Mathematics - 2015-11-07 (page 2 of 5)

Bungo

02:00

@AlexanderGruber yes classic

Alexander Gruber

@user her vocal range is better than I expected

user143442

i'm in the second song now

user143442

I like it

user143442

of course, she's a very good singer

user143442

she can sing live

user143442

02:02

Ariana Grande - Problem - Break Free and Love me Harder - AMA's 2014

►

Alexander Gruber

i'm definitely liking the other tracks better than break free, which is the song i'd heard by her most often

Mike Miller

@anon: you might appreciate this. i'm finding it pretty readable. maybe it's all stuff you know though

@AlexanderGruber: how do you like the coup

user143442

I'm also liking Zero 7, their sounds remind me of D.A.N.C.E. by Justice

user143442

I'm listening to a song with no singing

user143442

Seeing Things

Alexander Gruber

02:11

@MikeMiller DONT TRUST THE POLICE NO JUSTICE NO PEACE

Mike Miller

reasonable answer

Alexander Gruber

they're great

Mike Miller

insanely clever

Alexander Gruber

@user the girl singing with them is Sia btw

when I was in college I had to institute a strict ban on the pageant of the bizarre during parties because it makes me cry when i'm drinking

user143442

in which song

PVAL

02:19

@MikeMiller I asked a question on MO. I have no idea how hard it is, though I'd honestly be surprised if its tractable. mathoverflow.net/questions/222903/…

Alexander Gruber

the pageant of the bizarre @user

user143442

oh that's the one i'm listening to right now

Alexander Gruber

and You're My Flame and probably a couple others

user143442

what a coincidence

user143442

i love sia

Mike Miller

02:20

@PVAL: Are there no homology S3s where it's known that there's only a couple tight contact structures?

Alexander Gruber

Me too

PVAL

@MikeMiller I don't know. There's ones with finite amounts, but these are often computed in a way where I don't know how to get the Legendrian surgery diagrams for them.

Mike Miller

I can ask Ko about this next week if you want.

PVAL

@MikeMiller I've tried understanding the things people have said about ones that are SFS's , but maybe there is more known if I allow people to do whatever they want to with the boundary.

That would be nice.

If anyone would know..

I don't think Bob knows of an example, though I don't think I've asked this directly to him.

Mike Miller

I don't know if he thinks about Stein fillings but good odds he can produce homology spheres with a small number of say symplectically fillable contact structures.

PVAL

02:26

Are there ways of computing the classical invariants of knots in these structures?

Mike Miller

I wouldn't know.

@PVAL: Something I was thinking vaguely about yesterday. Gromov has a theorem that every almost symplectic structure (nondegenerate 2-form) on an open manifold is homotopic to a symplectic one. Are there any good ways of telling if something has an almost symplectic structure?

user174558

Hi @mike I hope you got my email about my new email.

Mike Miller

I did.

user143442

@AlexanderGruber I already finished the tracklist, thank you, it's very good music, I'll add it to my favorites list

user143442

@Jasper I didn't get your email

user174558

02:33

Hi @Mahnax I hope you got my email about my new email.

Mahnax

@Jasper Hi Jasper! Yes, I received it.

user143442

I feel excluded :(

PVAL

@MikeMiller Not that I know of. Immersions into codim-0 manifolds which are symplectic, J-holomorphically embedded submanifolds for tame ACS, and Stein manifolds are really the only ways of constructing symplectic structures I know about.

Mike Miller

Figures.

(In particular it would be nice to know which punctured compact 4-folds admit a symplectic structure.)

eg I wonder if $\#^3 \Bbb{CP}^2 \setminus \{pt\}$ does.

PVAL

What is the genus of the sum of the generators for $H_2$?

Mike Miller

02:41

No idea. Is there an obstruction there even for noncompact mfds?

PVAL

Well probably if it were convex at infinity at least

Alexander Gruber

@user great, glad to hear it

Mike Miller

Oh I'm not expecting it to be good near infty.

PVAL

theres probably things you can do if you assume something like "weakly convex at infinity".

Alexander Gruber

good god

how much algebraic topology do i have to take before i have any idea what the words that you are saying even are

PVAL

02:43

Well it isn't algebraic topology.

Alexander Gruber

...so, not very much then

Mike Miller

:)

Alexander Gruber

OK good I'm on track

Mike Miller

One other Q: are there known examples of M and exotic M (compact) that both support symplectic structures?

