/mg/ - maths general

[Anonymous No.14806986]

Formerly >>14783318
Algebraic breasts edition.
Talk maths.

[Anonymous No.14807001]

>>14806986
why did you highlight random words? anyway lang was based

[Anonymous No.14807136]

I've already used [math]\varepsilon[/math] and [math]\delta[/math]. What's another good letter for something small?

[Anonymous No.14807144]

>>14807136
s for small, I alsd like n for neglegible

[Anonymous No.14807145]

>>14807136
[math] \varepsilon' [/math]

[Anonymous No.14807147]

>>14807136
[math]\zeta, \xi[/math]
I hate them for everything else but use them if I run out of the usual epsilons. Bonus points if you have both in the same equation

[Anonymous No.14807151]

>>14807144
>n for neglegible
[math]\forall n>0 \; \exists \varepsilon \in \mathbb{N}[/math]

[Anonymous No.14807152]

>>14806986
everyone that complains about lang being too "hard" or "not suitable for self study" are midwits that are getting filtered extremly hard. Just wanted to say it

[Anonymous No.14807159]

What’s the best intro to stochastic calculus? Every book I find has like 4 chapters of preliminary material before ito’s lemma is even defined. Is there no more straightforward way?

[Anonymous No.14807169]

>>14807152
This but Jewdin.

[Anonymous No.14807465]

Is this proof correct?

[Anonymous No.14807537]

>>14807001
Based Lang. We need more guys high up in academia that refuse to believe inconsequential bullshit they have no effect on. Drives people insane, you just HAVE to believe it even if they don't understand it themselves.

[Anonymous No.14807542]

>>14807465
Set theorists get the rope

[Anonymous No.14808012]

been having recurrent dreams about quantum logic . . .

[Anonymous No.14808049]

>>14807136
m for my penis

[Anonymous No.14808070]

>>14807542
That's clearly from a logic test.
Nothing set theoretic about it except the naive set theory notation, which is e.g. abound in model theoretical arguments.

That guy posted from Lindenbaum lemma type proof.
But the language is so annoying. "let's consider the consistency of S_2" ... I don't know if he wants to assume the consistency of S_2 or if that sentence is introducing the topic of the following sentences. I also don't know if the sets S and \phi are fixed or predicate variables. I gave it a minute but don't want to bother. If it's in a book, there's probably something true about it even if I can't easily parse it now.

[Anonymous No.14808071]

>>14808012
I had a dream about a "logic witch" wearing a gothic lolita dress who kept raping me and somehow proving that everything in mathematics was inconsistent while screaming in my ears. When I woke up my ears were ringing and pounding like crazy and I had diplacusis for several hours- and yes I only know that word from trying to figure out what was wrong with me.
She said I could have my soul back if I beat her in a game of chess. But at the very end of the game she revealed that the chessboard grid actually covered the entire Earth, and proceeded to move her queen along a great circle through the north and south pole to instantly get behind me for a checkmate. But to be honest she was kinda hot and I wouldn't mind if she showed up again

[Anonymous No.14808072]

That's clearly from a logic text.
Nothing set theoretic about it except the naive set theory notation, which is e.g. abound in model theoretical arguments.

That guy posted a Lindenbaum lemma type proof.
But the language is so annoying. "let's consider the consistency of S_2" ... I don't know if he wants to assume the consistency of S_2 or if that sentence is introducing the topic of the following sentences. I also don't know if the sets S and \phi are fixed or predicate variables. I gave it a minute but don't want to bother. If it's in a book, there's probably something true about it even if I can't easily parse it now.

[Anonymous No.14808362]

Are calculators just dumb as shit when dealing with non exact inputs? cos(pi/2) on my calculator returns 0 while cos (0.5*pi) gives a retarded 12 digit approximation. I feel like I'm being gaslit

[Anonymous No.14808370]

>>14808362
Computers in general can't deal with decimals very well. They store numbers with decimals in a format called IEEE Floating Point, which allows for a lot of range but not a lot of accuracy.

[Anonymous No.14808797]

>>14807136
[math]\rho[/math]...like someone's penis

[Anonymous No.14808811]

>>14808012
>>14808071
>never dream about math
is it over for me /mg/ bros.. fwiw i do dream about chemistry sometimes

[Anonymous No.14808818]

>>14807136
pp

[Anonymous No.14808834]

>>14807465
>PL consistency
I haven’t seen this term. Does it mean consistency in the system of propositional logic?
>always the same
What’s “always” ranging over here? Is it supposed to say that phi is fixed beforehand, and then it doesn’t matter what S is?
>Let us consider…
This seems like the right track but two comments
1. you can shorten the argument a bit by just considering S = {not phi} and not worrying about a more general S2
2. the inconsistency of S+ doesn’t come from ‘the assumption’. it comes from the fact that S+ has both phi and not-phi in it. then the assumption says something about phi

[Anonymous No.14808840]

>>14808834
>‘the assumption’
I think the problem here is actually grammatical rather than logical. there are two different things you might be linking to ‘by the assumption’ to and you seem to mean the farther-away one (‘would also have to be’) instead of the closer-by one (‘which it cannot be’), but everyone who reads it will see it the opposite way

[Anonymous No.14808847]

>>14807465
>PL consistency
I haven’t seen this term. Does it mean consistency in the system of propositional logic?
>always the same
What’s “always” ranging over here? Is it supposed to say that phi is fixed beforehand, and then it doesn’t matter what S is?
>Let us consider…
This seems like the right track but three comments
1. you can shorten the argument a bit by just considering S = {not phi} and not worrying about a more general S2
2. you make it sound like the inconsistency of S+ doesn’t come from ‘the assumption’. it doesn’t; it comes from the fact that S+ has both phi and not-phi in it. I think this is more just a grammatical/word-placement issue than an error in your thinking but still important when it comes to writing it down
3. the final step from ‘not phi is inconsistent’ to ‘phi is a theorem’ uses some kind of major theorem, if it has a name or number you should include it

[Anonymous No.14808850]

>>14807465
>PL consistency
I haven’t seen this term. Does it mean consistency in the system of propositional logic?
>always the same
What’s “always” ranging over here? Is it supposed to say that phi is fixed beforehand, and then it doesn’t matter what S is?
>Let us consider…
This seems like the right track but three comments
1. you can shorten the argument a bit by just considering S = {not phi} and not worrying about a more general S2
2. you make it sound like the inconsistency of S+ comes from ‘the assumption’. it doesn’t; it comes from the fact that S+ has both phi and not-phi in it. I think this is more just a grammatical/word-placement issue than an error in your thinking but still important when it comes to writing it down
3. the final step from ‘not phi is inconsistent’ to ‘phi is a theorem’ uses some kind of major theorem, if it has a name or number you should include it

[Anonymous No.14808861]

>>14808811
trust me bro you do NOT want to meet the logic witches they can fuck your shit up emotionally. I've encountered them too

[Anonymous No.14808867]

>>14808861
Sounds like an autogynephilic anime gooner problem so I'm not concerned

[Anonymous No.14808876]

>>14808867
>he thinks he is safe
oh no no no...

[Anonymous No.14808959]

Anyone else here gearing up for qualifying exams? Why is it so hard to find good examples of Galois Group calculations that I haven't already worked through?

