Mathematics - 2015-03-22 (page 4 of 6)

Owatch

16:00

Gute Morgan Ted.

Gato

16:13

@DanielFischer Guten Tag. I would like to prove that if $f$ is a continuous function on a open set $U$ (non empty) witch admits locally antiderivatives then $f$ is holomorphic on $U$. I cannot get that, I just have that $f$ is holomorphic on a disk.

Daniel Fischer

@Gato Being holomorphic is a local property. For every $z_0\in U$, you know there is a disk $D_r(z_0)$ around $z_0$ such that $f$ is holomorphic on $D_r(z_0)$, hence ...

David Wheeler

And we can just choose a smaller disk, if $D_r(z_0) \cap U' \neq \emptyset$, so we may as well assume $D_r(z_0) \subseteq U$.

Theorem

@robjohn Hi , how are you ?

@robjohn Do you have any idea on interpolation between $L^2(\Omega)$ and $W^{1,2}(\Omega)$ ?

Gato

@DanielFischer hence f is holomorphic on $U$ because f is holomorphic on $D_r(z_0)$ for every $z_0\in U$ (this is the main point).

Sayan Chattopadhyay

@DavidWheeler u saw what I pinged you

Gato

16:28

@DanielFischer Does I need to spend more time on proving theorems in my course or doing exercise ?

(analysis complex)

David Wheeler

Yes, but there are some technical issues. @SayanChattopadhyay

Sayan Chattopadhyay

Is the idea right

David Wheeler

You can't deduce global behavior for $M(k)$ just from a small number of test points. At best, you have a heuristic (hand-waving) argument.

Sayan Chattopadhyay

But I did prove $$d/dx e^{x}=e^{x}$$

David Wheeler

Specifically, you are already ASSUMING that $M(k) \stackrel{\text{def}}{=} \lim_{n \to \infty} \dfrac{k^{1/n} = 1}{1/n}$ exists for EVERY $k > 0$, and is a CONTINUOUS function in $k$, and even more, that it is monotonic.

What you HAVE proved, is that $e^x = e^x \cdot \text{some limit}$, but you have not shown that limit is $1$.

Sayan Chattopadhyay

16:33

So what are the changes do I have to make @DavidWheeler

David Wheeler

What I would do, is back up, and take $k = e$.

Daniel Fischer

@Gato Some exercises should be proving theorems. But apart from that, the point is to understand the theorems, and doing exercises using the theorems helps much with that.

David Wheeler

The trouble you are going to run into is proving: $\lim_{n \to \infty} (1 + 1/n)^n = \sum_{k = 0}^\infty \dfrac{1}{k!}$

Sayan Chattopadhyay

I think that's what I have done

Gato

@DanielFischer ok. thanks.

David Wheeler

16:36

You proved the limit on the right DOES EXIST, and is between $2.5$ and $3$.

You have not shown the limit on the left exists, and that the two are EQUAL.

meer2kat

please say you all aren't still discussing the number e. it's been like ten hours

David Wheeler

Like I said, what I would do is define the sequence:

Sayan Chattopadhyay

And do what I did with the sequence

But @DavidWheeler then after I found $e$ I can describe $e^{x}$

David Wheeler

$a_n = 2 + \sum_{k = 2}^n \dfrac{1}{k!} \left(1 - \dfrac{1}{n}\right) \left(1 - \dfrac{2}{n}\right)\cdots \left(1 - \dfrac{k-1}{n}\right)$

Then show for any $n$, that $a_n < a_{n-1}$.

And from the binomial theorem $a_n = \left( 1 + \dfrac{1}{n} \right)^n$.

Sayan Chattopadhyay

@DavidWheeler I thought of a sequence and showed that it is e right

David Wheeler

16:44

Then show that $a_n < \sum_{k=1}^\infty \dfrac{1}{k!}$, so that $e$ is an upper bound for the sequence $\{a_n\}$.

Then you want to show that for any $n \leq t \leq n+1$, that:

$a_n \leq \left(1 + \dfrac{1}{t}\right)^t \leq a_{n+1}$.