PVAL

closed?

Mike Miller

02:43

yah

PVAL

I know plenty of compact not closed examples

Mike Miller

Yeah but those are pretty much just noncompact, so that's cheating.

Mahnax

Have a pretty simple linear algebra question if anyone is willing.

Not sure where to begin.

PVAL

Not really... they are Stein fillings of their boundary.

Alexander Gruber

@Mahnax ok so

PVAL

02:45

Any way theres examples here arxiv.org/pdf/1402.0801v3.pdf

I'm sure there's older examples.

Alexander Gruber

can you simplify (AB^{-1})^{-1}

Mike Miller

Here's one on $\Bbb{CP}^2 \# 5\overline{\Bbb{CP}^2}$.

Mahnax

@AlexanderGruber $(BA^{-1})$

Alexander Gruber

ok so what's $(BA^{-1})(AB^2)$

Mike Miller

I have a mild hope that one can tame smooth manifolds in 4-dim by thinking about symplectic structures, like maybe that there's only fin. many symplectizable ones.

PVAL

02:47

?

Mahnax

@AlexanderGruber No idea. I've never encountered that sort of operation with matrices before.

PVAL

well blow-up the plane n times

theres infinitely many of them

Mike Miller

I mean on a given topological manifold.

Alexander Gruber

@Mahnax Multiplication?

Forget that these are matrices. That isn't important.

Mahnax

I don't suppose you can just say that $(BA^{-1})(AB^{2})=I_{n}B^{3}$?

Alexander Gruber

02:49

You sure can

Mahnax

Well, that's nifty.

Alexander Gruber

so what's X then?

PVAL

@MikeMiller Symplectic structures help distinguish smooth structures though.

Mahnax

@AlexanderGruber $B^{-3}A^{-1}$?

Alexander Gruber

close

Mike Miller

02:52

@PVAL: But infinitely many of them? The standard constructions I know of infly many exotic structures are like Fintushel-Stern knot surgery which doesn't involve the symplectic structure.

Mahnax

Other way around?

$A^{-1}B^{-3}$?

Alexander Gruber

$\begin{eqnarray*}X^{-1}A&=&B^3\\X^{-1}&=&B^{3}A^{-1}\\X&=&(B^{3}A^{-1})^{-1}\\X&=&‌\cdots ? \end{eqnarray*}$

Mike Miller

@PVAL: I'm being silly. Dolgachev surfaces are all homeomorphic Kahler manifolds, none of which are diffeo.

Sigh.

Mahnax

$X=AB^{-3}$

PVAL

@MikeMiller Most invariants for smooth structures are based around Kahler/symplectic/Stein geometry.

Alexander Gruber

02:56

got em

Mahnax

Thanks very much for your help!

Alexander Gruber

No problem

user174558

No problem, LOL.

Mike Miller

I don't know ways to tell apart smooth structures that don't ultimately come down to instantons or monopoles.

PVAL

@MikeMiller Dolgachev gave a series of talks here. They were unintelligible.

Mike Miller

02:57

But this is probably just a corollary of my training.

lol

I felt the same when Okounkov came here.

user174558

When is Miller coming to my town?

Bungo

i thank you guys for that matrix discussion, as it motivated me to work out how to make mathjax work in this chat

PVAL

@MikeMiller Someone named Yasha gave a talk here about a week ago that I enjoyed, though I'm unsure if many other people did

Bungo

test: $\int (\liminf f_n) \leq \liminf \int f_n$

oh sweetness

Mike Miller

Emmy talked here a while back and was a good speaker. I didn't get much out of it, though, because I didn't know much contact geometry then.

What did he talk about?

PVAL

03:03

Everything.

Flexibility

Rigidity.

You name it

Mike Miller

Classic Yasha

PVAL

It was like he'd describe a problem that was very interesting that I could understand. Then he'd describe how to do it in some " easy" case (which I wouldn't understand). Then he'd describe how one should try to solve the open case.

He did that about 8 times

Mike Miller

I guess he probably just listed a bunch of things he'd like to know.

PVAL

basically

@MikeMiller For instance he talked about what conditions on $r_i$ and $s_i$ you need for a symplectic embedding $D^2_{r_1}\times \dots \times D^2_{r_n} \to D^2_{s_1} \times \dots \times D^2_{s_n}$. The total volume is one obvious condition, Gromov famously gave another, but given those two what else can you do?

