Mathematics - 2015-03-27 (page 2 of 3)

10:00 AM

have a look at dummit-foote, @Committing. it has a small chapter on lattices. recommend you read it.

(although, like many things in mathematics there are other types of lattices, that is just the kind Balarka was referencing)

Balarka Sen

i was talking about lattice of subgroups, @DiscipleofBarney.

Disciple of Barney

Yah, I guess I didn't make that clear, I was wanting to saying you were talking about the structure lattices

like the one I described

Balarka Sen

yes, sure, there are more general notion of lattices.

Committing to a challenge

Sorry I got a coffee

Yes I have a pdf of D&F I will check it out for sure

Balarka Sen

10:06 AM

a quick look at lattices tells you a lot of things, along with the first isomorphism theorem.

Committing to a challenge

I'll be taking a 4th year advanced algebra and a third year algebraic methods of physics next semester, so I have to work hard on algebra for the next 20 weeks

@DiscipleofBarney Essentially I try to get rid of the garbage on the site, noise that is worthless

Balarka Sen

for example, in the lattice of $Q_8$, you'll see a copy of the lattice of klein-4 group hiding inside it once you relabel $\langle -1 \rangle$ by $1$ and remove stuff below it.

that tells you that $Q_8/\langle -1 \rangle \cong V_4$

Committing to a challenge

What's the idea of a 'presentation'?

Disciple of Barney

@Committingtoachallenge Totally, the past couple days I have been using all my votes on old, bad, questions so Community will delete them.

Committing to a challenge

It looks like a way of lying down cycles?

@DiscipleofBarney What's your method of finding these?

Balarka Sen

10:11 AM

@Committingtoachallenge well it's a way to write down a group conveniently

Sayan Chattopadhyay

@BalarkaSen I have a doubt

Balarka Sen

if you have a huge group, then you can't just write the cayley table -- it'll take you years

Committing to a challenge

@BalarkaSen Writing it out in a way that requires no more information? Like putting cycles down to save space

Balarka Sen

rather, you can write down a few elements and a few relation between the elements that "generates" all the other elements and relations.

@Committingtoachallenge kind of

Committing to a challenge

@BalarkaSen Okay, I thought that was it, and I suppose that fits well with the name

Sayan Chattopadhyay

10:13 AM

If the number of elements in a set A is 15 and the number of elements in set B is 25 what is the range of elements in the symmetric difference of A and B @BalarkaSen

Balarka Sen

I see you have already asked that question above, @Sayan. Didn't you get an answer already?

Disciple of Barney

@Committingtoachallenge I havn't found t a great way, I have been using the search "answers:0 isanswered:no hasaccepted:no closed:no score:0" plus maybe some tag I want to look through anyways to see if there are any quesitons I would also like to answer. One could also try to get closed questions deleted so removed the closed:no, and maybe even the isanswered:no.

Committing to a challenge

@Dis
http://data.stackexchange.com/math/query/272758/find-posts-with-0-votes-and-0-answers

Sayan Chattopadhyay

@DiscipleofBarney he was not sure so I thought I would ask you

Balarka Sen

well, i'd say the question is not well-stated

what is "range of elements"?

Sayan Chattopadhyay

10:16 AM

That's what I don't know

Disciple of Barney

@SayanChattopadhyay That question doesn't make any sense, I would just get your prof to make it more clear.

Sayan Chattopadhyay

I am really confused

Balarka Sen

so it's not a sensible question

ask your professor or whoever gave it to you what he means by "range of elements"

Sayan Chattopadhyay

I called him and he said I have to find what the range of elements mean

Balarka Sen

figuring out definitions is not mathematics

Committing to a challenge

10:19 AM

You... 'called'... him?

That is the weirdest thing I have heard

You can call your professors in your country??

Disciple of Barney

@Committingtoachallenge Does that have any advantage over normal searching?

Committing to a challenge

@DiscipleofBarney It lets you open a tab and ctrl click a list and sort through which ones are garbage and not very easily

@DiscipleofBarney I do around 10 votes there a day(very rarely an upvote here, but often I skip them if they have high view counts and aren't garbage)

@DiscipleofBarney and the other 30 are across the new ones

Balarka Sen

@Committingtoachallenge Since you know a bit about cosets, here is a somewhat interesting exercise for you : $\Bbb R$ be the additive group of real numbers and $\Bbb Z \leq \Bbb R$ the subgroup of integers. Can you figure out how the quotient group $\Bbb R/\Bbb Z$ looks like?

