11:00 AM
@GustavoMontano it was 'kay :|

Reminds me of Dragonball Z. Did you ever watch that?

ya ,, used to watch it a long time ago ..

Reminds me....in that.....the delay the action!
Yeh, it was my first ever anime.

ya mine too :) .. DBZ the first 'anime' I ever watched, although didn't know it was technically an anime at that time ..

DBZ was cool.

11:04 AM
is cool :) .. although I haven't seen the GT or Kai episodes .. :{just heard about 'em
@Gus I see you're using your real name :-)

Indeed I am :p.

@r9m Kai episodes are cool

Same here - I never watched GT or kai.

Haven't seen GT

I was so attached to DBZ that I didn't want to see GT - especially due to the fact that it was not written by Akira Toriyama.

11:08 AM
Yeah

going to sleep night

GT was a let down.
I still haven't seen the original Dragonball.
>_>

The original one was exellent

Wait, AF? Isn't that a joke?

11:10 AM
@GustavoMontano haha, yeah

Dragoball - neither have I. Apparently its good! Some people prefer it over DBZ.

I never watched GT because the idea of an SS4 repulsed me.

@BalarkaSen, Haha, you almost got me ^_^.

@Khallil I have :D !! it was great :) loved the even after I grew a moustache :P

11:11 AM
SAME HERE!

@GustavoMontano It much much better than DBZ

You went from this super cool golden entity....to a guy in a red jumpsuit and a tail -.-'

SSJ4 was quite weird.
The way Vegeta became a SSJ4 was even worse.
All of his pride by that point, went out the window.
Helped by a robot to ascend. Really?
>_<

Let us not speak of GT xD.
It hurts my childhood.

Let us purge it from our minds.

11:13 AM
at this rate I feel like I'm never going to watch GT or Kai :P

"In 2002, in the week ending September 22nd, Dragon Ball Z was the #1 program of the week on all of television with tweens 9-14, boys 9-14 and men 12-24"
"and men", haha ^_^

@Khallil wat is that ? :o

The Dragonball AF (April Fools) concept.
It's the supposed SSJ5 Goku.

Oh damnit AF = April Fools. slowly walks away.

blows raspberry :Pzz
I haven't seen ssj4 yet :P

11:16 AM
You won't want to. It's only good in Budokai 3.

I thought the music of DBZ was incredibly.

@GustavoMontano agreed :)

Produced by Bruce Faulconer. I ended up buying all his CD's.
Pikkons theme - holy moly.

Speaking of music, check out this freestyle.

I missed my bus to school for this.

11:19 AM
This is more to my liking, @Gustavo.

I have to watch more anime!
I've heard great things about Samurai Champloo.

11:41 AM
@MartinSleziak They are both solved by $|x-y|+|y-z|=|x-z|\iff y$ is between $x$ and $z$. I figured that a difference can be written as a sum, but if enough people think otherwise, it can be reopened. Can you not vote to reopen because I closed it?

Yes I can. But I thought it is useful to hear your opinion.
And also to point at you for unilateral closure...
I am not sure to which extent the users are against unilateral closures by mods. I think I remember some discussion about mods posting their votes in comments, and if there are enough of them, then they use mod powers.
But I might be mistaken (maybe I mixed it with something else).

@MartinSleziak It was noted by someone else, and I agreed. That was a couple of years ago. I think the complaints about unilateral closures started later, or I would not have done it (but I could be mistaken).

In any case if the question you closed is a duplicate, then so are the two questions I have mentioned. (They are much closer, only numbers are different.)

@GustavoMontano Pikkon is not a namekian, right?
He looked much like one.

Even though he looks like one - he is not.
Used body weights like Piccolo too.

11:47 AM
@MartinSleziak so vote to close them as duplicate. I won't be closing them unilaterally nowadays.

I did.

@GustavoMontano Everyone uses body weights, not just Piccolo!
Goku used them once too

@MartinSleziak okay :-)

@BalarkaSen. That is true. But I think Piccolo was well known to "always" have them on.

It's a standard step in learning Martial Arts.

11:49 AM
@robjohn Good to know. I did not know what is the position of the mods on unilateral closure now. (But I think I have seen a few quite recently. Although I might have mixed them up with the new golden-badge-dupe-hammer.)