Finally, show $\{a_n\}$ is CAUCHY, so that $\lim_{n \to \infty} a_n$ = its least upper bound.

That will show that $\lim_{n \to \infty} \left(1 + \dfrac{1}{n}\right)^n$ exists.

I suggest you delay the proof that our two definitions of $e$ are equal until you study Taylor series.

Suraj Khosla

Could anyone please help me with the following derivation: gyazo.com/3276d0d2f65a17321685baa085a4b1dd

Firstly, am I right in presuming that the integral of dT/T=ln(T) because of the rule: integral 1/x = ln(x)?

David Wheeler

If $T$ is a function of a single variable, sure.

I have no idea what $\mu$ is, though.

Suraj Khosla

mu is the coefficient of friction, just a constant value

I don't understand how the ln(T) at limits T1 and T2 is equal to ln(T1/T2), I would have thought it would be ln(T1-T2)

David Wheeler

16:59

$\int_{T_1}^{T_2} \dfrac{T}{dT} = \ln(T_2) - \ln(T_1) = \ln\left(\dfrac{T_2}{T_1}\right)$

using $\ln(ab) = \ln(a) + \ln(b)$ and $\ln(c^{-1}) = (-1)\ln(c)$

Sayan Chattopadhyay

@DavidWheeler my book mentions e and $ln(e)$ first after derivatives

Ben Beri

@DavidWheeler David, hi. If set A contains all words that begin with a and set B contains all words that begin with aa, so intersection of A and B is just all words that contains all of the words that begin with a?

Sayan Chattopadhyay

@BenBeri its like a set contains numbers and the other set contains the multiples of it

David Wheeler

@BenBeri Convince yourself of this general principle: if $X \subseteq Y$, then $X \cap Y = X$.

Sayan Chattopadhyay

Am I right @DavidWheeler

David Wheeler

17:10

@BenBeri Is $ab \in B$? If not, how can it be in $A \cap B$?

Sayan Chattopadhyay

@BenBeri its like let a set be something like this:
$$A:{2,3,4,5}$$

David Wheeler

@SayanChattopadhyay Being right, and proving one is right, are two different things.

Sayan Chattopadhyay

But isn't he just asking about the idea

Not the proof

David Wheeler

@SayanChattopadhyay he is asking about the meet of two regular languages, not sets in general. Even so, most sets do not have a notion of "multiplication".

What if my set is $\{elephant,red\}$? What is a multiple of "red"?

Sayan Chattopadhyay

It can be that the other set contains the description of the first set

David Wheeler

17:16

Sets can contain each other, yes, but "multiple" is the wrong word.

Sayan Chattopadhyay

I was taking about the case of numbers

@DavidWheeler so what's should i do my book gives me e and natural logarithm first and then Taylor sereies

David Wheeler

@SayanChattopadhyay how does your book define $e$?

Sayan Chattopadhyay

It just starts like logarithmic differentiation and natural logarithm after implicit differentiation@DavidWheeler

The Emperor of Ice Cream

The reputation bar isn't giving notifications for me

David Wheeler

@Sayan somewhere in your book it mentions $e$ for the very first time. How do it do that?

Sayan Chattopadhyay

17:24

Oh wait in the appendix the Taylor series has been given for e but not how you get it

David Wheeler

I would start where it talks about logarithms, and look backwards.

kuhaku

Is there a problem with the latex on the site?

it doesn't load and I've tried two different browsers

David Wheeler

In most proofs on differentiating exponentials, one uses the limit: $e = \lim_{h \to 0}(1 + h)^{\frac{1}{h}}$, to conclude $\lim_{h \to 0}e^h = \lim_{h \to 0}(1 + h)$

Then, in calculating: $\lim_{h \to 0} \dfrac{e^{x+h} - e^x}{h} = e^x\lim_{h \to 0} \dfrac{e^h - 1}{h} = e^x\lim_{h \to 0}\dfrac{1 + h - 1}{h} = e^x(1) = e^x$.