Disciple of Barney

@Committingtoachallenge About the only reason why I want more rep is so I can vote to close. It does seem like a quicker interface, although adding a couple of restrictions so that a couple more relevant things are sorted out, to make the votes count as much as they can.

Balarka Sen

More precisely, show that $\Bbb R/\Bbb Z$ is isomorphic to the subgroup of the multiplicative group of nonzero complex numbers consisting of elements with absolute value 1.

This example is not only very interesting algebraically, but there is also a topological significance. The map $\Bbb R \to S^1$ that produces this isomorphism is an example of a covering space of topological groups. But you don't need that stuff to do it.

Jasper Loy

10:32 AM

Hi @Committingtoachallenge

Committing to a challenge

Hey @Jasper

Jasper Loy

@Committingtoachallenge I am scared I won't get my miracle.

Chris's sis

Greetings

Jasper Loy

@Chris'ssis Hi!

Chris's sis

@JasperLoy Hello!

Committing to a challenge

10:37 AM

@JasperLoy That is expected(feeling scared)

Chris's sis

Today I discovered something totally strange, I found an integral that produces the prime numbers in a perfect order. I mean the answer contains a string with the prime numbers in their increasing order.

infinitesimal simplicio

indefinitely?

Chris's sis

@infinitesimalsimplicio It seems so. I think the integral generates the whole prime numbers in the perfect increasing order.

infinitesimal simplicio

:-O

Chris's sis

I think you all know me enough to believe the mathematical things I say here. This is very strange to me too.

infinitesimal simplicio

10:41 AM

have you told rob?

Chris's sis

@infinitesimalsimplicio Rob seems away for 1 hour.

Committing to a challenge

@Chris'ssis Wut

infinitesimal simplicio

this could be big

Chris's sis

@Committingtoachallenge Exactly.

Committing to a challenge

@Chris'ssis Surely it stops after numerous iterations

Chris's sis

10:43 AM

@Committingtoachallenge I cannot confirm this. I still check large values.

infinitesimal simplicio

how large have you gone?

Committing to a challenge

@Chris'ssis Is there some no disclosure thing I can sign to see this?

Balarka Sen

@Chris'ssis Interesting. But probably not impossible.

Chris's sis

$2, 3, 5, 7, 11, 13, 17, 19$

Balarka Sen

I would say thought that I've never seen an explicit formula for the Copeland-Erdos constant. Can you post your integral?

Chris's sis

10:46 AM

@Committingtoachallenge @Committingtoachallenge @BalarkaSen first I need to check that for larger values. This is done with some difficulty by Mathematica.

Committing to a challenge

Yeah I don't think posting here is a good idea, probably by email instead(if she is willing)

Chris's sis

@Committingtoachallenge It's no problem to show it, but first I need to check that and see if I need to communicate the result. Then I show you the integral, no pb.

I show it to you all.

Committing to a challenge

I am keen

Chris's sis

(as I usually did with many of my results)

Balarka Sen

Ping me when you have decided to post it.

Chris's sis

10:48 AM

@BalarkaSen Sure.

Mathematica has a hard time for larger values of $n$.

Balarka Sen

@Committingtoachallenge Why do you think so? There are numerous formulas for generating primes.

Jasper Loy

The integral is \int dp_n, LOL

Balarka Sen

dp_n is nonsense, as p_n is not even a continuous function.

ᴇʏᴇs

Hi @JasperLoy, LOL

How are you feeling today @JasperLoy

Jasper Loy

@ᴇʏᴇs I am scared I won't get my miracle. I have made some plans for them to happen, but there are many obstacles.

@Chris'ssis Perhaps with your integral you are on your way to fame and fortune.

Chris's sis

10:56 AM

Update

Committing to a challenge

Has Did been banned before?

Chris's sis

$$2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47$$

Jasper Loy

Looks like you have found it.

Committing to a challenge

How did you find it? Intentionally or not?

