like this

@Physicsismylife or

@TedShifrin @robjohn

6:02 AM
I'd assume "the modulus of 2x-3 equals 9"

This is not usual English use for mathematics.

@robjohn yes. Or we have to write
@TedShifrin did you get how I got -₹

So, for the second possibility, you get $x=0$, not $x=-3$.

No.
How did you get -3?

6:04 AM
2x-3 = -9 , 2x = -6 , x = -3

Oh, you wrote the wrong equation the second time.
Right, $x=-3$ is correct as the other solution.

There are two solutions.

then why do we say that mod of -5 is always 5

Because mod means distance from the origin (0) on the number line.
The distance from -5 to 0 is 5.

6:06 AM
But in 2x-3 question , I got x = -3 as well. Which is negative

That's fine. No one is saying you have to take the mod of the answer.

@TedShifrin ok . Got it thanks

Cool.

One more thing
|x|/ x = x /|x| right

Yes (assuming x isn't 0).

6:09 AM
Ok.Great

and $x$ is real ;-)

Ok.@robjohn
Why is the interval of greatest integer function only from (-infinity , x)

Huh?

Like why is x not till + infinity

@Physicsismylife not sure what you mean.

6:11 AM
[x] = greatest integer in the interval (-infinity,x]
Exact line pasted now

[x] is in (x-1,x]

Yes, that's correct, but I would never say it that way.
Just think of it as the largest integer to the left of (less than or equal to) $x$.

For example if it is 4 , then interval is from 3,4 right

(3,4]
which means 4

Just think of rounding down to the nearest integer.

6:13 AM
because it is an integer

Why did my teacher write - infinity then ?

no idea

@TedShifrin and @robjohn got that part
Thanks still.What you wrote makes sense as well

The teacher is saying look to the left of x (including x) on the number line (so that goes down to $-\infty$) and take the largest integer. I wouldn't say it that way, but it's OK.

what they wrote is not technically wrong, but it is not the easiest way to understand it, imo

6:15 AM
Hmm yeah
Also , I can’t say that this interval means range of x right

Nope.
Don't get sloppy with your language.

@Physicsismylife: if you want to get the most from this room, you might look into MathJax and install ChatJax (the installation page is listed at the top of the sidebar to the right)

Good grief. Well, damn, there sure looks to be something missing. Did you click to see if there were unviewable characters?

6:19 AM
doesn't seem to be

I have gotten people mad at me when I've complained that things don't make sense, but this seems a clear case. What is that person's problem?

shrug
i mean, I think the "OP looks defensive" remark probably didn't help but

Somebody called me sarcastic and mean or something a day or two ago in here, and I wasn't even at that point — perhaps a day earlier I had been, though.

overreact much
yeah

I mean, seriously, if someone doesn't know what "at least" means, we have a long way to go with probability problems.

6:21 AM
i do wish I'd said my comment a bit more clearly, e.g., "You say you have a calculus-based solution, but you haven't actually said what the answer is supposed to be."

Yes, that would have helped.

so it goes

$P_{\{\varnothing,\{\varnothing\},\{\varnothing,\{\varnothing\}\},\{\varnothing,\{\varnothing\},\{\varnothing,\{\varnothing\}\}\}\}}$ ain't nothing.

It ain't much to look at.

6:28 AM
@robjohn ok.
guys , if you see this . This is how my sir drew the [x] on the number line

@Physicsismylife the latter one is $-4$

He took it to - infinity range

All you have to do is start walking to the left at $x$ and stop at the first integer you come to. You are never going to have to go all the way to $-\infty$, of course.
If you understand what's going on, stop insisting on his definition over and over.

@TedShifrin Yes.Got that from your point.But why would he draw this diagram then? It’s just that I can’t be easy to say that my sir is entirely wrong here. You getting it right

We've already told you he is NOT wrong.
We also told you none of us would explain it that way. We can't keep discussing it. Ask him why he chooses to use that instead of something else.

6:33 AM
your sir used a description that made sense to him and thought it would make sense to you

Ok.@TedShifrin

if it didn't, then asking "why" isn't going to help much

I'm sure plenty of times my students wondered why I used a different explanation or definition. Of course, when they asked me, I tried to convince them why I was right :)

Ok@TedShifrin and @Semiclassical

Ok, this is pretty ironic. A misprint in a textbook I am reading has a paragraph beginning with Step ${}$.

6:38 AM
LOL ... the missing step.
Or ... step lightly?