That is the "usual" proof that $\exp'(x) = \exp(x)$

@BenBeri Every string that begins with $aa$ also begins with $a$, but not vice-versa, so the intersection is all strings that begin with $aa$ (the more restrictive condition).

evinda

17:48

@DanielFischer I don't know.. Could we use a heap to merge k sorted lists into one sorted list in O(n lg K) time?

0

Q: Are the propositions right?

I want to choose if the following propositions are true or false and justify the reason for the choice. Polynomial: good, exponential: bad. Radix Sort works correctly if we use any right sorting algorithm to sort each digit. Given an array $A[1 \dots n]$ from integers, the time that CountingSo...

Does anyone have an idea for the above?

Ben Beri

@DavidWheeler Uhh man im having a very hard time understanding this whole intersection part, i don't know why ...

David Wheeler

18:09

It's like this: Suppose $L_1 = \{Tom, Ted, Thad, Bob, Tessa,Alvin\}$ and $L_2 = \{all\ people\ whose\ name\ starts\ with\ T\}$. What is $L_1 \cap L_2$?

Ben Beri

it would be {Tom, Ted, Thad, Tessa}

David Wheeler

Right. $L_2$ is the "bigger set" so it's easier to look at $L_1$ and weed out the ones that don't belong.

Ben Beri

yes i get that part, but it confuses me at some points like the question i stated, i dont know why

David Wheeler

If $L_1 = \{w| w = ax\}$ and $L_2 = \{w| w = aay\}$, given a word $w$ we check like this:

Is the first letter $a$? If not, it's not in $L_1$, so we reject it.

Ben Beri

yeah i get that part

user143442

18:14

hi

David Wheeler

Then we look at the second letter. If it is $a$ as well, it's in both $L_1$ AND $L_2$, so it is in the intersection.

user143442

I have a question on topology

David Wheeler

This shows that ANY word in $L_2$ is in $L_1 \cap L_2$.

Ben Beri

oh its based on the second set?

David Wheeler

The trick is showing that NO OTHER WORDS are in $L_1 \cap L_2$

user143442

18:15

Why can't I upload an image?

David Wheeler

We shown $L_2 \subseteq L_1 \cap L_2$, now we need to show it the other way around.

@user I have no idea-it could be the platform you're using, or your reputation level.

user143442

hmmm

David Wheeler

But showing $L_1 \cap L_2 \subseteq L_2$ is "obvious"-do you see why?

Ben Beri

ye

user143442

Can you watch it here please? postimg.org/image/8ub3zy0bj

user143442

18:18

I have a question about the 4th question

user143442

I don't know which is the quasicomponent of $x$

user143442

and is the component of $x$ just the line containing it?

Ben Beri

Is that true: $\begin{Bmatrix}a^n | n >= 0 \end{Bmatrix} \cap \begin{Bmatrix}a^n | n >= 1 \end{Bmatrix} = \begin{Bmatrix}a^n | n >= 1 \end{Bmatrix}$

David Wheeler

@BenBeri Yes, being greater than 1 always means that it's greater than 0, but not vice versa.

So for example: $\Bbb N \cap (\Bbb N - \{0\}) = \Bbb N - \{0\}$

Ben Beri

i see

David Wheeler

18:23

@BenBeri Read this: en.wikipedia.org/wiki/Lattice_(order)

The set of subsets of a given set forms a lattice under join = union, and intersection = meet. The (partial) order is called inclusion.

user143442

:(

Ben Beri

i see

{All words that begin with A} $\cap$ {All words that end with b} = {all words that begin with A and ends with b}

David Wheeler

logically, this corresponds to "or(non-exlusive)" for union, "and" for intersection, and "contained in" for inclsuion,

exactly.

