12:00 AM
Does it make sense to speak of the order inside a set?

define what that means

Yes sorry was still writing
For example if you were talking about the set of positive integers, would it be correct to say $1$ is the first member of the set?

that statement is meaningless unless you define what "first element" should mean

Is there a better way to phrase it, or is it left up to the author to define what they mean?

what you usually wanna do is put an order on a set, but that is a piece of additional structure and not intrinsic to the set

12:11 AM
Ok!
In math we call what makes up a set, either elements or members. Correct?
For example it would be correct to say "5 is a member of the positive integers"?

formulated in a non-pedantic way: yes it makes sense to speak of the order inside a set
but you have to define which order, and in different contexts, you may want to consider different orders on one set

@northerner yes

so there often isn't "the one true order" on a set

so your "yes" is actually still a "no"..

okay, you have a point, for "does it make sense to speak of an order inside a set" my answer would have been an emphatic yes

12:20 AM
i didnt know any two orders on a set are coherently isomorphic
curious

I ask because I was having trouble formulating this question. math.stackexchange.com/questions/3988199/… I hope at least my point is clear.

@Thorgott the government doesn't want you to know but its true

tfw every order is a well-order up to coherence

axiom of good choice
@Thorgott i wonder how many axioms of ZFC I can add until this can't be true. I think this breaks down very quickly
empty set for sure
but I don't wonder enough to actually check that out

well, you need power set for the concept of order to even make sense

12:29 AM
gotta go through the proof of fubini for stochastic integrals. This really frickin technical

and powerset plus subset should allow to construct a counter-example already

@Thorgott nah you can formulate the statement just fine
maybe you can't prove that orders are sets

Can all functions be expressed with the standard mathematical operators and elementary functions? In other words does their exist things that are functions but cannot be expressed using operators $+-*/$ and elementary functions such as powers, trig functions etc.?

ok..
at this point it becomes silly
but idk actually, how do you formulate the statement

I'm inclined to say no, because say $x=\{1,2,3\}$ and $y=\{10,2,1000\}$ now find an expression for that function

12:33 AM
no formula in the language of set theory depends on the axioms, it depends only on FOL and the relations/functions in the theory - in this case $\in$

@northerner this question only makes sense for functions from (subsets of) the real numbers to the real numbers and the answer is that almost all functions are not of this form
@user2103480 so how do you encode the concept of an order?

Why are most functions not of the form real numbers to real numbers? @Thorgott

that's not what I said
but also true, because most sets aren't the real numbers

and for orders that you can define by formulas, we can reason without resorting to a superset. A simple case is when you have a class $R = \{x \mid \varphi(x) \}$ defined by some formula and then $\psi(x,y)$ defines a total order by just the usual axioms. If $\psi(x,y) \land \psi(y,z)$ then $\psi(x,z)$, for arbitrary $x,y,z$ with $\varphi(x), \varphi(y), \varphi(z)$ etc

it doesn't really make sense to talk about classes now when we don't have any axioms ensuring their existence now, does it

12:42 AM
But expressing something like "all orders are isomorphic" is best done by just expressing the thing in set theory, else I think we have to go up one level and say that for all formulas that encode an order, there is a bijection between the classes
And in the end this pushes the real problem just one level higher in the hierarchy: the fact that all this is idiocy
@Thorgott not at all
bUt I hAvE mY mEtA aXiOMs

i regret engaging this conversation

people tend to say that after asking logic questions
I still don't know if its my fault or logic's fault

let me assure you it's the latter

But I think it's logic's fault, the area is the mathematical counterpart of the ACKCHUALLY guy

real hater hours

12:47 AM
no I love logic

well, I'm the ackchyually guy too
but i dont have stupid meta axioms

@Thorgott always one meta axiom system more than you
it's actually super silly

"yeah man, let's solve this by going a step higher up the hierarchy"
oh wait, that's just category theory...