Suppose $X$ is irreducible of dimension $0$. Doesn't sound like a killer step. Maybe intentional.

Well, Step 0 is allowed.

@KarlKroningfeld what kind of an object is $X$?

an irreconciliable object?

@robjohn It is the hazy middle between W and Y.
Or, to quote my stupid bio, What does it mean to find 'x', anyway?

6:46 AM

[x+[x+[x]]] , can we also where this like this [x]+ [x]+ [x] .

No. Try lots of examples.

Hindsight is 20/20 @Ted

6:52 AM

Why did we write it the 1st way which is a bit complex than 2nd one

@TedShifrin Who knows?
Any historians?

@TedShifrin ok.

actually he's right
because [x+n] = [x]+n for any integer n

7:07 AM
"The Malagasy Ariary is the official currency of Madagascar. The Ariary is one of only two circulating currencies in the world whose division units are not based on a power of ten."
So I dont understand how this means we calculate the fractional part of this currency
I'm working on an app involving currency conversions - I just did a quick search to see whether there were currencies with odd fractional parts and found this edge case.

do you have an example in mind?
like, of what the dollar value of X ariaries would be (or vice versa)

I dont even know how to *think* about decimal parts of money not based on power of ten :(

Closest example I can give: converting USD to XFA - I know USD uses 2 decimal places (for presentation, although more are used in sensitive calculations) and XFA does not have a fractional component.

If I were to convert 5 USD to XFA at a rate of 1 USD == 568 XFA, I'd end up with 2840 XFA
If I were to convert 5,000 XFA to USD, I would get 8.80282 USD

hrm
both of those seem unambiguous, though. do you have a case where you're not sure?
oh, but that's XFA not Ar

@LeakyNun \begin{align} \lfloor x+\color{#C00}{\lfloor x+\lfloor x\rfloor\rfloor}\rfloor &=\lfloor x+\color{#C00}{\lfloor x\rfloor+\lfloor x\rfloor}\rfloor\\ &=\lfloor x\rfloor+\lfloor x\rfloor+\lfloor x\rfloor\\ \end{align}

when i grew up it was pounds shillings & pence (amusingly denoted lsd).

7:21 AM
I do not - That currency is not even part of what I need to account for at the moment.

From wikipedia: "Today, only two countries have non-decimal currencies: Mauritania, where 1 ouguiya = 5 khoums, and Madagascar, where 1 ariary = 5 iraimbilanja.[1] However, these are only theoretically non-decimal, as in both cases the value of each sub-unit is too small to be of any practical use and coins of sub-unit denominations are no longer used."

culture is confusing

Just thought it wise to leave a note in the code about how to handle it later

@robjohn yep

I suspected that while coins of these sub units aren't used, it might be relevant in future to account for such tiny units when doing sensitive calculations - just how you wont find sub-cent coins in the US, but sensitive calculations in USD use sub-cent values

i don't have anything useful to say, but you might be amused by this old bit of TV

7:25 AM
I am having confusion in how to make notes actually . For example , you sir gave taught you about quadratic functions today . Then , started with trigonometry. Now, let us say there were some examples you had to write before starting trigonometry for quadratic functions . You then write those examples in the chapter of trigonometry. So this way I think things can become a clutter when you are going to revise notes.

So , should I make a notebook or just wrote on separate pages
separate pages mean like not a notebook but just A4 sheets
That way , I can just attach whatever information is needed at right position

@Physicsismylife any chance you can use a binder with hole punched pages?
as opposed to a notebook

The problem with sheets is that when I use my punching machine and put them in a file
those pages tear up after some @Will

haven't heard a guinea for at least a month...

Slowly as you keep openers them
Openers = opening them I meant here

Take mental notes

7:28 AM
Understandable :) I remember lugging around an ugly binder in high school with pages sticking out
Hanging on for their dear lives by only 1 hole

Yeah.@Will
any idea
@KarlKroningfeld I am not that great like you yet

nothing that doesnt subject you to loose pages still unfortunately

Hen you open the binder right. Slowly the pages also start to to torn away easily. That makes it look worse .

@Semiclassical "OPTIONS! OPTIONS OPTIONS!"

"How do we make money? The answer is simple: Volume."

7:31 AM
haha

Guys , any idea to help me
save my notes and make them easy for me so that I can revise them

@Physicsismylife the best idea i have is to use onenote. I have long discarded physical notebooks, for the ability to copy paste my notes to shuffle around as needed
Not practical for everyone unfortunately

Typing notes sounds like a bigger pain in the ass than it is.