@user it's not clear to mean the topology you're using in that figure.

user143442

I don't know

user143442

they don't say it

user143442

18:27

I think it could be the topology induced by $\Bbb R^2$

user143442

the relative topology

user143442

but then every square and line is clopen

Ben Beri

{All words that begin with a and ends with b} $\cap$ {all words that begin with a and ends with c} = {All words that begin with a}

David Wheeler

ya, but since it's "All white" I don't know what's in $X$, and what isn't.

user143442

and then the quasicomponent is the line coinaining $x$

user143442

18:29

the black lines are in $X$

Ben Beri

is that right

user143442

yes @BenBeri

Ben Beri

but if we have {All words that begin with c} $\cap$ {All words taht begin with a} = $\emptyset $

user143442

\emptyset

Ben Beri

yea

yeah i think i got it prettyt much now, try guys

Daniel Fischer

18:35

@evinda Yes. (Assuming $k > 1$ and that the lists are non-empty. If the lists can be empty, you need $\Omega(k)$ to go through the lists to check that they are empty. Then you can do it in $O(k + n\log k)$, but not in $O(n\log k)$.)

user143442

@DanielFischer how much reputation do I need to upload images here?

Daniel Fischer

@user It's not listed explicitly on the privileges page. I'd expect that "remove new user restrictions" at 10 would do it. Have you a problem uploading an image? If so, what happens when you try?

user143442

I don't see the button of "upload image"

Ropstah

Hi everyone

user143442

I just see the button "send"

user143442

18:43

I see it when I refresh the page but then it disappears

Ropstah

try a different browser perhaps?

user143442

nope

user143442

the button doesn't disappear when I log in with my other account with more reputation

Ropstah

ah fair enough

ᴇʏᴇs

@user You need 100 rep to upload images in chat

Ropstah

18:45

Is anyone able to review a question of mine about geometry? I'm not sure if it's difficult or unclear

user143442

thanks @ᴇʏᴇs

evinda

@DanielFischer So do we have to make k different heaps that will contain the elements of the sorted lists and then compare the values of the elements of each heap?

Daniel Fischer

@evinda No, you make one heap. What do you put into the heap? (Hint: where does the $\log k$ come from?)

robjohn

@DavidWheeler I find it easier to show that $\left(1+\frac1n\right)^n$ is increasing and $\left(1+\frac1n\right)^{n+1}$ is decreasing to show that $\left(1+\frac1n\right)^n$ converges.

David Wheeler

@robjohn OK

evinda

18:52

@DanielFischer Do we have to compare the first elements of the k heaps and put at the root of the heap the smallest, then compare the second smallest of the list from which the root of the heap is, with the smallest of the other heaps and put the smallest of them at the left side of the root and so on..?

David Wheeler

@robjohn There's...a lot of different ways we might go about defining $e$. Showing they're all equal is not always quite so easy.

Daniel Fischer

@evinda No. One heap of size $k$ (initially).

robjohn

@DavidWheeler Yeah. I showed a lot of them were equal when I first came to MSE.

There seemed to be a bit of interest at the time.

evinda

@DanielFischer So do we make a heap with all the first elements of the k heaps?

Daniel Fischer

@evinda You keep writing of $k$ heaps. You only make one heap.

evinda

18:57

@DanielFischer Sorry, I meant from the k sorted lists.

David Wheeler

Personally, I like $e = a: \int_1^a \dfrac{dt}{t} = 1$

Daniel Fischer

@evinda Okay. Then you're getting closer. But you don't put the elements of the lists into the heap. You put something else into the heap.

David Wheeler

It's pretty easy to define the properties of logarithms from that, and one can define $\exp = \ln^{-1}$ and use the inverse function theorem. Probably not the best approach for a first look, though.

evinda

@DanielFischer Do we maybe compare the elements of the sorted lists and put at the first position of the heap how many elements from the first list we use so that the array is sorted, at the second position how many elements from the second list we use and so on?

Daniel Fischer

@evinda No. Why do you want to put numbers in the heap?

evinda

19:05

@DanielFischer What else could we put in the heap? :/

Daniel Fischer

@evinda What property must things you put in a heap have?

evinda

@DanielFischer The left child of a node should have a less value that this of the node and the value of the right child should be greater than this of the node, right?

Daniel Fischer

@evinda So what is the property you use?

@evinda That, by the way would be a binary search tree, not a heap.

HowDoIMath

Hey all. The "math mode" of this site suddenly turned off for me, so it no longer shows the formula nicely, but shows them in their raw TeX format with dollar signs and all. Any idea what I did to obtain this (and how to reverse it)?

