Mathematics - 2013-06-01 (page 1 of 2)

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nerdy

00:22

I'm trying to relate Axiom Systems to Formal systems, can anyone help me ?
I know any formal system has 3 constituents, a language, a set of axioms, and rules of inference
what about an axiom system ?
is it a set of axioms ? does it also require a language ?
is it a specific kind of formal system ?

Peter Tamaroff

@nerdy You seem to have many questions. Why not ask this on main?

nerdy

It's actually one question : How is an axiom system related to the concept of formal system eheh but i think i'll do that

Peter Tamaroff

@nerdy Maybe @BrianM.Scott can help? How is your headache Brian?

1 hour later…

Tobias Kildetoft

01:49

well, that concludes "figure out if the spider in the corner is dangerous". Conclusion: Probably not, but let's vacuum it up anyway.

Peter Tamaroff

02:13

@TobiasKildetoft How mean.

1 hour later…

robjohn

03:20

@TobiasKildetoft I capture them in a jar and toss them in a bush outside, unless it's a black widow.

DanZimm

03:34

@robjohn I've never actually seen a black widow IRL - are they terrifying as I have heard?

Islands

03:50

nah

Cecile

Hello everyone, may I ask for your opinion on this question: "Shall I pursue a teaching career in Math, or shall I continue with PhD?" My deadline for paperwork is coming, and I still can't decide >_< I plan to work with Geometry for PhD, but I don't know about possible research topics on this field.

DanZimm

@Cecile what kind of geometry?

Cecile

I prefer Hyperbolic Geometry or Algebra Geometry, but I'm not sure on the difficulty level though. I just have the interest.

DanZimm

04:06

@Cecile how much math have you studied thus far and from what country are you?

cyclochaotic

@DanZimm we have black widows where I live, they have lighting fast reaction time, very quick

Cecile

So far I learn almost all undergraduate courses, except differential geometry and complex analysis. The "geometry" that I know so far is only Euclidean and some Hyperbolic geometry (the Klein and Poincare models). I hesitate on doing PhD on this field 'cause I'm afraid that my knowledge is not enough >_<

DanZimm

@cyclochaotic eek small things that move scare me at first sight

when they move away quickly its even wrose

@Cecile what country are you from? and have you taken topology?

Cecile

I'm from the U.S. I'm taking an intro course for topology now.

DanZimm

diff geometry from what i understand is usually a first year grad course

@Cecile I wouldn't really be the guy to talk to about geometry, otherwise in general I would say go for the PHD

cyclochaotic

04:14

@Cecile stay in school as long as you enjoy it

Islands

what is differential geometry

and why isnt it offered in undergrad

Cecile

it's offered in undergrad, but I didn't take it back then due to time issue (my classes all overlapped)

DanZimm

@Islands like calculus on manifolds (at least thats how i understand it) - from my experience that wasnt offered in undergrad

@Cecile you must go to a better school than i do xD

Islands

hm.. my school doesn't even offer it in grad

Cecile

I just keep thinking... if I really do apply for PhD, what would be a research topic that I can choose >_< I'm really uncertain on that. That's why I leave the option of teaching, but... ah, so hard to decide!

DanZimm

04:17

@Islands technically mine doesn't either, by our math grad program is only masters

@Cecile do you have a favorite prof of math youve run into?

cyclochaotic

@Cecile go talk to a professor about cutting edge research topics

DanZimm

@cyclochaotic I did that and my prof said exactly what he's researching right now xD

seems biased based on who you ask :P

then again depends what you consider cutting edge

cutting edge with relation to what

:P

Cecile

Yeah, I do have a really nice professor, but his main field is ... differential geometry >_<

I ask him b4, and he said ... "that's hard to choose"

Islands

does anyone know about chabauty methods?

Bageer

@Cecile (I am not in grad school but I plan on going too grad school) I pretty sure you sort of figure out what you want, and will, research in grad school. Of course it probably helps to have an idea of what field you want to research before grad school.

cyclochaotic

04:20

Perhaps read some preprints on arxiv.org to get some ideas

DanZimm

@Bageer just curious, what are you interested in studying?