@Thorgott >people who say that the natural numbers are uniquely defined

I thought they are, but I'm also afraid to make you expound

12:51 AM
@copper.hat lol w/e dude!... try not to lose it its a gem! its a glimpse of the future! do you like kuhnian paradigm shifts? physics revolutions? eg on the level of discovery of the photon? its 12:58 and think youll like it even more than random chat topics+chatter :)

@Thorgott they are inside the model
(of ZF and probably also weaker theories, that one works in)

>model
why are you like this

sorry

cries in not having meta axioms

@vzn slowly slogging through. some odd little arrow notation for vectors. unfortunately my day time is with much more mundane realities.

12:53 AM
So we assume that ZF is consistent and we prove in ZF that all the structures that satisfy arithmetic and second-order induction (any inductive subset must be the whole set) are isomorphic

COHERENTLY isomorphic??

I DONT KNOW MAN I DONT CATEGORY
so what this means is that for any class/set that "satisfies" the ZF axioms internally, all the natural number structures inside the thing are isomorphic
but across these things which we call models, the naturals can again be wildly different

Accordingly, a coherence law in an (n,n)-category such as a bicategory (n=2) or a tricategory (n=3) or a tetracategory (n=4) is in degree n+1 a complicated equation that asserts that a certain contractible space of higher morphisms is exactly equal to the point.

do I remember right that one hasn't even been able to automatize the process of stating these equations

@copper.hat ok know youre a different generation (like me), but anyone who doesnt watch 1 youtube video a day, possibly on their phone, is now abnormal :P "slogging thru" what? it sounds almost like grading papers... o_O

12:57 AM
wdym automatize

if you press me for rigor I'd say a program that enumerates these equations for each n

why would the set of these be denumerable?

but intuitively I mean that stating the equations is just a rote task but nothing hard

in fact, it's probably a proper class, no?

@Thorgott uhhh
@Thorgott yes in my axiom system it is
but at least the formulas are all well-orders
worth it

1:27 AM
tfw your axiom system is recursively enumerable so your theory is incomplete

tfw when your axiom system is complete but you don't know what your axioms are

1 big yike

reddurt murmernt

i dont need axioms, i have categories

and the things defining them? axioms. checkmate category theorists

1:35 AM
theyre defined recursively from 0-categories which are defined from -1-categories
negative thinking > axioms

lmao, ya got me there

logic = circumvented
aximos are just the loser version of contractible infty-groupoids anyhow

@Thorgott finally
@Thorgott we should foster constructive, abstract thinking more

arent infty-groupoids just topological spaces in an infty-trenchcoat?

I bet one can find at least 5 category theorists claiming one can teach topos theory to high-schoolers
its all so intuitive man just look at this diagram for the subobject classifier

1:40 AM
I mean... isn't that the *mily r*ehl stuff?

1

Why is neural networks being a deterministic mapping not always considered a good thing? So I'm excluding models like VAEs since those aren't entirely deterministic. I keep thinking about this and my conclusion is that often times neural networks are used to model things in reality, which often t...

@BigSocks starring in an infty-noir film

@BigSocks yeh but that is not the worst of it, I think she's well aware of what's appropriate and what isn't

if i could travel back in time and change one thing about my life, i would ask lurie to come to my high school to teach higher topos theory

@Thorgott cigarette smoke floats up in the forns of the associahedra that make me coherent
@user2103480 yeah for sure, I don't dislike her
does good stuff

1:47 AM
the category theory for engineers/applied sciences/programming books/courses are less convincing
CT is indispensible for programming language theory but for actually programming? really a stretch

hello mathematiks chat

Establishing shot. An empty back alley in Paris. It rains. The sound of footsteps, each making a splash, is slowly impeding at an increasing pace. The protagonist enters the screen in a hurried state. He wears a trench coat and a fedora, the only source of light emanating from him is the lit cigarette slowly burning out in the corner of his month. He hastily looks around, mumbles something inaudible (actually, it's just French), then continues hurrying, towards the camera.
Suddenly, a lightning strike. Then, a gunshot. Black screen. Silence. The black screen fades and the protagonist falls

I prefer Inspecteur Clouseau.

bravo. 100 on rotten tomatoes. Would watch again

2:02 AM
I cried

Well, you cry at everything.

there's a lot to cry about, @Ted

Spoilers: Ted shot the gun

Hard to argue that, @Edward.
@BigSocks: Extra credit for knowing at whom he aimed.