Daniel Fischer

@HowDoIMath Sometimes reloading the page helps (when the mathjax code hasn't been properly loaded), have you tried that?

HowDoIMath

19:10

Yeah. Also tried another browser, same thing. But on my phone, it looks ok for some reason

Daniel Fischer

@HowDoIMath JavaScript disabled in the browser maybe?

evinda

@DanielFischer Oh yes, right...
The trees should satisfy the heap property. In a max heap, the keys of parent nodes are always greater than or equal to those of the children and the highest key is in the root node. In a min heap, the keys of parent nodes are less than or equal to those of the children and the lowest key is in the root node.

HowDoIMath

Let me check

Yeah, it is

Daniel Fischer

@HowDoIMath That's probably it then.

HowDoIMath

Oh, sorry. I mean, it is _en_abled. :)

Mary Star

19:13

Hello!! Is someone of you familiar with characteristic curves??

HowDoIMath

Maybe it will reappear after reboot or so

Daniel Fischer

@HowDoIMath Ah. Pity, would have been a nice simple thing. Which browser and OS?

HowDoIMath

Firefox on Windows 7

Daniel Fischer

@HowDoIMath You already tried restarting the browser, I suppose?

@HowDoIMath Are you using NoScript?

HowDoIMath

Yeah, didn't seem to work

NoScript? I don't think so. Let me check

I have no process running resembling that (also don't recall installing it)

Thanks, Daniel. I will try a full reboot later tonight and see if it fixes it

Thought I had toggled some unseen option on the site

Daniel Fischer

19:17

@HowDoIMath It's a FireFox plugin. Not sure where the Windows version of FF tells you which plugins you have installed. Anyway, my non-expert ideas are coming to an end, so maybe you should indeed try to reboot, and if that doesn't help, post on meta.

HowDoIMath

Ah, let me check that as well

Nah, no such plugin

Owatch

How would you go about $\int{e^{\sqrt(x)}} dx$?

HowDoIMath

Thank you for the effort and time anyway. :) I'll post on meta, if it doesn't help

Mary Star

Hello @Hayden @quid !! Are you familiar with characteristic curves of PDE's??

quid

@MaryStar a long time ago I knew a little about it but I am not sure if any knwoledge remains.

evinda

19:21

@Owatch $\int{e^{\sqrt(x)}} dx$

We set $\sqrt{x}=u$. Then $\frac{1}{2 \sqrt{x}}dx=du \Rightarrow dx=2 \sqrt{x}du=2udu$

So $\int{e^{\sqrt(x)}} dx= \int e^u 2udu=2 \int e^uudu$

Can you continue?

Owatch

Where did you get $\frac{1}{2\sqrt{x}}$ from?

Mary Star

We have the equation $$2u_{xx}-u_{tt}+u_{xt}=f(x, t)$$

This is equal to $$\left (\frac{2\partial^2}{\partial{x^2}}-\frac{\partial ^2}{\partial{t^2}}+\frac{\partial ^2}{\partial{x}\partial{t}}\right )u=f$$

To find the characteristics do we solve the homogeneous equation $$\frac{2\partial^2}{\partial{x^2}}-\frac{\partial ^2}{\partial{t^2}}+\frac{\partial ^2}{\partial{x}\partial{t}}=0$$ ?? @quid

Owatch

derivative of sqrt(x) I guess

evinda

@Owatch $(\sqrt{x})'=\frac{1}{2 \sqrt{x}}$

Owatch

ok thanks

David Wheeler

19:24

$\dfrac{d}{dx}(\sqrt{x}) = \dfrac{d}{dx}x^{1/2} = \dfrac{1}{2}x^{-1/2} = \dfrac{1}{2\sqrt{x}}$

evinda

@Owatch :)

Owatch

Latex is not rendering

I have clicked start ChatJax several times, and also hit rendering on. But it never renders new stuff.

I have to keep pressing the bookmark

Thank you David

evinda

@Owatch Where do you try to start ChatJax?