I use a surface book - onenote is amazing with a nice screen and pen

7:33 AM
is pen & paper passé?
paper is cheap.

eh

Use pages and write page numbers on them
What if I use paper clips instead of binder

I used to do this back in my country haha. The amount of notes we got was insane throughout middle school. No one handed out printed sheets of material for you to put in your binder like they do in the US. Teacher wrote everything from their notebook and students copied it all :sobs:
Everynotebook I got, i spent a few hours writing numbers on all pages - sometimes skipping numbers by mistake lol. It was great for writing thing like "see X on page X"

i think there is some learning value to writing stuff down.

7:37 AM
What if you wrote sth on a page that you don’t need
will you remove the page

Okay dude are you a troll
This is funny, the exceptions you're trying to consider haha

@Will why ?

To answer your question - No, i wouldnt remove the page. I leave it, possibly cross out the bad content

@Will they are actually true and I am in tension of it

@Physicsismylife there are bigger things to be tense about!

7:39 AM
Understandable, are you just now entering a stage where you must take more notes than you;re used to? or you've entered a very competitive academic scene?

Competitive
JEE

jee?

Entrance exam to engineering
Out of 1.5million , 10000 get best colleges
I want to study computer science which is given to top 1000 students only

I see :D

For your notes, just take the time to write page numbers when you buy notebooks. Refer to content on specific page numbers as needed.
@Physicsismylife my broda :D

Ok.
I’ll try this

7:44 AM
@Physicsismylife Good luck on your path to a Computer Science career!
I enjoy it so much although it can be so frustrating at times - ever wanted to beat up your computer? XD
"behave and do what I want, dammit!" - while coding something wrong but not realizing lol

Hahaha

8:02 AM
33 hours to go...

yes :D

If f(x) or y = $(x-1)^2$ , then let us say g(x) or z = x^2 . Then z-1 or g(x-1)= x^2 - 1 right and not $(x -1)^2?$

could you express that less clearly?

If f(x) = $(x-1)^2$ , then let us say g(x) = x^2 . Then why is g(x-1) = $(x-1)^2$ ??

i really have no idea what you are asking.
what has the specification of $g$ got to do with the specification of $f$?

8:07 AM
It is just written g(x)to explain more

ok, if you have a quick actual question i can help, otherwise i am off to bed...

Did you get it but ?
What I am trying to say

no idea. i need full sentences, actual questions, etc.

f(x) = x-1) ^2 . Got this

is that a definition of $f$?

8:09 AM
.It is just written that way

are you asking a question or just typing stuff?

i don't mind either way, but if it is the latter i am off to sleep.

but trying to make you understand my question first
Then , g(x) = x^2

my comprehension is fairly good, but you need to communicate clearly.

8:11 AM
@copper.hat I am trying now.
@copper.hat got this

what do you mean when you say 'then $g(x)=x^2$?
what is the then part?

Ok.It is just another function g(x)

so the then is superflous.

Then is just English. Ofc it doesn’t mean anything in maths
right now

all we have is english here, i am a monoglot.
and this has taken 5 mins to get nowhere!

8:13 AM
Thrn I write g(x-1) = (x-1)^2

Got this part

excruciatingly

So , I didn’t get this part actually
why is it not x^2 - 1^2

what part? so far there are just definitions.
sorry, until you actually pose a question i cannot comment.

8:14 AM
g(x-1) the way we converted it from g(x)

huh???

I didn’t get the conversion

who converted what>

What is $g(y)$? @Physics

One second . I’m thinking @KarlKroningfeld
g(y) = x-1^2
with brackets ofc

8:16 AM
huh?

if you mean f(x) = y

No, $y$ is just some new variable.
Sorry for the confusion, if you're thinking about the xy-plane. Not that y.

I am not getting what to write it equal to then

g(x)=x^2 is telling you what to do if you give it an input x. Namely, square the input x. But I can call x something else. I am suggesting to call it y, because why not?

Yes@KarlKroningfeld right . Do you mean x^2 = y right
g(y) = y
I suppose

8:19 AM
No, no.
I'm just calling the variable by a new name, 'y' instead of 'x'.
So, the way in which g operates isn't changing.

ok. g(y) is new variable ok
Got this

Nope :) 'y' is the new variable. You can tell what g(y) is, actually.
Here's something more concrete. What is g(2)?