Jasper Loy

A fields medal is on its way.

Balarka Sen

10:57 AM

If not deceived by the strong law of small numbers... but I'd say it's likely you have found a formula. It's not impossible.

Chris's sis

It might also be $2^n=2(\text{mod} n)$

Disciple of Barney

Very cool, although does it produce 57

2

Committing to a challenge

Show the integral so I can play around with it on my mathematica :)

Balarka Sen

I'm eager to see it.

Chris's sis

I look at it with the eyes of a kid (full of excitement).

@JasperLoy lol, I don't even know what that means, but first I need to make sure it works.

Committing to a challenge

11:00 AM

I am dying @Chris'ssis plz

Jasper Loy

@Committingtoachallenge Don't die yet. Wait till you see me.

Committing to a challenge

I want to get back to my assignment haha, but I have to see and play with this first

Chris's sis

The prime numbers are represented like that $n1*\log(p_1)+n2*\log(p_2)+\cdots$

I mean they appear inside the logarithm in an increasing order. The numbers in front of logarithms are very ugly, large numbers.

Committing to a challenge

What are these $n_1,n_2,\dots$?

Balarka Sen

That's even more interesting.

You should OEIS the $n_i$s too, just in case there is a sequence.

Chris's sis

11:04 AM

Wait, another set is done. Let me put them on paper and post another update.

$$2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101$$

Balarka Sen

aww, 57 is missing.

infinitesimal simplicio

:D

Jasper Loy

What is special about 57???

Chris's sis

@BalarkaSen Is 57 a prime number? $5+7=12$ :-)

Balarka Sen

i was only joking :P

Chris's sis

11:07 AM

@BalarkaSen ;)

Balarka Sen

it's a grothendieck prime, nonetheless

Jasper Loy

57 is not prime!!!

A fields medal is still on the way.

Committing to a challenge

It's a joke, read barney's link :P

Jasper Loy

@Chris'ssis Don't forget me when you win the prize! =)))

Chris's sis

@JasperLoy I doubt a non-mathematician would ever win such a prize. ;)

Jasper Loy

11:09 AM

@Chris'ssis Miracles happen to those who least expect it.

Chris's sis

@JasperLoy :D

Committing to a challenge

$$\large\color{blue}{\text{:D}}$$

Jasper Loy

There can be miracles when you believe.

Disciple of Barney

@Chris'ssis You might make Mathematics Chat room a major math journal

infinitesimal simplicio

$$\large\color{red}{\text{:D}}$$

Jasper Loy

11:11 AM

I have made this chat my psychotherpy room.

Committing to a challenge

$$\large\color{green}{\text{:D}}$$

Chris's sis

@DiscipleofBarney hehe, I think @robjohn altready did that. :-)

Balarka Sen

now, now, let's not make this into a colorful smiley room.

Committing to a challenge

Yes, I am procrastinating, where shall I learn complex analysis hmm

infinitesimal simplicio

yes, your highness

Chris's sis

11:13 AM

I'm preparing for a new update!

infinitesimal simplicio

drum roooll...

Balarka Sen

@Committingtoachallenge I thought you were planning on doing algebra?

infinitesimal simplicio

Drum roll sound effect

►

Committing to a challenge

@BalarkaSen I love algebra so far, and am taking heaps of algebra next semester, but I am doing my semester now, and one of my courses is complex analysis(non optional course[but would have taken it anyway])

I am also doing functional analysis, and also cryptography+Coding theory

Balarka Sen

ah, i see.

Disciple of Barney

11:16 AM

(it would be funny if Chris'ssis was just making this up and just posting sequences of primes)

Committing to a challenge

@DiscipleofBarney I considered that

And started studying as a result

Disciple of Barney

She should have waited a week for April 1

Chris's sis

$2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,‌$ $107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199$

Committing to a challenge

Give us the integrallllllllllll

Disciple of Barney

I don't think you need math mode for just a sequence of numbers

Committing to a challenge

11:21 AM

True, I guess it is habit

Disciple of Barney

I do that too

out of habbit

Chris's sis

@Committingtoachallenge :-)

I'm concerned about 341 ... (not sure if this appears - I hope it won't appear)

Committing to a challenge

Why does it worry you?