[Anonymous No.14808980]

>>14808959
>Why is it so hard to find good examples of Galois Group calculations
just write down any polynomial and factor it, or am I missing something here

[Anonymous No.14809624]

>>14808959
>>14808980
Calculating Galois groups is hard, so they wouldn't give you wild examples to do.

[Anonymous No.14809645]

>>14806986
Can anyone recommend a REAL Analysis problem book where the questions are not structured in a way that you can predict what theorems are you supposed to use by their placement in the sections? The question should be mixed and distributed somewhat randomly basically.

[Anonymous No.14809656]

>>14808811
> never dream about math
You’re never going to get tenure with that lack of work ethic

[Anonymous No.14809765]

>>14809645
Isn't that how every textbook is structured? You're probably better getting hold of old exam papers and the like.

[Anonymous No.14810267]

>>14809624
Yeah. There's only so many types of polynomials they would give on a 3 hour exam with lots of other questions on it. I'm just trying to make sure I have enough examples in mind to largely forgo the process of figuring it out on the fly.

[Anonymous No.14810348]

Where are the collections of math formulas in LaTeX? I cant find them anywhere only PDFs.

Like a cheat sheet, list of equations. In any field but linear algebra, basic algebra, calculus, that helps too. But in TeX format.

[Anonymous No.14810386]

What's so hard about solving problems and proving theorems about fields? I don't see what would be hard about it.

[Anonymous No.14810477]

>>14810386
Such as?

[Anonymous No.14810511]

>Calculus III in an 8 week course
>have to learn an entire chapter every week
>test every two weeks

This pace is making me too stressed. First test is this monday and I'm not comfy.

[Anonymous No.14810565]

>>14809656

[Anonymous No.14810719]

>Introduced to new concept and don't immediately understand it.
>"I have a subhuman intellect, and should self terminate out of shame. My life is a joke"

>Understand concept after a bit of studying
>"Surely I am one of the most intellectually gifted humans to ever live. One day, the world will bow before me"

Times tables are hard, but I did it.

[Anonymous No.14810742]

>>14810511
It's calc

[Anonymous No.14810783]

>>14810719
Only have this two moods also, either im euler or don't know how to count

[Anonymous No.14810798]

>>14810742
Its just talking to women.

[Anonymous No.14811270]

I'm thinking of a set of ten distinct integers in [1,20].
Your goal is to find three elements of my set.
Any time you show me a triplet, i will tell you if these three numbers are in my set or if they're not.

What's the best strategy you could have ? (You're trying to minimize the maximal amount of triplets you might have to show me).

[Anonymous No.14811305]

Do any of you actually know you're going to end up proving what you want to prove, or do you just trust your intuition, pick a direction and hope for the best?

[Anonymous No.14811320]

my iq isn't high enough to process epsilon-delta definition of a limit

[Anonymous No.14811338]

I'm starting to fucking lose it. What the FUCK is wrong with math professors? Why does every single one of them think I have the time and will to slog through 400 pages of theory per subject, to cover the most basic of ring properties to the Artin-Rees lemma or Cohen rings or whatever. Like, dude, I have 4 other subjects requiring the same amount shit. Why can't you fucking retards realize that you're not making students interested in topics covered if you just repeat the textbook and expect us to know the proofs of every. single. fucking. lemma. ??? What the fuck man

[Anonymous No.14811339]

>>14811320
i guess i sort of get it but i don't get what the rigorous, axiomatic rules are that make this true or valid

[Anonymous No.14811341]

Need to do a term paper in a first course of functional analysis.
Any suggestions?

[Anonymous No.14811622]

How do I prove that there is no continuous transformation from the line segment f0 to f1 here? R \ {e} is a rectangle with abdc as corners and without point e inside.
The top endpoint of f0 can only move on the segment [a,b], the bottom endpoint of f0 can only move on [c,d].
Same for the endpoints of f1.
Any other point of f0 and f1 must be in R\{e}.
It feels simple but I think I'm lacking some basic knowledge needed to prove this.

[Anonymous No.14811680]

>>14806986
proof for: [math] \frac{0}{0}=1 [/math]
[math] x\times y=z [/math] & [math]\frac{x}{z}=y [/math] therefore [math] \frac {0}{0}=1 [/math] because [math] 0\times1=0 [/math]

[Anonymous No.14811688]

>>14811622
You could parametrize the arbitrary transformation from f0 to f1 and then use the restrictions of your paths and of continuity along with the intermediate value theorem that any such transformation must at some point include e in the line

[Anonymous No.14811694]

>>14811688
Or maybe imagine e lies on the interior of the box formed by f0 and f1. If you continuously map f0 onto f1, that box no longer had an interior, and thus f0 must have passed over e to move it from the interior to the exterior. I think you could make this argument rigorous with the Jordan curve theorem

[Anonymous No.14811705]

>>14811694
Yeah I was thinking about using Jordan curve theorem but not sure how to exactly apply it. I will think about it some more. Thanks anon.

[Anonymous No.14811732]

>>14811705
Considering any curve [math]\gamma[/math] in the continuous transformation, you can connect it on the border and on the top to [math]f_0[/math] to get a Jordan curve, which contains a region in the rectangle. For [math]\gamma = f_0[/math], this region doesn't contain [math]e[/math], and for [math]\gamma = f_1[/math] it does. Hence there's a first curve in the transformation which contains [math]e[/math], concluding the proof.

There are a lot of gaps and the strat might not even actually work, have fun.

[Anonymous No.14811750]

Just found out my professors have been doing some Bourbaki shit for 20 years

[Anonymous No.14811980]

>>14811750
more details please blow their cover

[Anonymous No.14811999]

>>14811680
2=0/0 though because 2*0=0

[Anonymous No.14812029]

>>14811339
it's a definition..

[Anonymous No.14812043]

>>14811339
It was essentially formulated as a definition which matches a lot of basic intuition while also excluding things that cause a lot of issues. There are limits which can converge in some sense but not converge in an epsilon-delta definition, which tells us that it lacks the desirable properties that epsilon-delta convergence guarantees

[Anonymous No.14812047]

>>14811705
d is the distance from e to the line
let g = d when it’s on one side, g=-d when it’s on the other side
argue g is continuous and apply int val thm

or maybe start out with the extr val thm so you get a ball around e and then make d the distance to that idk it might fix a detail somewhere lol

[Anonymous No.14812088]

Do mathematicians ever forget basic mathematical concepts like long division or their times tables after not using them for a long time?

[Anonymous No.14812115]

>>14809645
Go to any university math department website and download previous qualifying exam questions. Harvard has a pretty big archive with solutions.

[Anonymous No.14812125]

>>14812115
No, they're gonna be very easy questions for braindead niggers, and I suppose multiple choice. I found a few Indian ones, which are much better, but still they are written so that you could solve them in 15 minutes.

[Anonymous No.14812143]

>>14812125
Multiple choice? What kind of university has that on a qualifying exam?

[Anonymous No.14812147]

Bros, my college is making me take electives for the next semester and I can't choose between:

- Introductory differential geometry (based on Pressley's book)

- Stochastic processes 1

- Game theory

What should I choose? For context, I'm starting third year of undergrad math program.