Bageer

@DanZimm I am leaning towards algebraic type of subjects, last semester I did an independent study in geometric group theory.

@DanZimm I also really like the idea of category theory and topos theory, but I don't know much about them.

@DanZimm What are your interests?

Cecile

Does number theory seem to be the "easier" field? In my opinion, it's all about numbers, no topology or analysis is needed.

DanZimm

@Bageer ah very cool - all things I'm ignorant of

Islands

Cecile: what about all those easy-to-state, hard-to-solve problems?

DanZimm

04:24

@Bageer I'm currently doing independant study with a prof on measure theory and specifically lebesgue theory and then onto analysis of modern PDEs

Islands

there's a lot of them and they are all from number theory

DanZimm

@Cecile I find number theory the most difficult

cyclochaotic

Here's a simple problem, prove than any non-prime even number is the sum of two primes :)

Jayesh Badwaik

@cyclochaotic heh...

Bageer

@Cecile Going to grad school just to study the "easy" subject seems misplaced. I think you should go because your passionate about the subject. (maybe I am just reading to much into what you have been typing)

DanZimm

04:27

@cyclochaotic isnt that a conjecture?

Islands

I think this would be the most interesting problem to work on: en.wikipedia.org/wiki/Inverse_Galois_problem

cyclochaotic

Goldbach

DanZimm

ya

xD

cyclochaotic

We can't even generate arbitrarily large prime numbers.

Bageer

@DanZimm Hah, I know almost nothing about analysis. I plan on picking up some analysis and topology to do some sort of independent study on the gap conjecture (a conjecture in geometric group theory). It seems to have a lot of applications to differential geometry (I believe Milnor came up with the conjecture).

Cecile

04:30

@Bageer my meaning of "easier" is in terms of research topics, but in terms of the materials, I think topology is good. 'cause it's more to set theory (ex: open sets) than the "epsilon-delta" as in real analysis

DanZimm

@Bageer it's my thing, I love it! My school doesn't offer any sort of category theory or group theory classes. we have abstract algebra and advanced abstract algebra, the former im taking next semester and the ladder the semester after that

cyclochaotic

$250,000 to the first individual or group who discovers a prime number with at least 1,000,000,000 decimal digits at the EFF

Islands

no group theory?

seems like a standard 3rd year class?

DanZimm

@Cecile you can get pretty deep into topology and it can get analysis-y xD

@Islands thats in the abstract algebra class

you learn about groups rings and cosets

Cecile

yeah, although I took a whole year of real analysis, I'm quite lost after things get to 3-dimensional or more.

Oh, my friend once said Complex Analysis is "easier" than Real analysis 'cause there is no "epsilon-delta" to deal with. Is he correct? Or maybe just 'cause he's taking it?

DanZimm

04:36

@Cecile complex analysis can be "easier" depending on how the prof teaches it

it can be a very deep topic or a much more applied subject thats less analytic

@Cecile if youre ok with 2-dimension why not 3?

Cecile

'cause something like volume of a Hypersphere... I figured out the integral but have no visual picture in mind >_<

I also plan to pursue teaching credential in the morning ('cause I have to teach 2 classes), then do PhD from the afternoon. But my friends said that's too heavy of a workload. @_@

DanZimm

@Cecile gotcha - i suppose im more into general analysis as opposed to real analysis so I'm pretty used to the lack of visualization

@Cecile if you want to really understand that stuff topology helps

Cecile

I got freak out after going to the school website and seeing the requirement of "passing qualifying exam and core exam with MS grade level by the beginning of 2nd year". The topics are algebra, real & complex analysis, but I know nothing on complex analysis & shaky on real analysis >_<

DanZimm

@Cecile eek yea analysis will getcha

1 hour later…

DanZimm

05:53

merh

Ethan

@Alasdair Can you tell me exactly what you are trying to do?

I am having trouble reading your question

What exactly do the variables $x$ and $y$ represent?