(r_i,s_i denote radii of the disks)

Mike Miller

Did he give any other exs?

PVAL

03:13

I think he said that "stably" these are the only ones.

I.e. if you product on both sides by a bunch of big enough disks with the same volume it eventually always embeds

Mike Miller

Interesting

PVAL

He stated that a Legendrian knot on S^3 which bounds a Legendrian disk on the complement of the 4-ball always has tb 1. Therefore adjunction shows you can never have such a Legendrian disk on the outside of the 4-ball.

That was probably what I got out of the talk.

He mumbled about h-cobordism and the hairy ball theorem as well.

Mike Miller

Big fan of those.

PVAL

His example of a flexible result was h-cobordism and a rigidity result was the hairy ball theorem. I think the audience probably thought those results differed a lot more in difficulty then he did.

my words became jumbled

Mike Miller

They are pretty good examples though.

PVAL

03:24

I'm sure he said something about the nearby Lagrangian conjecture, though I don't remember what.

user174558

I finally got the Teacher Badge on this site.

user143442

@Jasper congrats

user174558

But most of my answers have 0 votes.

user143442

I'm gonna vote for all your answers

user174558

@user How are you feeling these days?

user143442

03:31

Good, why?

user174558

You seem very troubled.

user143442

why do you say so?

user174558

From the way you behaved.

user174558

If you have a problem, you can talk to me about it.

user143442

I don't have any problem

user174558

03:38

Then good. My job is done.

user174558

Yes, indeed.

user147690

05:41

@Ashwin How you doing buddy?

crocket

06:36

0

Q: Am I not ready for a math textbook if I have to resort to solutions early in problem solving?

I started studying "Introduction to Mathematical Logic, Sixth Edition" by Elliot Mendelson. I tried to not read solutions as long as possible, but most exercises were awfully difficult to me, and the content itself was not easily digestible. When I tried to solve exercises in the chapter about m...

crocket

07:22

Can anyone recommend some other textbooks that can replace "Introduction to Mathematical Logic, 2nd edition" by Elliot Mendelson for me? It's too difficult for a math beginner.

user174558

@crocket Michael O'Leary: Mathematical Logic and Set Theory

Secret

1) what's the difference between phase space and parameter space
2) Is there a term for "a family of phase spaces"?

felipa

hi.. anyone know about matrix norms? math.stackexchange.com/questions/1517103/…

crocket

@Jasper ok

user174558

@crocket Mendelson is a good book, but it covers NBG set theory instead of ZFC which is the norm.

crocket

07:28

@Jasper Did you read Mendelson?

user174558

@crocket Parts of it.

crocket

Is it suitable for a person who knows some highschool math and read "how to prove it, 2nd edition" by velleman?

That's basically my background.

user174558

I think you would lack the background needed for Mendelson, maybe even O'Leary, maybe.

crocket

ah

ok

Tell me about the background

user174558

If you only know some high school math, why do you want formal logic?

crocket

07:30

I want to do ordinal logic which is handy in AIs.

user174558

Usually, people study lots of courses first like calculus before reading formal logic.

crocket

Mathematical logic is handy for AIs.

user174558

Formal logic is a third year course for math undergrads.

crocket

Is calculus a prerequisite for logic?

user174558

No, it is true that there are no prerequisites for logic, other than "mathematical maturity".

crocket

07:32

I'm a lone wolf living in a cave who studies alone.

user174558

I do not know about AI, but the O'Leary book is very elementary and you can try it.

user174558

But it is a little expensive, about 100 USD.

crocket

I could sort of understand what the author wanted to say about multi-valued logic, but the exercises on it are too difficult at my level.

But, it took an hour to read a page on multi-valued logic. It was that difficult.

user174558

Many exercises are difficult in a math book!

user174558

Well, I understand your difficulties since you are not a math undergrad.

crocket

07:34

The exercises can only be solved by very advanced ones.

Some exercises can be solved by me, but most are difficult.

user174558

@crocket I think you can go to wiley.com, see the first chapter of what I recommended, and see if it suits you.

Chris's sis the artist

@Jasper Well-said! Wait to see my book! :-)

user174558

@Chris'ssistheartist Hi! I have not met Laura Ramsey, LOL.