@GustavoMontano =P

@MartinSleziak In "clear" cases, or spam, we do still do act unilaterally, but get posts in meta if "clear" is not clear enough.
@MartinSleziak but we often just leave them alone and move on to other flags

I should have done martial arts :p.

There's still much time to become a SSJ, @Gustavo!

Of course there is. Especially with the Hyperbolic Time Chamber.

11:51 AM
@Gustavo is not a Sayian, @Khallil

AKA Steroids. Hahaha ^_^.

Don't be silly.
@GustavoMontano I wonder if HTC is related to hyperbolic geometry somehow.

Hahahahah!
Find the connection and write a research paper on it.

@Khallil You still spell Sayia-Jin instead of Sayian? Seriously.

Oops, wrong chat.
Yes, yes I do, @BalarkaSen.
Is there anything wrong with that?

11:54 AM
wtf

Oh SSJ stands for Super Sayia-Jin.
Ahhh the more you know.

What's up, @skullpatrol?

Yes, @Gustavo

Chillin', you?

The same! Why'd you post the 'wtf' message?

11:56 AM
The first thing I saw was the gif when I came in :D

Hahahaha! It's no longer a math chat!
That was actually meant to go in the Maid Café!
^_^

icic

Herro, @Chris'ssis!
Long time.

@BalarkaSen Hi.

@Chris'ssis What happened to you?
You were away for like 2 days.

12:00 PM
@BalarkaSen I'm deeply sad, I lost the light of my life, a very clever, happy dog, smarter than half of the people I ever met and probably more honest than 99% of the people I ever met. If I should have paid more attention to her, maybe I could have done something, but I did mathematics. I hate myself for that and I don't wanna do mathematics anymore.
5
There is no thing in the world that I could have accepted for giving up that dog,no ammount of money, no book, no achievement, I don't give a s**t on all of them when it's about the life of someone I care about, the only being that made me happy. I'm only mad now.
Have fun here!
2

@Chris'ssis Ah, I suspected that
I feel for you. I really do.

That still doesn't excuse the 99% percent comment, but we're here for you @Chris'ssis.

You said @Chis'ssis that the tea made them healthy again, what happened?

Poor thing. I know how that feels.

12:08 PM
Don't blame yourself @Chris'ssis at least your dog is out of pain :'(

hi all. i'm revising some material on limits, a subject that i openly find intimidating. i'm trying to understand when to use various strategies. for starters, is it correct to say: 1) if limit is 0/0, try to factorize. 2) if limit is 0/0 with roots involved, use difference of squares. 3) if limit is 0/0 or infinity / infinity (not defined basically), use l'hopital?

Hello

@Vibhav Hey

@BalarkaSen hi
So, I needed some help with this question:

Eh, what question?

12:18 PM
Let $s_n = \frac{1}{n}\sum_{k=0}^{n-1}f(k/n)$, prove ${s_n}$ converges to $\int^1_0f(x)dx$

Gah gah gah
not interested not interested not interested
riemann sums riemann sums riemann sums

hehe

runs and hides

Yeah, that resembles a riemann sum, but im not sure how one would prove that

f is continuous?
Probably Riemann integrable suffices.

12:20 PM
@MartinSleziak Yeah, and its monotonically increasing on $[0, 1]$

If you are allowed to used them you can sandwich $s_n$ between lower and upper Riemann sums - as Balarka Sen indicated.

The initial excersice is to show that $s_n \le \int^1_0f(x)dx \le \frac{1}{n}\sum_{k=1}^nf(k/n)$

If it is monotonically increasing, you can simply rewrite $s_n$ as an integral of piecewise constant function. This function lies bellow $f(x)$ on each interval of the length $1/n$.

@MartinSleziak The upper integral is $\frac{1}{n}\sum_{k=1}^nf(k/n)$, right?

@VibhavPant Yes, this is the upper sum.
Basically one of the sums is area of the rectangles blow curve and the other one is area of the rectangles above the curve.
The function on those pictures is decreasing, not increasing, but I think they might help illustrate situation anyway.

12:27 PM
@topper. I guess one tries to factorise as best they can. Furthermore, one should try and implement any elementary manipulations to try and make the expression have an obvious limit. If none of these work and the numerator/denominator are continuous, then you can use L'Hopitals.
An interesting example though is $y=\frac{x^2}{x}$.

@GustavoMontano Eh, factorize?
$x^2/x = x \cdot x/x = x$

Yes. It's the line $y=x$ WITH the fact that $x\neq0$.