Alasdair

Well

They are not mathematical

Ethan

Ok

Just explain the problem

Alasdair

The variables represent agreement and disagreements (contradictions)

It's an equation for measuring agreement between different sources

My problem is only that I want to be able to include the number of sources in the study as a variable in the equation

The equation is meant to represent a minimum level of statistical significance

I can give you a link to the paper

Ethan

It seems you are assigning values to each variable what do these mean?

Ok

Alasdair

05:57

This will explain it:
http://stats.stackexchange.com/questions/60001/new-method-for-meta-analysis-to-determine-agreement-between-multiple-sources

Ethan

You seem to introduce alot of your own definitions, but regardless there is very often a huge number of functions that will satisfy some simple set of statements

Just because one function takes on several of your desired values and satisfys some propertys does not mean it represents what you want it to represent

robjohn

@DanZimm If you don't know what they can do, they are not any more terrifying than any other spider.

DanZimm

@robjohn whoop for ignorance of being in the midwest? xD

Alasdair

@Ethan, I don't understand what you mean

I understand that the value is not a true probability

Ethan

@Alasdair Can you clarify several terms for me you used.

"statistical significance"

"minimum probability"

Alasdair

06:07

Mutual agreement are multiple sources that appear (by the researcher) to agree with one another, i.e. they make statements that say the same thing, e.g. "the sky is blue"

Ethan

ok

How are you defining statistical significance?

Alasdair

Statistical significance is anything that meets a presumed level of acceptance, which in this case is the premise that 3 agreements with 0 contradictions is statistically significant

Ethan

The word significant by itself seems kind of vague, what one considers significant is certainly subjective to that particular individual

robjohn

@DanZimm do you have brown recluse spiders there?

Alasdair

Obvious that one has to be accepted by the reader as being logical

Yes

That's why I tried to explain it in the paper, but I will rewrite that bit if it is not clear enough

Babak S.

06:09

@somaye: Hi friend. I was watching TV. Monazereh mididam. mazerat mikham.

Alasdair

Minimum probability is similar to statistical significance, it is basically where I'm saying that 0.9 is AT LEAST = 90% probability

Ethan

@Alasdair I don't understand

Alasdair

It's how I convert the value output from the formula into something that can then be used mathematically

So I'm saying:

Ethan

@DanZimm Do you know about galvanic cells?

DanZimm

@robjohn never heard of them nor have i seen a brown spider so i guess not

Alasdair

06:11

If 3 sources agree and 0 disagree then this has at least 90% chance (or better to say less than 10% chance of not being the case) of representing a true agreement

DanZimm

@Ethan nope no idea xD

Ethan

@Alasdair I still don't understand what you are trying to do, can you explain in as simple terms as possible what you want

robjohn

@DanZimm They are in parts of the midwest

Alasdair

OK

Say I have 50 books about caring for rabbits. Of these 50, 3 of them say that rabbits need water everyday, 0 say that rabbits don't need water everyday, and 45 don't mention how often water should be given.

Ethan

k

DanZimm

06:13

@Ethan theyre cool though

Alasdair

I say there is a 90% probability that those rabbit books are all in mutual agreement from this

Or to put it another way:

Ethan

@DanZimm I have to draw a picture of several for my chemistry homework lol

Alasdair

There is less than 10% probability that the rabbits books agreed by chance

Ethan

How are you defing probability

Alasdair

That level of probability is only assumed, the reader has to accept it logically

Ethan

06:14

And how are you calculating it?

Alasdair

It is calculated with the equation

in the paper

Ethan

Ok

Alasdair

It works as I wanted it to

Ethan

You mean

Alasdair

I just want to now expand it to include the number of sources

Ethan

06:15

$1-\frac{x^2+1}{y^2+1}$

DanZimm

@robjohn id shit my pants if i saw that btw nice job with that $2^{88}$ post

Alasdair

$1-(1/\frac{y^2+1}{x^2+1})$

1-(1/(...

Ethan

its the same thing

Alasdair

Oh right yeah, I haven't got the hang of mathtex thingy

Ethan

lol

Ok and $x$ represents?

and $y$ represents?

Alasdair

06:16

y goes first, I put it the wrong way round on my first post, then edited it

y is agreements

x is contradictions

Ethan

Ok so we have a list of sources about somthing

Alasdair

Yep

Ethan

And $y$ represents the number of sources that agree with one and another?