Disciple of Barney

Is there a reason to believe 341 will show up

Chris's sis

Because $2^{341}=2(\text{mod} 341)$, and it's not a prime number.

Disciple of Barney

11:25 AM

Ah, woried it might be showing you that sequence

Chris's sis

Ready for a new update

Committing to a challenge

We aren't getting the integral are we?

infinitesimal simplicio

12 mins ago, by infinitesimal simplicio

Drum roll sound effect

►

Disciple of Barney

Or A216883 Primes p such that x^31 = 2 has a solution mod p.

infinitesimal simplicio

enjoy the moment

this is Chris'ssis' moment

Chris's sis

11:36 AM

$2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,‌$ $107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199$, $211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293$

OEIS doesn't recognize the primes numbers when add this input. They are all primes numbers in the perfect order.

One more update and then ... I wanna say something

$307, 311,313, 317, 331,337, 347,349,353,359,367,373,379,383,389,397,401$

Guys, I think it's about prime numbers!!!

Committing to a challenge

Int pls

Chris's sis

I never ever met such an integral before.

Committing to a challenge

You are solving for primes in fast linear time I imagine

Chris's sis

@Committingtoachallenge You'll see the integral, for sure, but I need to do some steps before diong that.

Disciple of Barney

Hah

Chris's sis

11:45 AM

@infinitesimalsimplicio thanks! This is a moment hard to manage, really!

One of the questions is: how important such a result is?

Committing to a challenge

I don't study complexity theory, but I am pretty sure I heard prime counting isn't linear time, and that would make this godlike if it is, but I don't know if you are in linear time either

infinitesimal simplicio

1 hour ago, by infinitesimal simplicio

this could be big

Chris's sis

As I mentioned, they appear in this form $$n1*\log(p_1)+n2*\log(p_2)+n3*\log(p_3)+\cdots$$

@Committingtoachallenge hmmm, I see.

Committing to a challenge

But more importantly, it would give us hints on how primes are distributed

Less interesting for me for some really odd reason :P

Chris's sis

12:00 PM

It works perfectly for the first 100 prime numbers (I just checked that):

rsok.com/~jrm/first100primes.html

Disciple of Barney

So are you just going to be teasing us?

Chris's sis

@DiscipleofBarney This is just real. As regards math, I never say words for the sake of saying words.

Committing to a challenge

When do you plan to show the integral?

Chris's sis

Maybe it's better to write $$Q1*\log(p_1)+Q2*\log(p_2)+Q3*\log(p_3)+\cdots$$

since they are rational numbers (the numbers in front of log).

detly

there is a famous series, involving alternating between two different calculations for the next term, that always seems to converge to the same repeating set of three numbers, but it's never been proven that it does

can anyone tell me it's name, because this has been bugging me all day

Disciple of Barney

12:07 PM

Collatz conjecture

detly

@DiscipleofBarney THANK YOU

Semiclassical

What do the Q's look like (aside from being rational)?

detly

@DiscipleofBarney I cannot tell you how many times I've tried and failed to google that

Disciple of Barney

@detly No problem

Chris's sis

@Semiclassical Very large as we consider larger values in the generating integral. It's under investigations.

Semiclassical

12:09 PM

Hmm

Chris's sis

@Semiclassical It works for the first $100$ primes numbers.

(I didn't check more yet)

Semiclassical

Sure.

It sounds like the chebyshev prime-counting function, though with coefficients

Committing to a challenge

But those take prime inputs right?

I was under the impression perhaps falsely that Chris'ssis didn't take prime input

Semiclassical

The chebyshev function? No

Chris's sis

@Committingtoachallenge I only use natural numbers in the generating integral.

Semiclassical

12:15 PM

All it does is sum up the logs of all primes smaller than $n$

But I think I was wrong to call it a prime-counting function

Disciple of Barney

Well I am guessing it will either be stared or not posted by the time I wake up. @Chris'ssis Good luck, it would be really cool, and I am sure exhilarating, for it to be proven to generate the primes. (Depending on how it works maybe some alt and independent proofs of infinitude of primes or prime number theorem)

Chris's sis

@DiscipleofBarney Thanks.