@GustavoMontano thanks. i guess what i'm really asking, is, if l'hopitals works for all 0/0 situations, and one has a reasonable handle on differentiation, is there any reason not to use l'hopitals straight away, rather than get involved with factorizing? sorry if this is a lame question

If you use L'Hopitals on that, you get a weird answer. What does that mean?
Well does it work for all 0/0 cases?
$y=x^2/x$.

@topper You can't L'Hopital x^2/x.

12:31 PM
I wonder why?

i figured that, i'm just trying to work out why annoyed face

Well, you can but you'd get a weird answer.

Exactly. So there's more too it. Therefore your question is not lame.

okay, i have 2x/1 when i differentiate numerator and denominator. what's the problem? i know the derivative of the denominator can't equal zero, but it's 1...

@GustavoMontano Nope.

12:36 PM

That's embarrassing.

i feel better now :P

It's fine to do L'Hopital. You confused me, @Gustavo

you didn't see anything. ~.~

12:37 PM
haha

So yeh, L'Hopitals should work.

my exam is in a week, i'm way behind, so thanks for the genuine laugh!

Haha. No problem. Good luck! Do as many questions as you can. With pace!

Which limit are we trying to find, @topper?

yeah, i'm doing that. currently involved in investigating functions, which is a good topic because it brings a lot of the other concepts together
@Khallil none in particular, i'm just trying to get a mental flowchart for solving limits... chat.stackexchange.com/transcript/message/17423250#17423250
i'll be a lot happier when the procedure becomes more like a flowchart of rational decisions and less like a bunch of panicked guesses :)

12:41 PM
If you have any examples, share them.

I guess it's something that you just become accustomed to with experience. That's probably true for all math, @topper.

for example, it's good for me to know that i can use l'hopital for any limit of type 0/0, without having to think about factorizing and other steps. i can just dive in and start differentiating

It's more of a safety net, if anything. It's good to think of different ways to tackle different problems. That's why integrals are pretty neat. There's no algorithm for tackling the problem.

i hear that

Integration by parts requires some process.
L-I-A-T-E.
If you've ever heard of that.

12:45 PM
Very true. But I hadn't heard of that until very recently!

Never fails 99% of the time.

Well ...
Have you tried integrating by deriving a reduction formula, @Gustavo?

Yes I have. It's a great process.

(For me, that fails a lot of the time. Although that's probably more telling of my ability than the questions I try.)
=P

Yes, I think I know where you are coming from.
Some expressions require a different type of motivation. I.e generating the original integral so you can get that nice formula.

12:54 PM
It's all pretty neat stuff!

Indeed - it's fun. A different type of math. Puzzle game.

1:13 PM

@GustavoMontano: I thought it was ILATE !

Ohh.....
I wonder if they both work :o

Indices, logarithms, ..., trigonometric terms, exponentials.

No!

Oh, I stands for Inverse Trig.

1:14 PM
What does the A stand for?
Oh, Inverse trig.

Algebraic expressions.
Sounds weird, like none of those "Special functions"

I is inverse trigonometric and A is algebraic.

See. I told you I've only heard of it once!
Algebraic expressions. Like polynomials?

Yes!!

Oh.

1:15 PM
Though, I believe you can have (1/x) and that still counts as A.

I just go on instinct with every integral I do.
That and a few standard subs.
$$\int_{a}^{b} f(x) \text{ d}x \ \overset{x \mapsto a + b - x}= \int_{a}^{b} f(a+b-x) \text{ d}x$$

1:27 PM
@r9m It looks good. This might be a simpler proof of one of the identities:
Or maybe it is about the same.

hi, @robjohn, @Khallil

@TedShifrin Howdy... is your weekend going well?

LOL, it just started, so I dunno :) First football game of the season clogging up the town tonight :(
Are yours? You pulling all-nighters again?

Hey, @TedShifrin!
^_^

@TedShifrin Oh god... is it day again already?

1:31 PM

glad you understand, @BalarkaSen, I'll go do seppuku now to preserve the honor of my family

My condolences @chris'ssis

You're going to disembowel yourself, @MickLH?

it's too early in the morning for that, boys

lol no sorry, it's a morbid joke
I told him I expect to finish a project on a timeline, then I had to throw that timeline out the window because of money

1:34 PM
Oh, I see.

throwing money out the window is not a good idea, @Mick.