Owatch

Bookmark

quid

@MaryStar sorry I do not know.

evinda

19:26

Where is this bookmark? @Owatch

Owatch

Where the bookmarks go, in the tab above the page?

evinda

Hello @Theorem

Mary Star

Ok... No problem... :-)

Theorem

@evinda Yes Sir

evinda

@Owatch I don't see it... Where is it exactly?

@Theorem How are you?

Theorem

19:28

@evinda I am doing ok . What about you ?

evinda

I am ok too :) @Theorem

Owatch

There

Theorem

@evinda Nice . I wish i was in Australia . it has got such wonderful weather :)

evinda

@Theorem How is the weather in Germany?

Theorem

@evinda still gloomy and wet

evinda

19:33

I don't see the bookmark bar... Where did you find it? @Owatch

@Theorem Aha..

Mary Star

We have the equation $$2u_{xx}-u_{tt}+u_{xt}=f(x, t)$$

This is equal to $$\left (\frac{2\partial^2}{\partial{x^2}}-\frac{\partial ^2}{\partial{t^2}}+\frac{\partial ^2}{\partial{x}\partial{t}}\right )u=f$$

To find the characteristics do we solve the homogeneous equation $$\frac{2\partial^2}{\partial{x^2}}-\frac{\partial ^2}{\partial{t^2}}+\frac{\partial ^2}{\partial{x}\partial{t}}=0$$ ?? @MikeMiller

Do you have an idea??

evinda

Hello @IlmariKaronen Could you take a look at this?

0

Q: Are the propositions right?

I want to choose if the following propositions are true or false and justify the reason for the choice. Polynomial: good, exponential: bad. Radix Sort works correctly if we use any right sorting algorithm to sort each digit. Given an array $A[1 \dots n]$ from integers, the time that CountingSo...

discrete-mathematics algorithms computer-science dynamic-programming

Owatch

@evinda It's right there in the picture.

Look above the chat.

evinda

@Owatch Above the chat, there are these bottoms: load older messages load to my last message full transcript highlights

Owatch

Nope, it says rendering on, rendering off, render MathJax.

evinda

19:40

Not at mine... :( @Owatch

Owatch

Well of course not yours, I'm not using your computer.

I'm saying I'm clicking the bookmarks supposed to run the JS that continuously renders Latex, and it isn't working.

Vrouvrou

@DavidWheeler please have you an idea on how to prove that $A=(\mathbb{Q}\times\mathbb{R})\cup (\mathbb{R}\times \{0\})\subset \mathbb{R}^2 $ is path-connected

Owatch

It's okay, doesn't natter.

evinda

@Owatch Did you press a button to activate the bookmark bar? Because I don't have this bookmark at my computer..

Maximilian

Hello

I need help finding the exact value with the half-angle identity for tan 195

Mary Star

19:42

Hello @Karl !! Are you familiar with characteristic curves of PDE's??

Maximilian

I know the answer is $2-\sqrt{3}$

Owatch

Oh look, it's Max.

evinda

Have you activated ChatJax? @Theorem

Maximilian

I have $\frac{\sqrt{1-\frac{\sqrt{3}}{2}}}{\sqrt{1+\frac{\sqrt{3}}{2}}}$

I then multiplied by 2 to get $\frac{\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}$

evinda

Do I have to write this?

javascript:(function(){if(window.MathJax===undefined){var%20script%20=%20documen‌t.createElement("script");script.type%20=%20"text/javascript";script.src%20=%20"h‌ttp://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-

Karl

19:49

@Mary Sorry I'm not. I'm a pretty useless mathematician truth be told.

Mary Star

Ok...

Hello @Huy !! Are you familiar with characteristic curves of PDE's??

Maximilian

So If I multiply the top and bottom by $\frac{\sqrt{2+\sqrt{3}}}{\sqrt{2+\sqrt{3}}}$

then I probably did this wrong but I got $\frac{1}{2+\sqrt{3}}$

Owatch

Hmm, are you sure you're multiplying by the conjugate correctly?

Maximilian

I don't think so

Owatch

Why are both +?

Could you paste the latex without the $ signs so I can edit it?

Maximilian

19:54

I don't know, I was just trying to get rid of the bottom

Would I multiply by the negative?

Owatch

The conjugate should be the opposite sign.