Ben Beri

12:33 PM

$W \in (X_a \delta X_b)$ - Where does it state that delta can mean that W is either in $X_a$ Or in $X_b$ but not in both?

I can't find it anywhere

Chris's sis

However, it might not be such a a clever thing as thought.

(more investigation is needed)

BBL

One more thing, it's not weird that we have primes numbers, since we take log of a natural number, say, and decompose it into such forms, but the fact that the log primes follow an increasing pattern, skip no prime number.

BBL

Ben Beri

1:06 PM

How do I find angles between to linear functions?

$4x + 18 = 2x - 7$

Ben Beri

1:17 PM

Whos there

Ted Shifrin

@BenBeri: Do you mean the angle between the two lines $$y=4x+18 \quad\text{and}\quad y=2x-7?$$

Ben Beri

yes

Ted Shifrin

What tools are you using? Trigonometry? Vectors?

Ben Beri

trigo

1 question, is the angle between -2x = 2x 90 degrees?

Ted Shifrin

First, stop writing equality of the different linear functions. That's not correct.

No, it's not. The angle between $y=2x$ and $y=-x/2$ is $90º$.

Are you doing this with pencil and paper or using a calculator? Your first line makes an angle $\alpha$ with the $x$-axis where $\tan\alpha = 4$. What about your second line?

Ben Beri

1:27 PM

I don't understand, im new to this

Ted Shifrin

@BenBeri: For your second question, look for symmetric difference $A\Delta B$ (not little $\delta$).

Ben Beri

ah

Ted Shifrin

Well, I have no clue what you know and what you don't know. You need to know basic trigonometry to answer the question. You don't know that slope of a line gives the tangent of the angle? Draw a picture and think about it!!

ᴇʏᴇs

Hi @TedShifrin

Ted Shifrin

hi mr eyeglasses

Committing to a challenge

1:34 PM

You know you should be sleeping when @Ted logs on

Ted Shifrin

I should be sleeping, @Committing?

Committing to a challenge

No I should be, because you logged on

Ted Shifrin

Well, go to sleep! :)

Committing to a challenge

It's almost midnight, but I needed to workout(just finished) because I failed to workout for 10 days and I am getting fat :'(

Ted Shifrin

I'm sure your notion of "fat" is still 30 pounds lighter than mine. :)

Committing to a challenge

1:35 PM

+I really needed to do some complex analysis

Ted Shifrin

You guys need to stop hating analysis. If this turns into a room of utter algebraists, I shall never return.

Committing to a challenge

@TedShifrin I was once literally anorexic(~56kg at 6ft) and then I reached 76kg pretty muscular, and now I am 84kg and much weaker

@TedShifrin Where did I hate on analysis here?

Ted Shifrin

You didn't this time ... but you and various other people have been talking about hating analysis. :P

Committing to a challenge

@TedShifrin Complex looks like it might be good, and I am not sucking at real analysis so much now, and we all know that doing good = having fun, doing bad = hating

Ted Shifrin

Well, at 6', I don't call 84 kg fat. Maybe not trim, and maybe not built ... muscles aren't just weight-dependent :P

Committing to a challenge

1:38 PM

I was benching 110kg and deadlifting 160kg and now I bench 90kg and deadlift ~120kg

Ben Beri

Guys how can I prove that linear function inverse creates 90 degrees?

Ted Shifrin

I don't think your table of equivalencies there is universal, @Committing. I have done well in things I didn't necessarily enjoy, and vice versa.

That is false, @BenBeri.

Committing to a challenge

Probably lost 2-4kg muscle mass while increasing in weight by 8kg, so 10-12kg fat gain

Ben Beri

@TedShifrin What do u mean?

Committing to a challenge

@TedShifrin But were they solely learning related or other?

Ted Shifrin

1:39 PM

You can start computing d(muscle)/d(weight), @Committing :)

Committing to a challenge

@TedShifrin xD

Ben Beri

@TedShifrin I was taught that if you inverse like x = -x/1 it always creates 90 degrees

Committing to a challenge

Is that division by 1?

Oh lol

Ted Shifrin

@BenBeri: That is not inverse. And you MUST stop writing ax = bx when you're talking about $y=ax$ and $y=bx$.

Ben Beri

How is that called?