Chris's sis the artist

@Jasper :-)))))

@Jasper It's still not too late for doing that!

:D

crocket

@Jasper Did you refer to "A First Course in Mathematical Logic and Set Theory 1st Edition" by Michael O. Leary 2015?

Secret

07:36

so annoying that there aren't many dynamical system guys on chat lately, cause I have a stockpile of dynamical system related conceptual questions that need help on and there's isn't many people with the backgroudn that can help

user174558

@crocket Yes, I did.

crocket

A first course? Does it mean it's for me?

user174558

@crocket Titles in math books mean nothing.

user174558

@crocket Download the pdf file there, it has the first chapter.

crocket

@Jasper How do you know about the book?

user174558

07:43

@crocket Well, I found it online and read the first chapter like you did, that is all. And also looked at google preview and the contents page.

crocket

I can't find pdf

Where is it?

user174558

@crocket Click on "read an exerpt" on the Wiley page.

user174558

as.wiley.com/WileyCDA/WileyTitle/productCd-0470905883.html

user174558

@crocket I am going out now, good luck.

user147690

@crocket For the record, taking an hour per page in a mathematics textbook, on content you have never seen before is quite normal

crocket

07:48

@AlexClark Do you think "Introduction to Mathematical Logic, 6th edition" by Mendelson is not suitable for me?

user147690

@crocket I don't know, I haven't read it, and I only skimmed the chat above

user147690

I am just saying not to be disheartened by moving through it very slowly

crocket

Is it totally normal to be unable to solve most exercises?

user147690

No, but mathematics it not at all like reading a book

user147690

You have to really think and keep trying

user147690

07:49

Try not to look at the solutions

crocket

I couldn't move a bit for half an hour with an exercise.

user147690

It'll become a necessary crutch very quickly

Mats Granvik

It is better to try than to think.

9814072356

"Mathematics is not a spectator sport".

user147690

@crocket Sometimes I am stuck for two hours on an exercise

9814072356

07:50

Sometimes I am stuck for days on difficult homework problems.

user147690

@crocket Sometimes a difficult homework has 3 questions and take me 3 weeks

9814072356

^

user147690

Amen to that @9814072356

crocket

Perhaps, you should move on after trying for days or weeks.

If you are not going to build your career on top of only those problems.

user147690

@crocket Nah I always get it, and when I see something similar I can work it out very quickly in comparison

crocket

07:51

You look like an advanced student.

user147690

Not really

crocket

I study math alone at home.

9814072356

As @AlexClark said. Often the best things in mathematics are hard won, and this requires persistence and effort (sometimes frustrating, but stick through it and you'll get it in the end)

user147690

Well take it from me, there are only 6 people left in pure math by final year at my university, and all of them have the same work ethic as I am talking about above

9814072356

Rarely are things super easy, the more advanced you get

user147690

07:54

I mean, there is no reason why you should give up after 30 minutes, there is no law saying to give up, it means you are out of motivation, and you have to remember why you are studying what you are @crocket, which I imagine is something to do with working better on your problems relating to AI?

crocket

But, I feel that some books are unnecesasrily difficult for beginners.

user147690

Well unfortunately, often there isn't a nice book for beginners, I couldn't find one for hopf-algebras

crocket

Still, "Introduction to Mathematical Logic, Sixth edition" by Mendelson is too difficult for an entry.

user147690

I'll have a look, one sec

9814072356

@crocket, it all sort of depends on how you define 'beginner'

crocket

07:56

I got a feeling that it makes concepts unneccesarily difficult.

user147690

Yes indeed, a beginner of the subject who hasn't got mathematical maturity will suffer

user147690

A beginner of the subject with mathematical maturity might find it easy

crocket

I know some highschool math and read "how to prove it, 2nd ed" by velleman. That's it

I have a bit of maturity

9814072356

For example, Enderton's and I think Mendelson's that you mentioned, is targeted to late undergraduate maths students. Which is considered 'beginner', I think, with no prior exposure to the material

user147690

Well I would recommend to any human being to atleast read a few chapters of rudin's principles of mathematical analysis

9814072356

07:58

<3 Rudin's

crocket

I'm like a freshman in a university.

user147690

Is that first year?

crocket

yes

user147690

Freshman-> sophomore-> junior->senior?