But then again, it depends on which you pick.

evinda

Hey @robjohn !!! Do you know where I can find the bookmark to activate ChatJax?

Maximilian

Ok let me try that

Owatch

And the problem is you need to multiply by the opposite sign on both sides. So you technically did it right.

Maximilian

Well.. I guess I did it

Owatch

19:56

If using the top. Maybe someone else has better in sight.

Maximilian

If I do the negative, the bottom is 1 and then I just cancel the square root on top and get $2-\sqrt{3}$

Which is what the book says

Owatch

So by picking the other side, you were able to achieve the answer from the book?

Maximilian

Ya

Owatch

Okay.

Saal Hardali

Let $f$ be a continuous function on $[a,b]$. Is there anyway i can simplify this limit?
$\lim_{\epsilon \to 0}\int_a^b \dfrac{\epsilon f(t) dt}{(t-x)^2 +\epsilon^2 }$

Chris's sis

20:02

Guys, there is an INCREDIBLY CRAZY GAME BETWEEN SIMONA HALEP AND JELENA JANKOVIC!

I barely can get these moments! It's simply craziness! :-)

I do no math now!

:-)

BBL (they began again)

Mike Miller

@Chris'ssis Thanks for the tip-off. I'll have to watch it in a few hours.

Chris's sis

@MikeMiller It's live now.

David Wheeler

@Vrouvrou Go from $(x_0,y_0)$ down to the $x$-axis (unless we're already there), move to $(x_1,0)$, and then travel to $(x_1,y_1)$.

Mike Miller

I have deadlines some things I need to get done soon, and shouldn't be distracted. (I guess that means I should also leave the room.)

Thanks again.

Mary Star

Hello @SimonBaars !! Are you familiar with the energy method at PDE's ??

Chris's sis

20:05

@MikeMiller I never saw such a game so far. Welcome.

Maximilian

I did another problem wrong:P

Need to find $tan\frac{\theta}{2}$

given that $sin\theta = \frac{3}{5}$

in quadrant 1

Owatch

Easy?

Maximilian

I used a pythagorean identity to find $cos\theta$ which was $\frac{4}{5}$

Owatch

Draw a right triangle.

Then write $\theta$ on one side (Not the right angle).

Maximilian

I then plugged in $sin\theta$ and $cos\theta$ in $\frac{1-cos A}{sin A}$

Vrouvrou

20:09

@DavidWheeler but where is used Q ?

Maximilian

So its $\frac{1-\frac{4}{5}}{\frac{3}{5}}$

Owatch

$sin\theta$ = 3/5, since sin = opposite/hypotenuse, that means you write 3 on the far end, and 5 for the hypotenuse. Then use pythagoras to find the remanining side

Maximilian

Ah... theres the issue, I kept it as 1 instead of 5 when multiplying by 5, or at least its 1 thing I didn't do, could be another issue

Let me try tht

Owatch

Since sin = 3/5, then cos must = adj/hyp. And then combine those to give you tan.

Maximilian

I got $\frac{1}{3}$, answer is just 3 :O

evinda

20:11

Hallo @Huy

Hello @quid

Maximilian

Owatch, when I multiply by 5 it should be $\frac{5-4}{3}$ right?

quid

hello @evinda How was your weekend?

Owatch

I dunno, I tried giving an answer but I don't think you read it.

Maximilian

You are talking about a triangle, I have to use half-angle identities to solve this

evinda

Yesterday I went out for a coffee and today I studied a bit.. How was your weekend? @quid

Owatch

20:12

Fine.

Maximilian

solving $tan\frac{\theta}{2}$

Owatch

Multiplying by 5 will give you 5-4

So that aspect is right

Maximilian

? divided by 3

Owatch

yes.

Maximilian

yes... which is $\frac{1}{3}$ in the end but should be 3

quid

20:14

It was somewhat similar to yours @evinda

Owatch

5-4 is 1

/3

evinda

Nice :) @quid

Maximilian

So how do I get 3?

Owatch

Oh, you want 3.

My bad.