Ted Shifrin

1:41 PM

What you should have been taught is that perpendicular lines have SLOPES that are NEGATIVE RECIPROCALS.

Committing to a challenge

This is for programming @Ben?

Ben Beri

@Committingtoachallenge Nope

Committing to a challenge

@BenBeri What is this for?

Ted Shifrin

yields the floor to @Committing

Ben Beri

@Committingtoachallenge Just a mate saying that changing the slope from plus to minus or vice versa creates 90 degrees

Committing to a challenge

1:43 PM

@TedShifrin But...but... I should be sleeping :P

@BenBeri Have you drawn any examples?

Ben Beri

Well he showed me this i.gyazo.com/92a60c2c5871795c625b1d373e33320f.png

Committing to a challenge

Which he looked at the scale for obviously

Did my sarcastic comment solve the problem?

Ben Beri

maybe

Committing to a challenge

What? Why maybe?

Ben Beri

because I am not sure what did you say lol

Committing to a challenge

1:46 PM

Does that answer your question then?

Ben Beri

Well he says that WA graph is not accurate

Committing to a challenge

Ben Beri

He sent me this gyazo.com/f0e8d44c75c8a3dae36c6c464652d71c

Committing to a challenge

He is either trolling or you are.

Sorry I am probably just tired my bad[he is still wrong though]

That 'inaccurate' graph weirdly had 2 different angles both of angle 90 degrees, pretty crazy

Did I do well minus the unnecessarily bad attitude[sorry Ben] @Ted

Ted Shifrin

I'm not criticizing you or your attitude, @Committing. :)

Chris's sis

1:54 PM

I need to formulate something in a mathematical way ...

Committing to a challenge

@Chris'ssis Don't we all :)

@Ben Are you there, sorry for being rude, is it alright now?

Chris's sis

A very nice question I created yesterday

Ben Beri

I am ok, but I dont understand why the graph wolframalpha.com/input/?i=%7By+%3D+x%2C+y+%3D+-1%2F2x%7D doesnt show 90 degrees

or I am just being blind

Committing to a challenge

@Chris'ssis How fast is your prime counting method? Did you do each by hand, or computationally

Chris's sis

Find $f_n(x)$ such that $$\int_0^1 \frac{1}{\log(x)}+\frac{1}{\log^2(x)}+\cdots+\frac{1}{\log^n(x)}+f_n(x) \ dx$$ converges.

@Committingtoachallenge Computationally.

Committing to a challenge

1:57 PM

Is that the prime one?

Chris's sis

@Committingtoachallenge No.

Committing to a challenge

@BenBeri Why do you think it should be 90 degrees?

Jasper Loy

Hi @Chris'ssis how is the integral?

Ben Beri

opps sorry for that one lol

Chris's sis

@JasperLoy Hi

Ted Shifrin

1:58 PM

Good night, @Committing :P

Ben Beri

@Committingtoachallenge Sorry, but that one wolframalpha.com/input/?i=%7By+%3D+2x%2C+y+%3D+-1%2F2x%7D

Committing to a challenge

@TedShifrin Why are you goodnighting me lol

Ted Shifrin

Because you said it was past your bedtime?

Committing to a challenge

@BenBeri Why do you think that is 90 degrees?

Chris's sis

@JasperLoy Related to the one with primes, it's still interesting for the fact it covers all primes in an increasing order following the patterns described above.

Committing to a challenge

1:58 PM

@TedShifrin It is haha

Ben Beri

Because of negative reciprocals or something?

Committing to a challenge

Do you know vectors?

Jasper Loy

@Chris'ssis Have you shown them the integral?

Chris's sis

@JasperLoy No.

Committing to a challenge

@JasperLoy No, I have waited for hours lol

Ben Beri

1:59 PM

no

Jasper Loy

@Committingtoachallenge I have waited for years to get well.

Ben Beri

Well yes

Committing to a challenge

@BenBeri Well yes? Can you write those directions(of the lines) as vectors

Ted Shifrin

hi @Jasper ... I said something earlier I was waiting for you to star :P

Jasper Loy

@TedShifrin Let me see...

Ben Beri

2:01 PM

oh vectors don't have reciprocals

Committing to a challenge

$(1,2)$ and $(1,-\frac12)$ right?