What process did you use to get 4.

g(2) = 2^2 I used

8:22 AM
Ah, so you replaced x with 2 in the expression g(x)=x^2

Yes
replaced 2 with x . I got 2^2

I am suggesting the same, except instead of 2, you have y.
So, it should be g(y) = ...

ok then it y^2

Yes. :)

Thanks got it so far then

8:23 AM
Now, here's the wizardry: you have this equation g(y) = y^2.
You can swap y out with something else. How about x-1?
So if you replace y with x-1 on the left, you get g(x-1).

then y = x-1
yes
it is x-1 to whole square

What's that in symbols?

Where @KarlKroningfeld

or g(*) = *^2

g(x-1) =( x-1)^2

8:25 AM
yeah
and that is the same thing as f(x)
2

@user85795 yes.Got it l thanks a lot @KarlKroningfeld

::applause::

i completely missed what the issue was there.

notation

$\lambda$ substitution.
good night folks.

8:29 AM
cya
The substitution principle is simple only in principle.

Haaaaaah ahaha

8:45 AM
hm

whatever

5 minutes is picayune in the scheme of things

@KarlKroningfeld why do you know this very particular word lol

GRE vocabulary

Uncommonly used words which have simpler, more common equivalents seem like very weak/worthless components of a vocab exam :/

8:52 AM
I like to spice up my expressions.
With words like scheme.

How to solve this

Hello guys..

Hello there

I am solving exercises from book.not getting these questions
a unique number because it is neither a prime number nor a composite number. It has only one factor, i.e, the number itself
Is this what they mean by in 2nd question
Anyone,any idea

9:25 AM
would anyone know of a place/website/forum where I can get good, difficult high school math questions? Or where people trade maths problems?
For example, I am looking for rates of change problems similar in difficulty to this:
of course, I appreciate even harder questions ;)
Perhaps something liek JEE or Korean CSAT type questions
My countries math syllabus isnt as strong as those countries
sorry if thats a bit of a wierd question haha

9:45 AM
Most Toughest exam
quesrions
you can get them anywhere online
@user71207

thank you
do they usually have worked solutions?

10:37 AM
any example of non-analytic function that satisfies cauchy-riemann equation?

why is that?

because satisfying the Cauchy--Riemann equations makes a function analytic

@AlessandroCodenotti Hi.

10:50 AM
hello everyone
Any ideas on solving the equation r^2(d/dr* (r^2 dv/dr)))=cv, for v=v(r), where c is a constant?
using elementary methods...

Is CET a commonly used abbreviation? Like if I say 15:00 CET, would an average European know what I mean?

@Balarka by any chance do you know if there is some kind of results along the lines of "if $G\curvearrowright X$ with a $G$-invariant measure $\mu$ and $G$ is topologically transitive, then the action is ergodic"?

@feynhat Central european time?

Yeah

@LeakyNun Well I know if the function satisfies the Cauchy-Riemann equation and each real and imaginary part functions have continuous partial derivatives then the given function is analytic

10:53 AM
@feynhat I know that the abbreviation refers to the central european time zone, but I need to look up when that is exactly because of DST (sometimes it is the same as my time, sometimes there is an hour of difference, I think)
But yeah if you're giving the time for a seminar or something it will be recognized

Okay cool.

I learned about the Cauchy-Riemann equations today, and my instructor used the following example to show that differentiability is not guaranteed if the partial derivatives are not continuous. Let  f(z)=f(x+iy)= \begin{cases} \frac{xy(x+iy)}{x^2+y^2},&\quad\mbox{$z\neq 0$}\\ 0+0i,&\quad\mbox{$... 11:14 AM strange.. the example satisfies Cauchy-Riemann on (0,0) but not in general. It seems hard to find the function satisfying Cauchy-Riemann on the whole domain but not differentiable I mean you can just look at the theorem I quoted or the article yes then what if the function is not bounded on D? then maybe the article has a counter-example ^^ 11:51 AM @Astyx @Semiclassical our prof just defines$f(T)(x) = \sum_n f(\lambda_n)\langle x,e_k \rangle e_k $for an ONB of eigenvectors to nonnegative eigenvalues that ought to work Huh wait actually I'm a bit surprised Usually you'd define the square root of$-\Delta$as multiplication by k, and this gives negative eigenvalues whereas your prof's def only yields positive eigenvalues I'd have to give this some more thought but I'm a bit short on time rn Weird This is normal, everyone disagrees on whether$\Delta\$ is pos def or neg def