Alasdair

y

Ethan

So If I have $5$ sources that say somthing is true and $3$ that say it is false

$y=5$ $x=3$?

Alasdair

06:18

Yes

1 - \frac{1}{ \left(\frac{y^2+1}{x^2+1}\right) }

Ethan

OK and you want the number of sources?

In terms of that

Alasdair

Currently 5 agreements and 0 contradictions = 0.962

DanZimm

@Alasdair you need to put it in \$\$

Alasdair

K

Ethan

Ok Alasaider the number of sources should be $x+y$, because this is the total number of true sources and false sources

Alasdair

06:19

Well no

Ethan

That is assuming all your sources are declaritive on a given topic

Alasdair

They don't

Also some can both agree AND contradict

Ethan

what do you mean?

Alasdair

The sources are books, sometimes the authors say one thing, then later say something that contradicts the first thing

Ethan

Give me an example using that rabit stuff from before

Ok then $x$ and $y$ are assigned to each statement in each source?

Alasdair

06:21

Yes

DanZimm

merh

Alasdair

Oh wait

No

It's just the total

Ethan

ok

the total number of sources

Alasdair

So in theory x+y could be > z

y is number of sources that agree

x is number of sources that contradict

Ethan

You need to express your desired quanity in terms of $x$ and $y$

Alasdair

06:23

???

Ethan

Ok alasdair

You want the total number of sources

Alasdair

I have the total number of sources

Ethan

Based on the value $$t=1-\frac{x^2+1}{y^2+1}$$

Alasdair

What I want it the total number of sources to be a factor in the equation

The number of sources is not calculated from y or x

Ethan

I don't understand, then add it to the equation?

What do you need help with?

You want $t$ to be significant some how by adding in another factor?

If this is this case it is still not clear exactly what $t$ is representing other then its given equation

Alasdair

06:25

All I want to do is modify the equation so that the exponential curve levels off at the number of sources

Ethan

I would avoid using specific terminology like 'exponential'

Alasdair

if y==z then t=1

Ethan

It is not clear what you are saying is exponential and with respect to what, there are 2 variables

And either way I don't see anything with exponential growth

Alasdair

y^2

Ethan

@Alasdair what do you mean levels off

@Alasdair it increases quadratically

with respect to y

Alasdair

06:28

Yeah, I need to look into definitions

Anyway

Ethan

@Alasdair don't worry about it

Alasdair

By levels off I mean becomes 1

If the number of agreements (y) = the number of sources (z) then the product (t) should be 1

Oh, also assuming that x=0

Ethan

If $x=0$

wait

what is $z$?

Alasdair

z is number of sources

Ethan

If $y=z$ then $t=1$ is what your saying?

robjohn

06:30

@DanZimm Thanks. As you can see by the step-by-step, nothing deep is used.

Ethan

And $x=0$

Alasdair

Yes

DanZimm

@robjohn yea I'm a bit lost in step 4 atm but I was gunna come back tomorrow when I could think more clearly

Ethan

How about $$t=1-\frac{x^2+1}{y^2+1}+\frac{x^2+1}{z^2+1}$$

Alasdair

But if z=100 and y=3 and x=0, then t should still be pretty high

Like >0.5

Ethan

06:31

substitute $y=z$ and you get $t=1$

Alasdair

Because y is much more important than z

Ethan

@Alasdair $$t=1-\frac{x^2+1}{y^2+1}+\frac{x^2+1}{z^2+1}$$ satisfies those conditions

If we set $y=z$ we see that

Alasdair here use this

because the $\frac{x^2+1}{z^2+1}$ cancels with itself

Alasdair

I'll need some time to figure out mathtex language to read that

Ethan

@Alasdair I will post it on your question ok?

robjohn

@DanZimm $\cos((90-k)\pi/90)=-\cos(k\pi/90)$ and $\cos((90-k)\pi/180)=\sin(k\pi/180)$

Alasdair

06:34

OK

anon

chatroom has latex support

DanZimm

@robjohn but I don't see where $cos((90−k)π/90)$ comes from

Ethan

@Alasdair refresh your question I edited a bit

Do you see my comment?

robjohn

@DanZimm The product on the right; the indices are changed from $46\dots89$ to $44\dots1$

Alasdair

y = agreements, x = contradictions

DanZimm

06:36

oh i think im getting it now

Ethan

Yes if they are the same $t=1$ in your equation isn't that what you wanted?