9814072356

(I have no idea, I'm not American)

oh, cool

sophomore goes in there somewhere?

user147690

07:59

Ahh forgot that one

9814072356

Speaking of, I'm actually starting a seminar using Enderton's next term

Agawa001

freshman ! thats new term for me

9814072356

(set theory) Debating between Jech's and Enderton's though, @AlexClark, have you used either of those?

user147690

We have no courses on logic :\ @9814072356

crocket

"A First Course in Mathematical Logic and Set Theory" by Michael O. Leary seems adequate for my level.

9814072356

08:01

His set theory book, not formal logic, I think

user147690

No set theory or formal logic at my university

9814072356

Jech's might go a bit fast, but Enderton's might be a bit slow. Hmm, something to think about

user147690

Wait wow, we will have one next year for the first time in years uq.edu.au/study/course.html?course_code=MATH3306

9814072356

Ohh, that's a shame. We don't have an undergraduate course in that either, and the graduate one hasn't run for many years

Agawa001

its good to wake up the morning and learn new terms

9814072356

08:02

interesting

user147690

@crocket Where are you in Mendelson?

user147690

The first chapter looks very standard first semester first year

crocket

"1.5 Independence: Many-Valued Logics" <-- This is difficult

I understood the chapter intuitively, but I couldn't solve the exercises there.

I do not have rigorous understanding yet

9814072356

@AlexClark, quick google search yields jhtm.nl/tudelft/tw3520/Introduction_to_Mathematical_Logic.pdf

user147690

@crocket Well are you writing down stuff while you do the chapter?

user147690

08:05

@crocket Or just reading?

crocket

I write down solutions to exercises.

But, I just read content.

user147690

Well there is the first problem :p. You should be verifying things that are written on paper

crocket

I verify things in my mind.

user147690

Yeah that isn't enough

user147690

Otherwise everything seems good, and you forget it all immediately

user147690

08:07

It doesn't just seep into your brain

crocket

@AlexClark Exercises help me overcome illusion of competence, though.

The author sprinkles exercises everywhere to help with that.

user147690

You can't do the exercises without looking at the solutions

crocket

If verifying some claims about many-valued logic takes too much computation, I wouldn't do it

I'd rather hire a computer for that

It's not amenable to human computation.

My guess is that trying to solve exercises helps understand concepts even if I can't solve them.

user147690

Struggling does definitely help you understand what is going on, that's why some mathematicians hate computational 'proofs', since they lose all the intermediate information that is gained in actually doing the proof

crocket

I can't solve every exercise in the book because it'll take 4-5 years to read the book by solving every exercise I can.

Probably more than 4 years

I don't want to spend that much time on a book

From time to time, I could go back and solve some exercises.

user147690

08:13

Huh, there are ~370 pages, how much time do you have each day to dedicate to it?

crocket

2 hours a day

not more than that

user147690

You think doing every exercise you couldn't finish it within 3,000 hours of work?

user147690

That's 62 weeks of the recommended work frequency at university(doing 4 subjects), which is about 4 semesters of study

crocket

"A First Course in Mathematical Logic and Set Theory"

I study every day.

user147690

I think most people here do

Agawa001

08:21

@AlexanderGruber prolog is also needed as a mathematician

crocket

Now, I think the book I was reading is not really an introduction.

1

Q: Can you recommend a replacement for "Introduction to Mathematical Logic, Sixth Edition" by Mendelson for a neophyte?

I started studying "Introduction to Mathematical Logic, Sixth Edition" by Elliot Mendelson. I tried to not read solutions as long as possible, but most exercises were awfully difficult to me, and the content itself was not easily digestible. When I tried to solve exercises in the chapter about m...

reference-request logic advice

Chris's sis the artist

09:30

People in Tex room are always really great!

robjohn

09:55

@Chris'ssistheartist why do you say that?

Chris's sis the artist

@robjohn They are friendly, always answer back to you nicely and are really helpful. There is a positive attitudine in there you can easily perceive.

Agawa001

i see that this chatroom is the most helpful in se netwok

as it remains so (excluded trolls exhibitionists and haters)

Secret

how often do dynamical system background users visit this chat, because I have some chaos theory related questions but so far the users I have seen on chat are from an algebra background?