After all, money doesn't grow on ... Wait a second.
=P

lol ooooh yeah I guess it really is that easy, thanks government for tricking people into thinking green paper is worth human life

1:48 PM
ah the mean square

Has anybody got any nice reduction formulae questions?

@Khallil: What's the reduction formula... (Apologies, I'm bad with names)

Oh, sorry. Yea, it goes by different names. It's like setting up an integral in terms of a number that can be expressed in terms of a number that's less than the original number. i.e. $I_n = 5I_{n-1}$ where $I_n$ is the original integral, @Nick. The whole point is to eventually reduce your original integral down to one that you can evaluate on it's own. Like how the Gamma function ends up as a bunch of terms multiplied by the integral of $e^{-x}$.

The formula for an element of a Fibonacci Sequence is an example.

@Khallil: ... I'm not as far in integration as you are. but can you show me $$\int{(x\cdot \sin x)\cdot dx}$$ using that method.
@GustavoMontano: What's that formula?

1:58 PM
Well, integration by reduction formula usually involve repeated integration by parts.
In that sense, you'd be more likely to be asked to find $\int x^{n} \sin x \text{ d}x$.

What would be the opposite of a "geometric proof"

An algebraic one? Is there an opposite to geometry? That seems like way too open a question to get a definitive answer.

@Nick $F_n = F_{n-1} + F_{n-2}$.

@VibhavPant: An aerometric proof Da dum tshh..!! (Reference to Avatar: Book 2, rock is the opposite of air)

@Khallil Geometric as in proofs that make use of a functions (in question) graph

2:00 PM
The series converges to the Golden Ratio.
Now that golden ratio is an amazing thing.

@GustavoMontano: ..... I hate recursion.

It's tedious!

@GustavoMontano $\{ F_n \}$ converges to the golden ratio?

Wait........no, the nth term converges to GR?
Correct me if I am wrong, sorry.

@GustavoMontano: My best question is about the Golden Ratio

2:02 PM
@Nick. Like I was saying, tedious. Though, using it to find the expression of an integral is nice.

@GustavoMontano IIUC, it looks divergent.

I remember the first time my tutor showed me. I "wowed". Not because it was incredibly amazing, just different.
What am I saying....obviously it's divergent.
Oh wait....I remember now.

Math and Memory do not go well.

@Nick \begin{aligned} \int x^n \sin x \text{ d}x \ & \overset{\text{I.B.P}_1}= -x^n \cos x - \int -nx^{n-1} \cos x \text{ d}x \\ & = -x^n \cos x + n \int x^{n-1} \cos x \text{ d}x \\ & \overset{\text{I.B.P}_2}= -x^{n} \cos x + n \left( x^{n-1} \sin x - (n-1) \int x^{n-2} \sin x \text{ d}x \right) \\ & = -x^{n} \cos x + n x^{n-1} \sin x - n(n-1) \int x^{n-2} \sin x \text{ d}x \end{aligned} Now if we call our original integral $I_{n}$, then our final answer will be in terms of $I_{n-2}$.

And math requires memory >_>.

2:04 PM
IIRC, If we define $g_n = \frac{f_{n+1}}{f_n}$, $\{g_n\}$ converges to $\phi$

A different type of memory.
That's right, @VibhavPant. Thanks for that.

@GustavoMontano: RAM, lol

I've been terrible today. I said the derivative of $x^2$ was 2..... -.-'
And I couldn't figure out why L'Hopitals rule was not working. ANYWAY xD

@GustavoMontano: L'Hospitals rule seems to fail everytime i have a tan or cot that doesn't cancel out.

2:05 PM
heh

That's a fairly basic example of integration through deriving a reduction formula. The whole essence of the process is to use integration by parts (or some neat tricks) to reduce an integral down to one that we can evaluate easily, @Nick.

L'Hospitals rule has been a bad habit for me

There are conditions. I.e the denominator can never be 0 and the functions have to be continuous in the interval you are investigating.

Yep, integrating by parts is usually the best way to set up a reduction formula.

Got it

2:07 PM
I actually can't think of another way.

Oh, you edited. I just used integration by parts on the second integral on the second line.
Another way for what, @Gustavo?

Another way to set of a recursion formula for integrals
IBP is the only way I know.

@GustavoMontano: Could you tell me the formula for this sequence: oeis.org/A007908

How on earth.....haha
I couldn't tell you right now, or in a while.
That looks rather complicating.