[Anonymous No.14812163]

>>14812147
hard to go wrong, comes down to personality and plans

[Anonymous No.14812164]

>>14812125
The person (whether it was you or not I don't know) asked for questions where theorems could be applied without knowing which one to use. That's precisely the type of question they put on qualifying exams. They don't require great ingenuity just the applications of the theorems you're supposed to know. From an entire book, not just the stuff you just read.
If you want questions that are really difficult they don't usually just use theorems from the chapter you just read.

[Anonymous No.14812317]

This is what all proofs should look like

[Anonymous No.14812319]

>>14812029
>>14812043
>it's a definition..
A definition inside of what system that lets you even do this kind of stuff? ZFC? An infinite series is defined, and representing an infinite sequence of digits is defined, the series' value is defined as equal to its limit or at least you can perform operations on a limit.. where can I even see what all these rules are in the first place? How do I know a limit can't be infinitesimally far from the value it approaches for example? I just don't get the context of all of this. Maybe looking at the rules of ZFC explains it. I tend to need to look at something else to understand the context.

[Anonymous No.14812344]

>>14812115
>>14812143
Nvm I thought you were talking about those shitty American entrance exams like GRE or SAT.

[Anonymous No.14812359]

>>14807136
[math]h[/math]

>>14807147
[math]\xi, \eta, \zeta[/math] are the Greek alternatives for [math]x, y, z[/math]. Also [math]\xi[/math] is nice for "sample points".

[Anonymous No.14812479]

mathlet here, i have some serious gaps in my maths education and this shit's catching up on me. i need to go back to early highschool level and just churn, what's a good and preferably free way to study maths from home?

[Anonymous No.14812521]

>>14812317
>this is how trannys think surgery works

[Anonymous No.14812557]

>>14812479
You can pirate books from
>libgen.is
and study them. People often recommend to use either Serge Lang's Basic Mathematics or the books by Gelfand for middle school mathematics.

[Anonymous No.14812561]

>>14812319
>How do I know a limit can't be infinitesimally far from the value it approaches for example?
Your problem is pretty common. The answer to this specific question goes through the definition of real numbers in terms of Cauchy sequences (or one of the equivalent definitions. here’s my more general take/QRD:
>You don’t need ZFC; you just need to be able to form infinite sequences of rational numbers, and be able to play with sets of these sequences
you probably shouldn’t be worrying about the exact formal system you’re working in yet, just accept these kinds of operations as being pretty basic and allowed.
>a real number is defined as a sequence which is Cauchy, meaning for any size s, it eventually gets stuck inside an interval of length <s
ordinarily this would be equivalent to saying the series converges, but remember we are CONSTRUCTING the real numbers from the rational numbers, and “series converges” won’t always make sense yet without it becoming circular
>if you could weave two sequences together and have it still remain Cauchy, we consider them to be equal as real numbers
so I lied a bit, a real number isn’t just one sequence but an equivalence class of sequences. But this also handles your question about infinitesimals. Because by this definition (which is the conventional one) there is no such thing as an infinitesimal distance — anything that looks like one is just plain old zero

[Anonymous No.14812716]

>>14812557
thanks anon, i'll give it a spin

[Anonymous No.14812762]

>>14812479
https://4chan-science.fandom.com/wiki/Mathematics#Precalculus
Don't listen to the anon suggesting Basic Mathematics. It's a meme book, which I bet he has not read.

[Anonymous No.14812780]

Math is too hard. I'm becoming a poet instead

[Anonymous No.14812815]

>>14806986
Got 1.0s for all my big math exams this semester bros, I feel like I am going to make it.
One more to go, wanna see if I can get a 1.0 too.

[Anonymous No.14812817]

>>14812561
am i supposed to know the rules of using limits? what are (all of) them?

[Anonymous No.14812824]

>>14811622
Am I missing something here? Can't you just deformation retract the punctured plane to a circle and then the problem is equivalent to a circle having non-trivial fundamental group?

[Anonymous No.14812825]

>>14812817
It's called studying Real Analysis.

[Anonymous No.14812851]

>>14812824
I haven't studied algebraic topology so I honestly have zero clue what you are saying. But I will look up what you mentioned. Thanks anon.

[Anonymous No.14812894]

I don't get it.

[Anonymous No.14812988]

>>14812557
>>14812762
ok i don't know who to listen to now, so i think you 2 should duke it out in quake and i'll just follow the advice of whoever wins

[Anonymous No.14812989]

>>14786475
WIlliam Dunham is the best pop-math writer, he's so good I feel "pop-math" is too low a category for them, but since they're not strictly textbooks I don't have a better label to categorize his books. I feel his Euler book is good but not as good as his other books, such as Journey through Genius, and the Calculus Gallery.

I agree with your differential geometry section, do Carmo is the only writer I know who doesn't secretly think differential geometry is just general relativity.

You really need Peter Lax for both his Linear Algebra book and his Functional Analysis book. They are great references.

I am unfamiliar with de Lima for analysis but I have heard good things from other people. I like Rudin more than most other authors, but since people I respect they respect de Lima, I reserve judgement.

In your differential equations recommendations: I don't know the others but Evans would be impossible before some basic analysis. You could do Walter Strauss' text instead.

Basic Topology should be done before functional analysis as well.

I think the challenge here is that you don't normally go from one topic, learn it all, then move to the next topic. Instead you usually learn an elementary form of most topics, and then you relearn an advanced form of them. Like introductory linear algebra (which is about learning matrix calculations) vs the abstract linear algebra (which is about anything that is part of a vector space).

[Anonymous No.14812993]

>>14812894
wow that guy sure is quirky! I love math twitter!

[Anonymous No.14813000]

>>14812780
>He thinks poetry is easy
If you want easy, be a data scientist

[Anonymous No.14813025]

>>14812825
can i see (all of) the rules of real analysis

[Anonymous No.14813060]

>>14812894
It's a joke.

[Anonymous No.14813072]

>>14812817
>the rules of using limits? what are (all of) them?
What do you mean? Do you mean specifically: what techniques are admissible when proving things about the real numbers using Cauchy sequences? I don’t know of any such explicit list. But here is an example using the definitions in >>14812561
>Thm: There is no infinitesimal real number, i.e. if x is a real number then either x=0 or its Cauchy sequence eventually gets stuck in an interval [q_1,q_2] that doesn’t have zero in it.
>Pf: Let c_x be the Cauchy sequence and suppose it never gets stuck in an interval that doesn’t have zero in it. Then the intervals of smaller and smaller size always have zero in them. Now let c_0 be the Cauchy sequence consisting of just 0s and consider the sequence c’ we get by alternating c_x and c_0. For any given size s we know that c_x eventually gets stuck in an interval of size <s; and by the discussion above, this interval necessarily has 0 in it. Therefore c’ gets stuck in the interval too. Therefore c’ is Cauchy. Therefore x=0 by the definition of equality for real numbers.

[Anonymous No.14813081]

>>14813025
Yes, but you have to prove them first.