2:05 AM
L*rie?

@TedShifrin I do like this book HTTLaM.

2:36 AM
@copper.hat I have solved the problem..But tell me something...How to stay motivated that the events are independent of each other pkease explain this to me.
It is nowhere mentioned in the question
So plz justify.

@zacts Huh?

@TedShifrin Hi.....I solved the problem myself
It came out to be d
but tell me something
How to stay motivated that events are independent of each other?

@TedShifrin heh, sorry. you linked the book to me how to think like a mathematician on here a while back. I got the book, and I like it so far.

Oh. Got it. I didn't recognize the letters and I can't remember whom I told what, but I'm really glad you like it!!

thanks! sorry, I should have explained that with my 1st post.

2:47 AM
I think it's a reasonable assumption, @user586228, although it may not be. After all, if I'm terrible at math, I will probably be terrible at physics, too. But this is multiple choice. You have to pick the best answer, and it's the only reasonable answer.

is anyone here familiar with Apostol's Calculus?

Yes.
I like Spivak better, but Apostol is a good book.

cool

Plus he was at the last supper

There are more interesting proof problems by far in Spivak's book. Apostol is not so deep on theory.
Well, we don't need any catholic excuses, Edward.

2:50 AM
What is the difference between a book on real analysis and Apostol/Spivak?

They're all discussing calculus in the famous mural
sorry I'll shut up

Real analysis will be more advanced, typically, although if one does the harder proof problems in Spivak one has seen a lot of that material.

hum....

@user586228 it is an assumption that i made. you would need to check with your instructor.
@vzn slogging... i can't tell you otherwise i would have to kill myself.
@user586228 i don't know what the context of source of the problems are, but generally there are some implicit assumptions that can be made. again, ask your teacher.

Apostol's Calculus seems to be a bit like physical Calculus with just a bit of theory added on?

2:54 AM
Spivak's book should be called Intro to Analysis or something.

@copper.hat lol so dramatic job related? are you still working at a job?

@Balarka

@copper It's a multiple-choice standardized test.
@NoName But Spivak assumes no prior knowledge of calculus whatsoever. An analysis course would assume that and also wouldn't teach the concrete and more applied things.

huh? you can make an analysis course without presuming calculus knowledge just fine

I don't agree.
You don't need to have done computational calculus exercises (like volumes of solids), but you need experience with calculus. But I'm running off to dinner now.

3:06 AM
@TedShifrin Makes sense. I think Spivak actually talks about the title in the preface (in one of the editions).

3:18 AM
@vzn not really, a plethora of ndas. i would kill myself trying to unravel the combined implications should anyone want to cause me bother :-).
@TedShifrin Thanks!
many decades ago, my wife & myself traveled around the globe. i brought exactly one book with me the whole way, spivak's calculus on manifolds.
figured it would be useful for getting a grip on the not so flat earth :-).

Actually, @copper, I think Calculus on Manifolds is his worst book. I think you have to know the subject (and certainly know multivariable calculus) before attempting that book. I much prefer my own. (Duh.)

Have you @ted heard of Dolciani's introductory analysis book?

@TedShifrin i agree, but it needed to be light :-). my analysis was good back then, i was interested in forms, etc. i always found the notion of formal sums a little entertaining until i hit tensor products.

i did not know that dali was still alive...
and doing 'mathematics'

3:28 AM
@TedShifrin Why are u so harsh and sarcastic?

the wine will be starting momentarily. queue loud dance music which reminds me to do hip replacement research.