@Alasdair There are numerous ways to have this condition satisfied though

DanZimm

well I'm getting off have a good night all

Ethan

@DanZimm night

Alasdair

Sorry, Internet died

I think you have x and y the wrong way round

y = agreements

Anyway, let me put the equation into Excel and see what the table produces

Ethan

No I have it right you, said if $y=z$ then $t=1$ right? then that equation satisfies your conditions

I am still not seeing the significance of this though

There are numerous equations that satisfy this property

Just because some function interpolates the values you want and satisfies several conditions, does not mean it will be an accurate model

Well I guess I have to clarify the exact definition of "accuracy", and this is dependent on a number of other things, though regaurdless

Hopefully you get the underlieing idea

Alasdair

06:47

OK, the results are interesting

But now it always equals 1 at y=10 if z=10, even if x>0

Ethan

What other condition did you want?

You want it only to work if $x=0$?

Alasdair

I want it to work with any values

I mean...

You equation seems right, except that is only works when x=0

If y=10 and x=10 then obviously t cannot be 1

As that is 100% agreement

But there are 10 contradictions

If y=x then t=0

Ethan

if y=x then t=0?

Alasdair

Yes, if agreements = contradictions then significance level is 0

0 means no significance

Your equation looks like this:

0 1 2 3 4 5
0 0.010 -0.980 -3.950 -8.901 -15.832 -24.743
1 0.510 0.020 -1.450 -3.901 -7.332 -11.743
2 0.810 0.620 0.050 -0.901 -2.232 -3.943
3 0.910 0.820 0.550 0.099 -0.532 -1.343
4 0.951 0.902 0.755 0.511 0.168 -0.272
5 0.971 0.943 0.857 0.714 0.514 0.257
6 0.983 0.966 0.914 0.829 0.709 0.555
7 0.990 0.980 0.950 0.899 0.828 0.737
8 0.995 0.989 0.973 0.945 0.907 0.857
9 0.998 0.995 0.989 0.977 0.961 0.940
10 1.000 1.000 1.000 1.000 1.000 1.000

For z=10

Ethan

@Alasdair one second

@Alasdair How about this, I posted something new on your question

Alasdair

06:55

k

Hmmm...

2 problems with that, (1) it's not quadratic, and (2) t is still 1 where x>0 (it should only be 1 if x=0)

Squaring it makes the numbers too small as well

I think I get the idea though

Harsh Bhavsar

07:12

what is the use of fuction truncate in maths?

4 hours later…

Jayesh Badwaik

11:23

Hi, I have kind of a silly question. Janich's topology book gives the the definition of topology as a pair $(X,T)$ where $X$ is a set and $T$ is a set of subsets of $X$ (called open sets), such that
1. Any union of open sets is open.
2. The intersection of any two open sets is open.
3. $X$, $\phi$ are open.

My doubt is, in the second condition, what prevents us from applying transfinite induction to the rule of intersection and extending the rule to "Any intersection of open sets is open" (which is obviously incorrect) ?

Even why can I not apply the simple mathematical induction?

Julian Kuelshammer

You can apply mathematical induction to conclude that any intersection of a finite number of open sets is open. Can't help with transfinite induction.

Jayesh Badwaik

Hmm, yup, any finite intersection is good.

Martin Sleziak

11:52

@JayeshBadwaik If you tried to do the transfinite induction, the limit step would fail.

You would be able to prove this for $\omega+1$, assuming that it holds from $\omega$.

But the assumption that it is true for each $n<\omega$ is not enough to prove this for $\omega$.

BTW topological spaces such that any intersection of open sets is open are called Alexandrov spaces or finitely generated spaces.

Jayesh Badwaik

12:19

@MartinSleziak Thank You :-)

Zetta Suro

13:04

Hello all

Can anyone recommend me a reference for self teaching complex analysis?