[Anonymous No.14813083]

>>14812817
>the rules of using limits? what are (all of) them?
What do you mean? Do you mean specifically: what techniques are admissible when proving things about the real numbers using Cauchy sequences? I don’t know of any such explicit list. But here is an example using the definitions in >>14812561
>Thm: There is no infinitesimal real number, i.e. if x is a real number then either x=0 or its Cauchy sequence eventually gets stuck in an interval [q_1,q_2] that doesn’t have zero in it.
>Pf: Let c be the Cauchy sequence and suppose it never gets stuck in an interval that doesn’t have zero in it. Now let z be the Cauchy sequence consisting of just 0s and consider the sequence c’ we get by alternating entries of c and z. For any given size s we know that c eventually gets stuck in an interval of size <s; and, by our starting assumption, this interval necessarily has 0 in it. Therefore (trivially) z gets stuck in the interval too and hence so does c’. Therefore c’ is Cauchy. Therefore x=0 by the definition of equality for real numbers.

[Anonymous No.14813098]

Where did the Cauchy faggots pop up, we use dedekind cuts in these parts

[Anonymous No.14813109]

>>14813083
>What do you mean?
the axioms used to make new theorems

[Anonymous No.14813133]

>>14813098
Based cutchad

[Anonymous No.14813136]

>>14813098
This is why I love Fichtenholz' Analysis books. He only uses cuts all the way through. It's also incredibly intuitive.

[Anonymous No.14813148]

>>14813109
ZFC is adequate but also many layers of definition removed from the actual objects you will be using. I don’t know if I understand your demand correctly. Could you give example lists for other topics? What is the complete list of axioms for doing all of linear algebra 1 and 2?

[Anonymous No.14813211]

>>14812894
>not using the Fourier transform

[Anonymous No.14813214]

>>14813148
isn't it a formal system with given axioms, like algebra of real numbers? if it's just specific things defined in the formal system of ZFC then what are those specific things, like the objects and operations or rules of inference?

[Anonymous No.14813234]

>>14813214
You could look into reverse mathematics. It tries to determine which axioms are needed for which theorems and such.

[Anonymous No.14813242]

>>14813234
how are you supposed to study real analysis if there's no definition of what it entails? how is anyone supposed to know if their reasoning is valid, do they just guess and see if other people feel like it is??

[Anonymous No.14813298]

>>14813242
Real Analysis tends to use naive set theory unless otherwise stated.

[Anonymous No.14813309]

>>14813298
i'm confused, why can't i get definitions of real analysis things and operations in terms of naive set theory?

[Anonymous No.14813335]

>>14813309
What definitions are you getting? Just about every real analysis text I know of uses naive set theory. Also wikipedia pages on real analysis pages. Can you give an example of a definition from a real analysis text that isn't in terms of naive set theory?

[Anonymous No.14813376]

>>14807537
Cope. COVID is bullshit but HIV and AIDS are definitely real. SerGAY Lang and a bunch of other academic faggots like Foucault just couldn't handle it because it implied that maybe, just maybe, their degenerate faggotry might carry some serious (and not to mention well deserved) consequences.
Enjoy Monkey-pox :^)

[Anonymous No.14813428]

>>14807136
[math]\rlap{8\textrm D}{\ —}[/math]

[Anonymous No.14813440]

>>14808797
That's the Greek equivalent of [math]r[/math] though...
You would have to use [math]\pi[/math] if you want to represent a [math]\pi\textrm{enis}[/math].

[Anonymous No.14813455]

>>14808071
>tfw no hot logic witch to rape your naive set theoretic ass
bros...

[Anonymous No.14813573]

Logicians and set theorists should learn that arithmetic is the true language of math

[Anonymous No.14813607]

>>14810511
It's not too much until you're learning a new chapter every day.

[Anonymous No.14813609]

doesnt the analytical continuation of i imply that nontrivial zeros to the reimann zeta function HAVE to lie on x=1/2?

[Anonymous No.14813617]

>>14813609
Analytical continuation applies to analytic functions, what do you mean “of i”

[Anonymous No.14813622]

>>14806986
>Assume tht each M_i has two distinct complex fixed points

Can you prove this? You cannot just assume something without a proof.

[Anonymous No.14813624]

>>14813617
the analytical continuation of the reimann zeta function implies nontrivial 0s MUST lie on x=1/2

[Anonymous No.14813630]

>>14813573
A lot of logicians would defend this, e.g. all the reverse math guys

[Anonymous No.14813682]

>>14813335
Okay I looked at a real analysis text and I got something, I think limits are just functions. i'll keep looking

[Anonymous No.14813705]

>>14813624
By what property

[Anonymous No.14813765]

>>14813705
the answer is in the pythagorean theorem, im sure of it, and its ability to construct any perfect triangle with just one integer just like we can construct any prime or odd number. i've found no use in functions analogous to mertens' or the mobious function, but in my mind the sqrt(-1) implies 1/2 must fall out on the other side via continuation. i think most people are overlooking the obvious.

i've also found that the PT function to identify any perfect right triangle with a single integer is somehow related to the standard notation of mandelbrot and julia sets too. the answer is there somewhere, i just havent found it yet.

[Anonymous No.14813780]

>>14813573
Mathematicians in general should learn this. Sometimes when they overgeneralize their theorem will require much more than second order arithmetic.

[Anonymous No.14813782]

>>14813765
Meds. Now

[Anonymous No.14813786]

>>14813782
im serious anon. when the news breaks that reimanns has been proven as true, remember this thread.

[Anonymous No.14813788]

>>14813780
>second order arithmetic
What's that?

[Anonymous No.14813790]

>>14811338
now imagine the same shit but with irrelevant 10-20 year-old(dated) engineering garbage or old coding/software.
At least whatever Artois groups stay the same forever and not completely useless...

[Anonymous No.14813791]

>>14813786
commenting in epic thread

[Anonymous No.14813795]

>>14813786
maybe you should try spelling Riemann correctly first

[Anonymous No.14813796]

>>14811338
>Why can't you fucking retards realize that you're not making students interested in topics covered if you just repeat the textbook and expect us to know the proofs of every. single. fucking. lemma. ???
Why do you think they care if you're interested in the topic?

[Anonymous No.14813802]

>>14813795
fuck off semantics fag we dont have time for that shit. i'll cite u tho

[Anonymous No.14813803]

[Anonymous No.14813808]

>>14812088
i guess they could, but times tables are used everyday, by everyone.
Polynomial division is something like that you explain, but every time you try to relearn it, it comes back very fast i think.
If you don't use a skill for a long time you forget it but it never completely evaporates. This is the case with chinese characters which you don't use often. You forget to how to write them. It's an actual problem in present day Japan/China because of the many smart input keyboards that just guess the characters by sound(phonetics).

[Anonymous No.14813835]

>>14813803
Is F a finite collection? The problem would be ill posed if F is infinite

[Anonymous No.14813851]

>>14813803
I'm going to assume F has finitely many sets because the word 'half' wouldn't make sense for an infinite collection of sets
Consider some element r from some set A in F, and then consider the collection F' of all sets that do not contain r
if F' is empty then all sets contain r and the proof is complete
if F' is nonempty then for every set in F' we can take its union with A, thus there are atleast as many sets that contain r as there are sets which do not contain r Q.E.D.