Jealous

of hip replacement? don't be, i assure you.

I live in student housing where nothing is happening on a Friday or Saturday night
lol

harsh and sarcastic is the culture of this room

3:33 AM
that must be awful.

I'm sooooooo lonely pls help

dont discriminate copper for that!

wtf

hey, i may be abrupt, but i help people when they ask.
i feel bad for my 17 yo son who is stuck at home with two parents
one of which is me,

@user586228 That was neither harsh nor sarcastic. What are you talking about?

3:34 AM
poor dude

his sister is in college in the uk, just finished exams and is partying (still, i believe).

I was talking about multiple choice test taking strategy.

jealous

stuck at home with two parents?

If I am terrible in math,I will be terrible in Physics too..

3:35 AM
Finishing exams and partying
Except I have no exams
so I just wanna party
but alas

but if you ar egood in physics then you will be good in math

That was suggesting that they are not independent events. And I said "I," not "you," so I wasn't addressing that at you.

sorry Edward.

But I am fine with not talking with you any more in the future.

life is much easier if you develop a thick skin.

3:37 AM
growing it can be painful

everytime i return to ireland to see family i am reminded how little abusive conversation i have here.
sorry, i meant that in a good way.

loool

You are asking for a scene from Monty Python, @copper.

@copper.hat glad to hear that this doesnt change over time
family will be family

@TedShifrin life of brian was banned in ireland growing up!

3:38 AM
Ah, the leg-chopping incident?
I was thinking about "I've come for an argument" and the ensuing abuse.

so many things. maybe every sperm is sacred :-)

Everyone in the UK is assigned a walk from the Ministry of Sillywalks and must carry this for life

@copper.hat how does one have ndas without job(s)? lol

we tried to get it shown at highschool (i was in boarding school last year). it was a franciscan seminar. not too surprisingly they did not go for it.

I'm not sure they'd even approve of Keeping Up Appearances.

3:40 AM
Is the first derivative zero here?

how times have changed. i think i saw that movie about 5 times in school

which?

@user586228 yes.

a serbian... uhh life of brian

hahaha

3:41 AM
@vzn my life is relatively simple nowadays. used to need to pore through every detail of the legalese.

Why? It is neither a maxima nor minima
@user85795

-mum

@user586228 what is the question?

@EdwardEvans kebap

Kebabmum

3:42 AM
@copper.hat I intend to draw the fist derivative curve from here.

shes the best

note the softening of the terminal p

@user586228 The tangent line has slope = 0

@EdwardEvans very british

@copper.hat hard to follow! are you saying ndas currently apply to you?

3:42 AM
my terminal p softens

@user586228 divide into positive, zero, negative parts first.

But for inflection points it should not happen
Yes@copper.hat

@EdwardEvans rip

@vzn yes. i do consulting (fancy work for wrting tcl code).
i appear in most major names in the silicon valley from time to time.

ah interesting just today am trying to line up a consulting job myself right now :)

3:44 AM
if i was to live life again...

@user586228 that's not true

@copper.hat you mean media? or consulting for misc corps?

@vzn no. much lower level. when the chips get designed & verified.
very mundane.
used ot be more fun, had a startup.

Would you class your work as "software development" or a branch thereof?

3:45 AM

ah, chip design/ verification is not so mundane. yeah got to do a few startups myself back in the days.

@user586228 you have to develop the skill of drawing tangent lines

@EdwardEvans was that addressed to me?

Yeah sorry, I forget to @

3:45 AM
@vzn you did a stint at mgc, right?

@TedShifrin I can't believe I was telling you about what it says in this preface when your name is right there xD

mgc what is mgc? someone else. worked on 2 internet startups, also a software engr near startup, etc

@EdwardEvans it would be classed as software development, but it is a bit more complex. i am familiar with both design flows, eda tools and am broadly trusted in the south bay.