I know as high as vector calculus. If anyone could give me a recommendation that'd be great :)

Lord_Farin

@ZettaSuro Hello. Perhaps #160132 adresses your needs?

Also #30749

Peter Tamaroff

@Lord_Farin Explain that Complex Analysis has certain prereqs, man.

@Lord_Farin See this

Lord_Farin

@PeterTamaroff Oh, you're right. I might have momentarily misread vector calculus as multivariable calculus.

Peter Tamaroff

@Lord_Farin Mhm.

I'm off now.

Lord_Farin

@PeterTamaroff Bye!

badp

13:13

Dear flagger: the only reason I dismissed the otherwise 100% absolutely valid flag is that it was made 20 hours late. And I can't honestly understand the reason of this appalling delay.

3

Zetta Suro

@Lord_Far What are the prereqs?

I have done multivariable calculus as well

Chris's wise sister

Greetings

Gustavo Bandeira

@amWhy Sorry, I wasn't - I'm visiting my mother and girlfriend. What's it? Someone made a question in portuguese?

Lord_Farin

@ZettaSuro As Peter rightfully remarks, there are some prerequisites to starting with complex analysis. It is highly recommended to first progress through real analysis, and one will benefit from multivariate real analysis (although it is not strictly necessary).

@Chris'swisesister A good afternoon to you.

Chris's wise sister

@Lord_Farin hello! The same to you! :D

Zetta Suro

13:16

ohh I see. I have been interested in real analysis for some time, but have never taken it and don't know much about it

out of curiosity, what are the uses and applications of real analysis?

Lord_Farin

@ZettaSuro It is basically the rigorous version and foundation of limits, integration, differentiation. The ideas used are employed to generalise many concepts to more abstract settings than the real line.

N3buchadnezzar

Heya

Zetta Suro

ohh ok. Is it used in applied mathematics, or is it all theoretical?

Lord_Farin

Also, it is usually one of the first points in education where students encounter mathematical proof-writing. // It is used in applied mathematics all the time (the results, anyway), but in principle it's all theory. Getting a good grip of the techniques employed is a very important part of attaining some sort of mathematical maturity.

Hello @N3buchadnezzar, @Dominic.

Dominic Michaelis

@Lord_Farin Hi

Lord_Farin

13:21

@Chris'sw, @Dominic How are you doing today?

Zetta Suro

cool. I think I'll look into it. It seems to also be a very popular topic here

Dominic Michaelis

Thinking about chain complexes

Chris's wise sister

@Lord_Farin I'm working on a very beautiful product $$\prod_{k=1}^{\infty}\frac{k^2+k+1}{k^2+k}$$ How about you?

Lord_Farin

@ZettaSuro It's one of the topics where people tend to get stuck, so they come here a lot to ask their questions. :)

Gustavo Bandeira

@amWhy Look. If Zev threatens my family, I'll blame you! :P

Lord_Farin

13:23

@Chris'swisesister :(. Slacking through another day I could use to do useful things. :S

Zetta Suro

ah makes sense. Thanks for your assistance!

Lord_Farin

@ZettaSuro Most welcome! Good luck!

@DominicMichaelis That's those things used for, say, de Rham cohomology, right?

Dominic Michaelis

yeah but right now I only need them for some category theory

Lord_Farin

@Chris'swisesister Product converges; I'm not good at evaluating them, though.

Chris's wise sister

@Lord_Farin yeah, I know. It's an amazing product ...

Lord_Farin

13:27

@DominicMichaelis That's not something I have seen before; but then I'm not really into that part of the subject.

@Chris'swisesister A reflex is to take log and use the power series expansion (warranted as $\frac1{k^2+k} < 1$ for all $k$), subsequently interchange summation.

But I'll be going now, trying to salvage a bit of my day.

Chris's wise sister

@Lord_Farin I see. That product can be viewed as another superb product.

Lord_Farin

Bye all.