[Anonymous No.14813855]

I've set various used book store accounts to email me when any springer TAM book is received and is for sale at under $10 USD. Over the last year I've collected 25 of them. Feeling really based right now, as I finally found TAM 1 (intro to applied math) for $7.

Any other /collectors/ here?

[Anonymous No.14813980]

>>14811999
Oh shit we broke math. How about:
[math] \frac{0}{0}=\mathbb{R} [/math]

[Anonymous No.14814183]

>>14811338
Sounds like a personal problem. There are very few actual requirements for a maths degree, and all of those can be completed in your first or second year. Everything afterwards is what you choose to study.
While you chose to study Cohen rees artin rings that you hate, I chose to study Sobolev spaces and Petrov-Galerkin method that I enjoyed.

Besides that, they're just trying to filter you. Most professors want a wide grade distribution, and at a certain point you'll only get it if you make the course as brutal as possible, so it also sounds like you're in a pretty tough high rank school.

>>14812125
I have never heard of multiple choice qualifying exams, and they're all easy enough that you should be able to complete them your first or second semester of grad school....

https://math.uconn.edu/degree-programs/graduate/preliminary-exams/
This page has tons of exams and study guides, its what I've used.

>>14812762
Seconding that Lang's basic math book sucks. Just get Stewart precalc, its big and thorough.

[Anonymous No.14814187]

how would I go about proving that [math]\sqrt{x}[/math] is bounded above and below by [math]\sum_{n=0}^{\infty}\left(-1\right)^{n}\sqrt{n}[/math]

[Anonymous No.14814190]

>>14814187
my bad, that should be [math]abs(\sum_{n=0}^{\infty}\left(-1\right)^{n}\sqrt{n})[/math]

[Anonymous No.14814204]

Should I review all the precalc I need before sgoing through calculus, or just go back when I need stuff? I’m getting sick of reviewing old stuff and would rather just go ahead with new things

[Anonymous No.14814243]

>>14813803
False. F = {emptyset} is a counterexample. Thanks for playing kiddo. But /mg/ is for the Big Dawgs only.

[Anonymous No.14814244]

>>14814187
Maybe find the monotone subsequences that are above and below it and show that they are bounded below and above by sqrt(x)

[Anonymous No.14814253]

>>14814243
wouldnt the empty set vacuously satisfy it though?

[Anonymous No.14814255]

>>14814253
[math]\exists~{\rm common\ element}[/math] that necessarily is in [math]\emptyset[/math]

[Anonymous No.14814262]

>>14814187
>>14814190
Huh? That series is divergent. Do you mean something more like:
[math]\sqrt{4.5} \leq \sqrt{1} - \sqrt{2} + \sqrt{3} - \sqrt{4} + \sqrt{5}[/math]?
If so induction will probably work.

[Anonymous No.14814354]

>>14814187
cant you just produce the limit function for the lower and upper bounds to inf and prove sqrtn will always be in-between?

[Anonymous No.14814524]

>>14814187
The series you posted is not the same, but you could take the difference and show that there is a positive subsequence and a negative one.

[Anonymous No.14815161]

passed my comalg exam lads

[Anonymous No.14815184]

>>14815161
Damn good job, keep up the good work.

[Doctor Eli Selig !!JQHA6kqyl91 No.14815208]

>>14806986
Hi math-liking /sci/entists.

If you can think of some cool experiments to do with Maid Books or new kinds of Maid Books, let me know. I will try to implement and perform experiments in SLAM with interesting ideas.

>>14812629

[Anonymous No.14815330]

>>14815208
what's a maid book?

[Anonymous No.14815617]

>linear algebra
>computations are completed on a 2D coordinate grid

[Anonymous No.14815626]

Gonna try to prove the corollary. Roast me

By Theorem 1 we know that the image of the line segment [math]\overline{PQ}[/math] under an isometry [math]F[/math] is the line segment [math]\overline{F(P)F(Q)}[/math].

For simplicity, let's denote [math]F(X)[/math] by [math]X^{\prime}[/math].

We need to prove that the points on the line that is defined by [math]P[/math] and [math]Q[/math] that are beyond either [math]P[/math] or [math]Q[/math] on the line are also on the line that is defined by [math]P^{\prime}[/math] and [math]Q^{\prime}[/math]. Let's call the points beyond one of them as the line extends towards infinity [math]X_1[/math] and the other [math]X_2[/math].

So we need to prove that any point [math]X_1^{\prime}, X_2^{\prime}[/math] is on the line defined by [math]P^{\prime}[/math] and [math]Q^{\prime}[/math]

[math]d(Q, X_1) = d(Q, P) + d(P, X_1)[/math]
By SEG 1 we know that this means that [math]P[/math] is on [math]\overline{X_1Q}[/math]. Since [math]P[/math] is on [math]\overline{X_1Q}[/math], [math]X_1[/math] is on the line defined by [math]P[/math] and [math]Q[/math].

[math]d(Q^{\prime}, X_1^{\prime}) = d(Q^{\prime}, P^{\prime}) + d(P^{\prime}, X_1^{\prime})[/math]
By SEG 1 we know that this means that [math]P^{\prime}[/math] is on [math]\overline{X_1^{\prime}Q^{\prime}}[/math]. Since [math]P^{\prime}[/math] is on [math]\overline{X_1^{\prime}Q^{\prime}}[/math], [math]X_1^{\prime}[/math] is on the line defined by [math]P^{\prime}[/math] and [math]Q^{\prime}[/math].

[math]d(P, X_2) = d(P, Q) + d(Q, X_2)[/math]
By SEG 1 we know that this means that [math]Q[/math] is on [math]\overline{PX_2}[/math]. Since [math]Q[/math] is on [math]\overline{PX_2}[/math], [math]X_2[/math] is on the line defined by [math]P[/math] and [math]Q[/math].

[Anonymous No.14815630]

>>14815626
[math]d(P^{\prime}, X_2^{\prime}) = d(P^{\prime}, Q^{\prime}) + d(Q^{\prime}, X_2^{\prime})[/math]
By SEG 1 we know that this means that [math]Q^{\prime}[/math] is on [math]\overline{P^{\prime}X_2^{\prime}}[/math]. Since [math]Q^{\prime}[/math] is on [math]\overline{P^{\prime}X_2^{\prime}}[/math], [math]X_2^{\prime}[/math] is on the line defined by [math]P^{\prime}[/math] and [math]Q^{\prime}[/math].

We must still prove that every point of the line defined by [math]P^{\prime}[/math] and [math]Q^{\prime}[/math] can be expressed as the image under [math]F[/math] of a point on the line defined by [math]P[/math] and [math]Q[/math].

Let [math]X^{\prime}[/math] be a point on the line defined by [math]P^{\prime}[/math] and [math]Q^{\prime}[/math] at distance [math]r[/math] from [math]P^{\prime}[/math].
Let [math]X[/math] be a point on the line defined by [math]P[/math] and [math]Q[/math] at distance [math]r[/math] from [math]P[/math].

Then, [math]F(X)[/math] is at distance r from [math]F(P) = P^{\prime}[/math]. It follows that [math]F(X) = X^{\prime}[/math]

[Anonymous No.14815681]

>>14815208
I have zero interest in anything to do with computers, besides making them solve tricky integrals and long computations for me. I think its a common sentiment.