Ben Beri

well yea

Committing to a challenge

$(1,2)\cdot(1,-\frac12)=$

Not bad, $0$ hence orthogonal(90 degrees)

Chris's sis

@JasperLoy How should I specify mathematically that $f_n(x)$ cannot contains the terms with the negative signs above? I'd like my question be clear enough.

Committing to a challenge

But it doesn't look like it, weird. Ohhhh the scale changes on WA because WA is annoying and QED

Good now?

Jasper Loy

2:03 PM

@Chris'ssis Which question?

Chris's sis

Otherwise one might say, for example $$f_n(x)=-\left(\frac{1}{\log(x)}+\frac{1}{\log^2(x)}+\cdots+\frac{1}{\log^n(x)}‌\right)+1$$

Committing to a challenge

@Ben hellloo

I'm getting loopy as David would say lmao

Chris's sis

@JasperLoy the integral I posted above ...

Ben Beri

@Committingtoachallenge So the answer is that WA drawing in inaccurate?

Committing to a challenge

@BenBeri No

@BenBeri It is accurate, butttttt the scale isn't 1:1

If the scale was 1:1 it would look like you think it should

Chris's sis

2:05 PM

I mean the integrand must be consisted of $$\frac{1}{\log(x)}+\frac{1}{\log^2(x)}+\cdots+\frac{1}{\log^n(x)}$$ and thus $f_n(x)$ cannot cancel any of them.

Committing to a challenge

If the scale was 1:100000000000000000000000 it would still be write(other than display error) but it would just be a straight like on the axis

Ben Beri

Ahh i see

Committing to a challenge

Whatever axis that is, too tired to work that out right now

Ted Shifrin

write = right, hence goodnight @Committing :P

Committing to a challenge

I know roflmao

Nice rhyme though I will sleep because it was too good

Ted Shifrin

2:06 PM

I no you know.

Committing to a challenge

Thanks @Ted I can rest piecefooly naow

Jasper Loy

@Chris'ssis Hmm, I don't know, cannot think now.

Committing to a challenge

Cya guys, hope that helped @Ben

Ben Beri

@Committingtoachallenge you're da boss

Chris's sis

@JasperLoy OK. If you have any idea, let me know. No hurry with that.

Ben Beri

2:07 PM

gyazo.com/9253681ded430d56772e6a8cda0c5fce

Committing to a challenge

Yay scales are 1:1 :)

Jasper Loy

@Chris'ssis I just got back from dinner with a friend. Pork with curry!

Committing to a challenge

Have a star

Chris's sis

@JasperLoy :-) You're not a muslim, that's sure! :-)))

Jasper Loy

People are queuing up for ten hours to pay respects to my dead first prime minister.

Many people fainted and had to be carried away.

Even my mum went.

I did not go.

The only person I would pay respects to is my mum.

4

@Chris'ssis I am sort of Buddhist. One day you may want to study Buddhism.

Chris's sis

2:13 PM

@JasperLoy I might reach this way the Nirvana of integrals. :-)

Jasper Loy

@Chris'ssis In a way, Buddhism explains science and other religions to me.

Chris's sis

@JasperLoy I realize every day that the complexity of life becomes deeper and deeper to me, it's like a black hole from which no one escapes. I lost much of my courage to find a meaning in all things that happen around.

Life is too complex to me to ever understand anything.

Jasper Loy

@Chris'ssis I have lost most of my will to live on. I have struggled for too long with mental illness.

@Chris'ssis Like you said, sometimes there is nothing to understand. Things just are.

Chris's sis

@JasperLoy Still, life is beautiful, and if many things happen without a meaning, that's not a reason to give in, but we can give noble purposes to our lives. Trust me, it is worth living your life and never give up.

Jasper Loy

@Chris'ssis I hope so. Maybe the meaning of my life is to meet you one day, LOL.

Chris's sis

2:19 PM

@JasperLoy :-)))))

Jasper Loy

@Chris'ssis I am wondering why those people don't want to give you the job.

Chris's sis

@JasperLoy Asking too much for them? That's the reason (well, they think it's too much, but no, it's less).

Ben Beri

Guys is slope is just the tangles of the angle?

Jasper Loy