2

I am wondering whether or not this is the right sketch of the derivative in the picture below: UPDATE: Here is the function as it appears in the question (please disregard the pencil marks):

Check this problem out..

mostly during dotcom era. not too long at the startups lol the startups were not too long! o_O

3:47 AM
@EdwardEvans point being that it is a bit of software dev but a lot is the people side.

@copper.hat okay, I'm hoping to start out in software development at the moment, so I'm just lurking

my Co has headquarters in foster city, a few ppl from there on my team :)

@vzn we did hours just on the tails of the dotcom stuff. talk about a bad time to start. we did sell to cadence many years later.

"hours," consulting hours?
yes my 2nd dotcom disbanded a 7person r&d dept about 6mo after 911. also right in middle of market crash.

@EdwardEvans a few things to keep in mind. 1. its never about the software. 2. its about keeping your customer happy. 3. if the software looks good you have wasted time.

3:48 AM
loool thank you, I was gonna ask for "tips for newbies"
The company I'm hoping to get a job places big emphasis on agile software development (scrum)

why?

lol had a very bad experience with scrum but also thankfully very brief )(

@user586228 try to sketch out what is happening to the slope of the tangent line

I don't know enough about it to know why, but it appeals to me from a newbie perspective; it looks like it's easy to track your own progress

it reminds me of that rational stuff years ago (booch, brady, etc).

3:51 AM
alas feel scrum is not so agile with too much emphasis on estimation, @#%& at least thats how it played out near me o_O in the sense of "exploding grenade" being "near" o_O

@EdwardEvans i have too many things to say about it, this is not the right place :-).
i have seen teams destroyed by 'agile'.

:D Okay, I guess if I get the job I'll experience it for myself. The good thing is that the position has a good "intro program" and the company has very good reviews as an employer

the agile hype/ wave seems to be subsiding these days.

@user85795 Everything seems fine but why should I consider inflection point to have a tangent line parallel to the x axis

ultimately you need someone who cares, has a little experience and knows how things get done and what to watch out for.

3:52 AM
I guess that's applicable everywhere

@user586228 because it is flat at that point

@EdwardEvans good luck! keep looking for mentors.

@copper.hat thanks :) Keep your fingers crossed for me, I wanna get out of grad school loool

Yes but what has being flat to do with derivative being to zero
It should be constant

@user586228 what is the definition of a tangent line?

3:54 AM
That is where my problem lies @user85795

@user586228 the slope of the line is the derivative.

@EdwardEvans are you doing a thesis?

Ok then how do I differentiate between maxima minima and inflection point

Study the definition of what a tangent line means @user586228
Max, min, etc will follow

@vzn I'm in my master's at the moment but I'm not doing well enough to justify continuing. I've been trying to force it for 1,5 years and my mental health is just divebombing so I need to get out to retain my sanity.

3:56 AM
@EdwardEvans i don't know you so this is prob not good advice. it is a good idea to get
a broad idea of how everything fits together at a company, not just focus on one silo.
@EdwardEvans that can happen working too.

@EdwardEvans sorry to hear that is it on number theory so far?

@EdwardEvans grad school trauma is real

@EdwardEvans sales people work to the maxim ABC = always be closing. while not directly applicable ti research, it is a good reminder to decide the course and follow it out.

@user586228 try the khan academy for visual evidence :-)

I need to do something other than study at the moment and I'm looking to develop new skills elsewhere. Programming at university was fun and I always had an interest in it, so I guess I'll dive into it at a company that seems to have a nice atmosphere and a nice working culture. After I get some experience I can always move around.

3:59 AM
different strokes for different folks.

@vzn Yeah I have a great interest in number theory but I'm looking to change it into a hobby/interest
Unfortunately i'm just not in a position to continue with the master's at the moment, hence the change