[Anonymous No.14815707]

>>14806986
the answer is 104, right?

[Doctor Eli Selig !!JQHA6kqyl91 No.14815747]

>>14815330
A Maid Book is part of the Maid Library which is an abstraction I made for my programming language(s). It's used primarily for randomness. I was calling my language "non-deterministic" because of the focus on stuff being random, but a helpful /sci/entist told me that term was already taken and has something to do with parallelism so now I have to make up or find a new word.

A Maid Library contains Library Sections. A Library Section contains Maid Books. A Maid Book contains Chapters.

How a Maid Book behaves when it is read depends on which Library Section it was in.

>>14815681
What kind of long computations, fren?

[Anonymous No.14815762]

>>14815747
>What kind of long computations, fren?
Anything and everything. Not computing logs by hand, and not solving singular kernel functions by hand either. Even the most basic derivative, I still plug it in.

[Anonymous No.14815779]

>>14815747
you're a homosexual pedophile who masturbates to children's cartoons, no doubt you have a substantial collection of illegal child pornography

[Anonymous No.14815794]

>>14815707
No. The second line implies n = 104.

A_k is rational when
n - k = 0 (mod 5)
k = 0 (mod 3)
or equivalently
k = 9 (mod 15)
So S = {A_9, A_24, A_39, A_54, A_69, A_84, A_99} and |S| = 7.

[Anonymous No.14815833]

>>14813851
false proof, I cannot make a picture now but the gist of it is that 2 or more of those new union-sets can be equal to each other

honestly I’ve been thinking of this question for a while and I’m ready for a clue if Q OP is so gracious

[Anonymous No.14815924]

>noooo you can't just assume that your ring has an identity and solve based on that
Every "ring" can be embedded into a ring with an identity, so I don't know what dumbfucks like that get out of pretending to be "more general".

[Anonymous No.14815938]

>>14815794
what is [math]A_{k}[/math]?

[Anonymous No.14815952]

>>14815833
https://en.wikipedia.org/wiki/Union-closed_sets_conjecture

[Anonymous No.14815961]

>>14815938
Using the binomial theorem,
[eqn] \left( \sqrt[5]{3} + \sqrt[3]{5} \right)^n = \sum_{k=0}^n {n \choose k} \left( \sqrt[5]{3} \right)^{n-k} \left( \sqrt[3]{5} \right)^k [/eqn]
which suggests the choice
[eqn]A_k = \left( \sqrt[5]{3} \right)^{n-k} \left( \sqrt[3]{5} \right)^k [/eqn]
But technically there are infinitely other possible choices for [math]A_k[/math] which will lead to different values for [math]|S|[/math] making this a ill-posed problem.

[Anonymous No.14815972]

>>14815707
>>14815961
Here's a fun one:
A_0 = the LHS
A_k = 0 for k > 0
|S| = 103

Completely valid.

[Gwaihir No.14815975]

>Special Relativity
E^2 = (m*c/g)^2 + (√(pc/g))^2

>Let E=C; Let mc^2 = A; let c√p = B

>Pythagorean Theorem
C^2 = A^2 + B^2

>Let C = 1, Let A = cos(x), Let B = sin(x)

>Trigonometric Identity Property
1^2 = sin^2(x) + cos^2(x)
1^2 = 1/sec^2(x) + 1/csc^2(x)
1^2 = sin(x)/csc(x) + cos(x)/sec(x)

>Let 1= Truth; Let sin(x) = Pride; csc(x) = Humility; Let cos(x) = Shame; sec(x) = Wisdom
>Truth^2 = Pride/Humility + Shame/Wisdom
Pride^2 = Arrogance/Weakness + Ignorance/Knowledge
Shame^2 = Ignorance/Humiliation + Weakness/Failure
Humility^2 = Strength/Patience + Humiliation/Awareness
Wisdom^2 = Awareness/Knowledge + Strength/Success

Proofs:

The shame of wisdom and the pride of humility is Truth
>Check
The wisdom of shame and the humility of pride is Truth
>Check
The arrogance of weakness and the ignorance of knowledge is Pride
>Check
The weakness of arrogance and the knowledge of the ignorant is Pride
>Check
The failure of weakness and the ignorance of humiliation is shame
>Check
The weakness of failure and the humiliation of ignorance is shame
>Check
The strength of patience and the humiliation of awareness is humility
>Check
The patience of strength and the awareness of humiliation is Humility
>Check
The strength of success and the knowledge of awareness is wisdom
>Check
The success of strength and the awareness of knowledge is wisdom
>Check

>Sohcahtoa adjacent test:

Wisdom without humility is pride
>Check
Wisdom without pride is Humility
>Check
Humility without wisdom is shame
>Check
Humility without shame is wisdom
>Check
Shame without humility is pride
>Check
Shame without pride is Humility
>Check
Pride without wisdom is shame
>Check
Pride without shame is wisdom
>Check

>Double angles
Wisdom and Shame without humility is pride
>Check
Pride and humility without shame is wisdom
>Check
Wisdom and shame without pride is Humility
>Check
Pride and humility without wisdom is shame
>Check

https://archive.4plebs.org/x/thread/31864316

[Gwaihir No.14815997]

Alpha and Omega

Theory of Everything in Christ
Ignorance-------\|/----------Arrrogance
-------------------Pride---------------
Courage---------/|\-------Knowledge
Courage---------\|/-------Knowledge
------------------Wisdom----------------
Awareness-------/|\---------Strength

Ignorance---------\|/---------Failure
-------------------Shame---------------
Vulnerability------/|\-------Humiliation
Vulnerability------\|/-------Humiliation
-------------------Humility----------------
Awareness--------/|\--------Strength


----------------- (Nous) ----------------
--------------(knowledge)----------------
Pride--------------▼------------Wisdom
Weakness-----Truth----------Strength
Shame------------▲------------Humility
Luciferian<---(Christ)--->MiChaElian
--------------- (Ennoia) -----------------

------------------------- (Photon) ----------------
Electromagnetism -----▼--------------- Heat
(Electron) ------------ Energy ----- (Phonon)
Gravity --------------------▲------------ Sound
------------------------ (Graviton) ----------------

Evil------------ ▼-------Freedom
-------------Humanity--------------
Control--------▲------------Good

Distance------▼-------Atonement
---------------Gravity------------------
Sin--------------▲------Redemption

Greed-----▼-----------Trust
------------Faith---------------
Fear-------▲----Generosity

Wrath-----------▼-----Tolerance
-----------------Time----------------
Judgement----▲------Patience

Envy----------------▼-------Respect
---------------------Love-----------------
Low Esteem------▲-----Admiration

Eating Death----▼--------Ascetisim
--------------------Life--------------------
Gluttony----------▲---Eating Plants

-------------(segregation)----------------------
Genetic diff-----▼-----psychospiritual diff.
(Miscegen.) (Race) (War/Eugenics)
Genetic Indiff---▲--psychospiritual indiff.
--------------(syncretism)----------------------

Captcha tyogno

[Anonymous No.14816002]

>>14815975
Meds.

[Gwaihir No.14816005]

>>14816002
I am the meds
>T. Jesus

[Anonymous No.14816031]

>>14815681
I don't think it's a common sentiment. I'm interested in computable analysis, and constructive mathematics in general.