Maximilian

Yes, the answer is just 3 but I have $\frac{1}{3}$

Owatch

20:15

You would have done something wrong earlier I assume. Your question about simplifying the fractions was what I looked at.

evinda

@quid Could I ask you something? Have you enabled ChatJax?

Maximilian

if sin=$\frac{3}{5}$ then cos=$\frac{4}{5}$ ya?

quid

@evinda no I do not have enabled ChatJax. But I manage to read the math (sometimes by copying it somewhee else.)

So if you want to write math it is fine

evinda

@quid I do it also like that :D

Owatch

@Maximilian Yes.

Maximilian

20:18

In an example in the book with tan$\frac{\theta}{2}$ they use the half angles of sin and cos though, but the formula does not, so am I supposed to find the half angles of sin and cos first and use those?

ᴇʏᴇs

@Maximilian What is your profile picture

Maximilian

A lego

ᴇʏᴇs

@Maximilian It looks scary

Maximilian

It's Vitruvius from The Lego Movie

Vrouvrou

@DavidWheeler i must take two points $M_1=(x_1,y_1)$ from $\mathbb{Q}\times \mathbb{R}$ and $M_2=(x_2,y_2)$ from $\mathbb{R}\times\{0\}$

ᴇʏᴇs

20:21

@Maximilian I never saw it

Maximilian

Well its amazing

ᴇʏᴇs

@Maximilian Oh you are a wizard

Maximilian

lol

Ben Beri

how do you add text between { } in latex with spaces?

Maximilian

I go to Hogwarts

Vrouvrou

20:22

and i must find a continuous function $\varphi:[0,1]\rightarrow A$ such that $\varphi(0)=M_1$ and $\varphi(1)=M_2$ right @DavidWheeler

Ben Beri

nvm

Maximilian

@owatch the issue was because I forgot to make cos a negative... oops

Owatch

At least it's done.

Maximilian

Solved

Lol

So many formulas

Vrouvrou

@DavidWheeler if i say $\varphi(t)= ((1-t) x_1+ t x_2, (1-t) y_1 +t y_2)$ it is true ? but where is the importance of Q ?

Ben Beri

20:28

how can I describe string length in math symbols? e.g #_w(c) length of c's in w but theres no # in latex for me

Vrouvrou

@DavidWheeler ?

Ben Beri

$L_1 = \begin{Bmatrix} \text{All words that begin with bb} \end{Bmatrix}

L_2 = \begin{Bmatrix} \text{All words that end with aa} \end{Bmatrix}

L_3 = \begin{Bmatrix} \text{All words that do not begin with bb} \end{Bmatrix}

L_4 = \begin{Bmatrix} W | W \in \begin{Bmatrix} a, b, c \end{Bmatrix}, \text{length of c mod 3 = 1}\end{Bmatrix}$

Is it true that $\begin{pmatrix}L_1 \cap L_2\end{pmatrix} \cap \begin{pmatrix}L_3 \cap L_4\end{pmatrix} = \begin(Bmatrix) \text{All words that don't begin with bb, but they begin with aa and the length of c's mod 3 equals 1}$

I mean: $(L_1 \cap L_2) \cap (L_3 \cap L_4) = \begin{Bmatrix} \text{All words that don't begin with bb, but they begin with aa and the length of c's mod 3 equals 1}) \end{Bmatrix}$

Chris's sis

20:51

I'm f***ing proud I'm Romanian! Simona won!!!!!!! The game was completely madness!

The last hour or so was an hour by hell. She finally did it!

Danu

I've got a random terminology question: Why is it that mathematicians seem to prefer the prefix "skew-" over "anti-" (e.g. antisymmetric vs. skew-symmetric, anti-Hermitian vs. skew-Hermitian) while it seems to be the other way around in physics (being a physicist, I see more logic in the latter, but maybe that's just bias :P)

The Emperor of Ice Cream

who is sos440?

Danu

We are all sos440

@TheEmperorofIceCream Nice Kandinsky you got there, btw

The Emperor of Ice Cream

@Danu thanks, good eye.

Danu

I live in Munich---the Lenbachhaus there has quite a lot of his work

Transcript for

$Mathematics$ Mathematics