I tried for 5 hours. I'm an idiot.
You, being a mathematician, can do better.

2:11 PM
How does one define a mathematician?

@GustavoMontano: ... one leaves it as an exercise for the reader.

What? haha xD

@GustavoMontano Erdos said that "A mathematician is a machine for turning coffee into theorems."

I like that.

@VibhavPant: If it were the other way around, I'd be much more fond of hanging around them.

2:13 PM
heh

For some reason - coffee has no effect on me.

Maybe you're having a dark roast

Whats a dark roast?

@GustavoMontano: ... go to the deviant-art chatroom. Try to chat. You will fail, Drink coffee, you can actually talk!

@GustavoMontano Dark Roasts have beans that are roasted to higher temperatures, so they loose most of their caffeine content (which iirc is responsible for the no-sleep thing)

2:16 PM
I see.

Check your coffee, it may be a dark roast

The next time I have coffee, I will. I usually resort to green tea.
It "feels" good for you :p.

Ive heard green tea works too
Also, I needed help with this one: math.stackexchange.com/questions/913933/…

@GustavoMontano: According to the scientists at 4chan, green tea is a nootropic.

What's nootropic?

2:27 PM
@GustavoMontano: You don't have to ask. We live in the 21st century. Use google.

Haha, that's true.

Incase Pakaku is reading this, welcome to StackExchange.

2:40 PM

i'm looking for a formal description of when a factor is moved outside the limit to ease calculation e.g. lim x->infinity 1/2 (ln 2-x), the 1/2 can be moved outside the limit to give 1/2 lim x-> infinity ln (2-x). what is this operation called?
preferably a web reference that i can summarize in my notes

@topper: I'm looking to read that math in LateX but I think if you try, you can prove why it comes out.

oops, sorry, my latex-fu is about as good as my maths blush
/me notes link on right regarding latex

Is it ln(2)-x or ln(2-x)?

ln(2-x)

2:51 PM
$$\lim_{x \to \infty} \frac{1}{2} \ln(2-x)\\ = \lim_{x \to \infty} \frac{1}{2} \cdot \lim_{x \to \infty} \ln(2-x)\\ = \frac{1}{2} \cdot \lim_{x \to \infty} \ln(2-x)$$

^ Exactly.

can now, just got chatjax working. how good is that!

It's not an operation. It utilises a rule about limits and their algebra.
It's great isn't it!
Put it in your bookmarks (y).

@Nick!

@Nick thanks! so pathetically simple!

2:53 PM
@topper: There's a property which states: $$\lim_{x \to n} f(x) \cdot g(x) = \lim_{x \to n} f(x) \cdot \lim_{x \to n} g(x)$$ Did you know that?

@Nick yep. just didn't apply it when it mattered. no worries, i learnt something

@BalarkaSen: Good evening, BalSensai ! What goes on :D

There's one for addition, subtraction and division (with the can not be zero condition).

@GustavoMontano: The property which i stated now. What is the formal proof for it.

Great question. I do not know.

2:56 PM
See, I learnt it the same way as well.

Well, at the end of the day, you're applying a substitution, aren't you?
So it feels intuitive.

@topper: You were one inch away from stoopifying us.

is that the same rule that means i can take the square root sign out of the limit in $$\lim_{x \to \infty} \sqrt(\frac{1}{2} \ln(2-x))$$

It's a substitution with a twist. You're substituting direction...hmmm
\sqrt{type stuff here}

@GustavoMontano: Treating $\frac{dy}{dx}$ as a fraction is intuitive. Doesn't mean it's absolutely right.
@topper: actually, it's more like can you take the limit into the square root sign?

2:58 PM
Well, $\frac{dy}{dx}$ is mean't to represent $\frac{\Delta y}{\Delta x}$?

The property you outlined isn't a hard and fast rule is it, @Nick?
I'm sure there are exceptions to that rule.
4 mins ago, by Nick
@topper: There's a property which states: $$\lim_{x \to n} f(x) \cdot g(x) = \lim_{x \to n} f(x) \cdot \lim_{x \to n} g(x)$$ Did you know that?

@Nick same question, but i guess you'll tell me i'm seeing it wrong? :)

$f(x)$ and $g(x)$ have to be continuous in the interval you are considering?

Was that in response to me, @Gustavo?