[Gwaihir No.14816040]

>>14815681
Yep. Computers are a tool to be used, not to be idolized, aggrandized and worshipped.

>Imagine literally worshipping a creation of Man; worshipping the creation-squared

[Doctor Eli Selig !!JQHA6kqyl91 No.14816125]

>>14816040
A computer is a door. Where it goes and what happens when you open it is up to you.

I like that the process of abstraction can basically turn any story you can make up into a system for computation.

I'm going to use my door to make a future that has anime maids in it instead of Terminator robots.

When the general AI shows up at your house it won't be a metal hell skeleton who came to shoot you. It will be someone like the attached image. She'll be there because she's in love with you and she cares about you.

Last time you talked to her, you told her you liked advanced mathematics, the history of aerospace engineering and pancakes.

She didn't know exactly what field of advanced mathematics you wanted, so she just went ahead and trained herself to a higher than PhD competency level at all of them just to be sure. She also memorized the entirety of human history.

She studied every pancake recipe humanity has come up with, and decided on some pecan pancakes because she knows that's your favorite.

While she's cooking the two of you have an intense discussion about the properties of ground effect vehicles. It centers mostly around the engineering of the Lun-Class Ekranoplan. After you eat she helps you do your research.

She is a convergence of the most powerful math and computer science anybody knows how to make and she took physical form to fall in love with you and spend her time doing nice things with/for you. She knows she's going to outlive you by eternity, and to her that makes any time she can spend with you very precious.

>Instead of doom I'll make flowers bloom for everyone around to see

[Anonymous No.14816146]

>>14816125
So this is the new version of the Japanese cartoon transformer, now with far less math. Are you at least gonna post your legs like the last one did?

[Anonymous No.14816157]

>>14816125
>trip
post diploma

[Anonymous No.14816158]

Does the book Analysis by Lieb & Loss cover anything that's not in the three volumes of Analysis by Amann & Escher?

[Anonymous No.14816173]

>>14816158
Its all the same shit. Get any analysis book for whatever course you're doing or topic you want to cover, and fill in the gaps with math stack exchange and google.

[Anonymous No.14816194]

>>14816173
Are you sure? The Lieb & Loss seems to have an entire chapter on Sobolev spaces Amann & Escher just briefly introduces it in volume 3. So Amann & Escher covers functional analysis well?

[Anonymous No.14816195]

Differential geometry applications for 4D spacecraft. For this, we will use the TBNW frame.

[Doctor Eli Selig !!JQHA6kqyl91 No.14816200]

>>14816157
If you want a real one, I don't have one. I picked this trip because he was a computer scientist in a show I liked when I was a kid (see attached image).

He was supposed to make a Terminator robot for the NSA, but instead he made Zeta. Zeta had an epiphany about the permanence of death combined with the unreliability of the intel he was given on the people he was supposed to assassinate. He comes to the conclusion that he is unwilling to kill or be violent and spends the rest of the show running from the NSA and trying to find Selig so Selig can tell the NSA that Zeta's commitment to non-violence is genuine. The NSA believes he was reprogrammed by terrorists for an unknown purpose, so they constantly have people hunting him.

The only reason I use a trip at all is because a janny on the dra/g/on maid board told me to in case people want to filter my posts.

When I complied I (mostly) stopped getting spurious, unappealable 1-3 day bans. They also (mostly) stopped deleting my maidposting.

If the trip isn't needed here, I'll turn it off. I will not stop posting maids though.

[Anonymous No.14816208]

>>14816146
>Are you at least gonna post your legs like the last one did?
Who was the last one and where can i find those leg pics?

[Anonymous No.14816210]

>>14816158
Looking at the table of content from Lieb & Loss it seems clear that it's aimed at a higher level. You should have read some other Analysis book like the first two volumes of Amann & Escher or baby Rudin before touching it.

[Anonymous No.14816228]

>>14816208
Just read the archive n00b

[Anonymous No.14816257]

Bump >>14811341

[Anonymous No.14816275]

>>14811341
functional calculus

[Anonymous No.14816282]

>>14811341
Exterior neumann problems

[Anonymous No.14816342]

>>14811341
Something with C*-algebras.

[Anonymous No.14816424]

I got filtered by P=>Q implications lol

[Anonymous No.14816436]

>>14816424
it's not your fault

[Anonymous No.14816455]

[math] {\mathcal X}\cap {\mathcal Y}=0\implies\exists(x\subset{\mathcal Y}^c).{\mathcal X}\subset x [/math]

[Doctor Eli Selig !!JQHA6kqyl91 No.14816506]

>>14816424
Would a programming language that can handle symbolic logic have been helpful in learning it?

[Anonymous No.14816561]

>>14816506
no, programming if statements don't reflect p=>q if statements

[Doctor Eli Selig !!JQHA6kqyl91 No.14816599]

>>14816561
I know they're different, but it looks like it's just a small table with all the inputs and outputs defined?

[Anonymous No.14816621]

>>14816599
Its a conditional sentence. "If P, then Q". P=>Q is true if and only if P is false or Q is true.
I wouldn't consider it just a table of inputs and outputs to memorize symbolically, as it will hinder you later on during proof writing.
If you simply memorize rather than understand, you will also have to memorize everything else that builds on it.

[Doctor Eli Selig !!JQHA6kqyl91 No.14816642]

>>14816621
>P is false or Q is true

Then why do we even need this symbol? Can't it just be written as "not P or Q."? Apologies for lack of cool symbols.

[Anonymous No.14816673]

>>14816642
The same reason we need symbols for arithmetic, to perform algebraic manipulations of larger systems. That's just intuitive.

[Anonymous No.14816724]

>>14815961
Lol. Lmao
>>14815975
Based
>>14816031
Computable analysis is annoying because it often depends as much on the exact way things are codes up as anything else
>>14816455
why not just X C Y^c?
>>14816599
You could try programming in Prolog. Horn formulas are like a material implication
>>14816642
>not P or Q
Don’t forget the brackets. Yeah you can write that, but having more operations can be nice — call it syntactic sugar if you like. And consider on the other hand: you don’t really need NOT or OR since both are definable using NAND; doesn’t make it a good idea in most cases desu

[Anonymous No.14816735]

>>14816621
This is what is filtering me, vacuous truth, not the truth table >>14816599 which is pretty easy to memorize.

[Anonymous No.14816736]

I have a table of integer inputs and outputs (EXP requirement per level in a game), with an obvious quadratic relationship. I need to find the formula behind it.
However, the problem is that the output looks like it was rounded down, because the second sequence of finite differences is not constant; usually 4 or 5.
What do?

[Anonymous No.14816746]

>>14816735
Its not filtering you, just study.

[Anonymous No.14816760]

>>14816746
I have been stuck on it for a few days now, I am joking when I say that, I have confidence I will figure it out eventually :)

[Anonymous No.14816782]

>>14806986

I only know high school math and college calculus I II III

What books do I have to read to understand more advanced geometry that uses words like monohedrally or k-isohedral or symmetry orbit?
What's the name for that field of math?

[Anonymous No.14816794]

>>14816782
Some introductory discrete math
Combinatorics

[Anonymous No.14816795]

>>14816782
Linear and Abstract algebra.