Chris's wise sister

@Lord_Farin bye

amWhy

@GustavoBandeira I see! Thanks! ;-)

1 hour later…

BenjaLim

14:53

@JulianKuelshammer Procrastinating not studying for my DG exam by computing some hilbert polynomials

Peter Tamaroff

15:31

No upvotes? BoooOooO!

Charlie

15:44

@N3b Hi! :DDD

N3buchadnezzar

yo

Cortizol

Hello, I need moderator some, is there any?

Charlie

@N3buchadnezzar how are you?

N3buchadnezzar

exams

Charlie

@N3buchadnezzar ow :-/

Peter Tamaroff

15:45

@Cortizol What happened?

Cortizol

math.stackexchange.com/questions/408017/…

look at comments

Peter Tamaroff

@Cortizol Oh, let me see if I can fix it.

$$\sum\limits_{m = 1}^k {{{\left| {\frac{1}{m}\sum\limits_{n = 1}^m {\frac{{{n^{ - q/2}}}}{{{{\left( {\sum\limits_{n = 1}^k {{n^{ - q/2}}} } \right)}^{1/p}}}}} } \right|}^p}} = \sum\limits_{m = 1}^k {\frac{1}{{{m^p}}}} {\mkern 1mu} {\left( {\sum\limits_{n = 1}^m {{n^{ - q/2}}} } \right)^{p - 1}}$$

Should it look like that?

Cortizol

@PeterTamaroff Yes

maybe it's too big for comment

Peter Tamaroff

OK, delete the comments and add it.

No, it had some failing code.

Charlie

@Chris'swisesister hi, Chrissy, how are things?

Cortizol

15:49

@PeterTamaroff I can't see edit button for some reason

Peter Tamaroff

@Cortizol Just delete those comments.

Cortizol

@PeterTamaroff I mean, delete button

@PeterTamaroff See i.imgur.com/JnDJUbW.png

Peter Tamaroff

@Cortizol LOL; you just broke the internet.

Chris's wise sister

@Charlie hi. I'm fine, thanks!:-) I was working on some series. How about you?

Cortizol

@robjohn are you here?

Chris's wise sister

15:53

@Charlie previously I worked on a nice product $$\prod_{k=1}^{\infty}\frac{k^2+k+1}{k^2+k}$$

Charlie

@Chris'swisesister I don't know, I'm studying some set theory, it's nice, but I don't know if I'm fine

Chris's wise sister

@Charlie I can't say "I'm fine" every day but there are some exceptions :D

Peter Tamaroff

@Chris'swisesister I think he/she means "good"

Chris's wise sister

@Charlie Another version, more beautiful (working on the generalization right now) $$\prod_{k=1}^{\infty}\frac{k^3+k^2+k+1}{k^3+k^2+k}=\text{sech}\left(\frac{\sqrt‌{3}\pi}{2}\right)\sinh{(\pi)}$$

Peter Tamaroff

Thank you. i figured it out now! <3 Peter muah

user image

Jayesh Badwaik

16:17

@Charlie

Charlie

@PeterTamaroff you almost don't like.it, huh...

Peter Tamaroff

@Charlie Ah?

Charlie

@jayesh

robjohn

@Cortizol just back, but leaving again soon

off for some hours, bbl

DanZimm

17:01

howdy all

Peter Tamaroff

@DanZimm Hello.

DanZimm

@PeterTamaroff how you doing on this fine day?

Peter Tamaroff

@DanZimm It is a fine day? Where?

DanZimm

@PeterTamaroff I'm sure it is somewhere xD

Charlie

17:21

@DanZimm anything nice going on?

DanZimm

@Charlie it seems to be a nice day out by me

Charlie

@DanZimm good to know

Hi @anon

Dominic Michaelis

mh mac lane says that here it follows by exactness of the second row that that $f(x')=0$. But you don't need exactness there as we are in Ab anyway ?

anon

17:37

sorry, I'm on the internet for offishal bizniss

can't talk

Dominic Michaelis

You don't need to talk you just need to type ;)

Charlie

@DominicMichaelis how are you today, Dommy?

Dominic Michaelis

@Charlie I think it is going slowly upwards

I draw some colored commutative diagrams :)

Charlie

@DominicMichaelis I'm glad to know

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