Agawa001

and ofcourse (moderators coming fom other planets just to apply their megalonania in a chatroom they r not elected moderator in)

Secret

10:23

Is there exist something more general than category theory?

Secret

10:46

https://en.wikipedia.org/wiki/Space_(mathematics)
what is the highest mathematical structure in the hierarchy that has a name?

More generally, what is the mathematical 'thing' that has category theory and multiset as special cases?

Tobias Kildetoft

11:13

@Secret I am not sure I see any useful "thing" with that property

Secret

so the general consensus is that anything that is a generalisation of cateogry theory is expected to be not very useful?

Tobias Kildetoft

@Secret depends on what you mean by generalization

Secret

something like "the inner product is a generalisation of the dot product of vectors in R^n"
"n dimensions is a generalisation of 3 dimensions", "an ideal is a generalisation of integers"

something along the lines of this...

I don't know if there's a term to describe this kind of generalisation but in mathematical education more abstract mathematical concepts are often introduce this way with motivational examples before giving definitions

such as how in most courses that taught about hilbert space it first start with vector spaces and inner products in $R^n$, $C^n$ etc. before the definitions are stated

Tobias Kildetoft

@Secret You have seriously had courses on Hilbert spaces that did not presume knowing vector spaces?

Secret

nope

the hilbert space topic in our uni proceed in the usual way

however some uni taught hilbert spaces and other advanced topics like this:
http://www.math.lsa.umich.edu/~kesmith/infinite.pdf

they give some motivational exmaples in some spaces we encountered before as a stepping stone to the abstract definitions and axioms

that's the type of generslisation I am trying to ask

Secret

11:29

so put it in another way if there are lecture notes that is structured like the above link, but the topic is <the thing I want to ask what it is if there is one> and it uses concepts and theorems in category theory as motivational examples, then what would this <> be?

Tobias Kildetoft

@Secret I can't think of anything like that. The usual "next step" after categories are some of the more specialized things in category theory like monads or $2$-categories and above. But these do not really have categories as a special case.

Agawa001

@Secret i dont know wheras u v pinged me or not but thats way over my head sorry

Secret

@Agawa001 O I was orignally trying to ask you about dynamical system users but right after the ping is sent, I realised you have left the chat thus I want to take back the ping later by deleting that message "which really only consist of the words (insert at symbol)Agawa001"

It seems the ping was still being sent , sorry for the confusion

@TobiasKildetoft I see, so category theory is pretty much the highest in the hierarchy of mathematical structure (in terms of generality) that mathematics community has a name for it?

Tobias Kildetoft

@Secret Well, the highest that I can think of. There might be "higher" stuff that I am not aware of

Secret

ok

Tobias Kildetoft

11:37

(technically, semicategories are one such thing, they just don't seem to ever be studied)

Balarka Sen

@Secret Not sure what you mean by "highest in the hierarchy of mathematical structures". A category basically has no structure at all.

If you want something which has lesser structure, consider sets.

Secret

I thought the mophism arrows have given some kind of "structure" due to how it relates two mathematical objects together?

Balarka Sen

Morphisms have no structure.

In a general category, I mean.

Secret

i see

Balarka Sen

A category is just a set of objects such that for each pair of objects there is an associated proper class (plus a few desirable axioms). There's literally no structure assumed on a category.

The morphisms are just the elements of that proper class.

Slereah

12:26

Hey is there a specific name for the torus embedded in $\mathbb{R}^3$

As opposed to the flat torus

Balarka Sen

there are several ways to embed a torus in R^3

if you mean the standard one, just say "standard embedding of the torus in R^3" :P

Slereah

The standard one indeed

If you have any idea of how to solve the Helmoltz equation on it too that would be appreciated!

Balarka Sen

I am not familiar with the Helmoltz equation, sorry.

Slereah

Laplace equation + a constant

Well $+ k y(x)$

Balarka Sen

I hardly know anything about differential equations, so I am not the right person to ask :)

Slereah

12:31

I asked on stack exchange but so far not much luck :p

There's a known solution for toroidal coordinates but they don't seem to be directly related to the torus metric

Huy

@Slereah: Try MO?

Slereah

Maybe

The overflows are a bit of a bother really

No automatic way to transfer questions

felipa

12:54

hi.. anyone know anything about matrix norms? math.stackexchange.com/questions/1517103/…

it would be great if someone could help

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$Mathematics$ Mathematics