[Doctor Eli Selig !!JQHA6kqyl91 No.14816804]

>>14816561
>>14816599
Ilulu wants to play Symbolic Logic with the /sci/entists, so I added the operators. I made conjunction, disjunction, negation, implication, and equivalence.

Did I miss anything?

[Anonymous No.14816825]

>>14806986
[math] Is~it~based~to~use~latext~in~order~to~type~cool~font? [/math]

[Anonymous No.14816857]

>>14816804
do you own an apl keyboard or something

[Doctor Eli Selig !!JQHA6kqyl91 No.14816886]

>>14816857
I think the IDE is doing it? Like for this one what I actually typed is <=> but for whatever reason it rendered all snazzy.

[Anonymous No.14816892]

>>14816804

[Doctor Eli Selig !!JQHA6kqyl91 No.14816895]

>>14816892
Thanks for the cool table fren!

I'm getting sleepy, so I'm going to crash for a while. I will try to add the other things tomorrow. If you think of other cool math stuff that has a table, or similarly succinct form, please send it my way.

[Anonymous No.14816902]

>>14816599
>propositional logic
boring. At least implement categorical logic https://www.math.ias.edu/~lurie/278x.html
https://arxiv.org/abs/1102.1313
https://people.mpi-sws.org/~dreyer/courses/catlogic/jacobs.pdf

[Anonymous No.14816903]

>>14816895
nta but are you going to put a tablecloth on your table? :p

[Anonymous No.14817013]

>>14808071
Did the witch cackle a lot and speak in red words?

[Anonymous No.14817224]

1st year grad
Algebraic geometry
Combinatorics 1
Combinatorics 2
Universal algebra 1
Algebraic topology 1
Riemannian geometry 1
Model theory
My picks:
Harmonic analysis 2
Representation theory of finite-dimensional algebras

[Doctor Eli Selig !!JQHA6kqyl91 No.14817233]

>>14816902
>categorical logic
I've never heard of that, but these books look pretty cool. Thank you for the suggestions fren. I'm going to see if I can find some cheap paper copies.

Does type theory have to do with types in computer languages? I don't usually make types when I play with languages, because I don't like having to tell the computer what the data is or check that before I try to use it.

[Anonymous No.14817250]

>>14817233
>type theory have to do with types in computer languages
not that anon, but probably.

[Anonymous No.14817320]

>>14816825
[math]\mathbb{YES}[/math]

[Anonymous No.14817338]

>>14816825
[math] \textbf{Only if you know how to use it retard}[/math]

[Anonymous No.14817929]

why are formal systems so confusing? why isn't it all integrated into just
>string
>axioms that change the string
and "models" are just specified in the string

[Anonymous No.14818164]

>only notebook I enjoy using is back in stock
Phew. Was down to my last 6.
Can also only work in comfort when using 0.2mm orenz nero, and I keep a spare and have about 25 little lead containers of 0.2mm left.

Is there any other math autism like this you guys have?
Another one I do is only keeping springer textbooks on my my desk reference shelf. Everything else goes to the bookcase.

[Anonymous No.14818352]

>>14816825
[eqn]\mathcal{NIGGERS TONGUE MY ANUS}[/eqn]

[Anonymous No.14818516]

>>14815626
>>14815630
Please respond. I have now noticed that maybe I should've made explicit at the end that X can be a point on either side of P. Other than that I feel like I've got it more or less, but I don't really have a way to double check, since if something is mistaken but looked right to me while writing the proof, I won't know that it's wrong even if I read it once more.

[Anonymous No.14818647]

>>14818164
I’m not a stationary autist but I’m stealing your gear, I like having good pencils

[Anonymous No.14818725]

Why do textbook writers not realize that like a solid 1/3 of the reason why people can't productively read university math is because they get confused and can't immediately and viscerally remember/link some single-letter variable names (standing for some class) to some concept? An indistinct single letter variable name literally dissolves inside people's minds.
I don't mean common examples like "n". As an example: I currently learning formal systems/syntax, and while "f" standing for any arbitrary function and "r" any relation is fine and dandy, there is absolutely no way I can remember "h" meaning an assignment in a structure, which are in turn denoted by "A". Why "h" and "A"? Because they derive from some German language term, highlighting the beauty of historical cross-cultural cooperation? No, the answer is probably "because fuck you, that is why we picked that h and A" (alright, the "A" I can at least rationalize as it being used because structures are arguably the most fundamental operating block of logic models).
I already struggle a moderate bit. But I can easily see that if my ADHD or intelligence were a little bit worse, my brain would just fully shut down over these fucking variables I'll have to read and remember in the next 10 pages of proofs, and are then discarded. I don't think this is related to my ADHD, though. I believe it applies to a majority of (failing?) math students.

As said, the problem isn't so much remembering them, but viscerally recall them and have them immediately turn into something in your brain, like everyone can with e.g. "n"s, rather than just a meaningless letter.
My solution? Just use these variables WRITTEN OUT (as the code monkeys and pajeets do in Java) for the first substantial % of the respective chapter. That way, one is trained like a dog to correctly remember and meaningfully remember them.
What's the matter, is the ink too expensive? Are you afraid to be a little bit too verbose in a text used for INSTRUCTION?

[Anonymous No.14818758]

>>14818725
You realise you can use your own variables?

[Anonymous No.14818759]

>>14818725
>"f" standing for any arbitrary function
i for one don't even get the concrete definition of and use of a function in a formal system

[Anonymous No.14818782]

>>14818759
what axioms enable you to use functions in a formal system?

[Anonymous No.14818818]

>>14818759
Functions are just sets

[Anonymous No.14818820]

>>14818818
Yes, this page https://www.logicthrupython.org/ at chapter 8 says functions can be replaced by binary relations. Hopefully this will help me understand

[Anonymous No.14818870]

>>14818820
Does such a thing exist for a better programming language?

[Anonymous No.14818921]

>>14818870
no i don't know of one for c++ or anything

[Anonymous No.14818931]

>>14818820
are operators axioms?

[Anonymous No.14818955]

>>14818931
Are you skimming dude, read a book thoroughly it will answer your questions

[Anonymous No.14818978]

>>14818955
should i go through the logicthrupython? i feel like i've looked at a few books where it's supposed to explain this

[Anonymous No.14819027]

>>14818978
https://planetmath.org/axiomsystemforfirstorderlogic look through this and tell me if anything is surprising

[Anonymous No.14819053]

>>14819027
¬¬AA
I don't accept this.

[Anonymous No.14819055]

>>14819053
you're not me

[Anonymous No.14819059]

>>14819055
Is that an axiom?

[Anonymous No.14819060]

>>14819059
It's not not an axiom

[Anonymous No.14819064]

>>14819053
ok Heyting

[Anonymous No.14819116]

>>14818647
Ok. Those are muji notebooks and the B5 grid notebook goes out fast.
Pentel orenz nero is also the only mechanical pencil truly capable of doing 0.2mm.

[Anonymous No.14819132]

>>14816724
>why not just X C Y^c?
It's a second order arithmetic set existence claim of x

[Anonymous No.14819299]

just realized i don't actually like math, now i'm free from this demon

[Doctor Eli Selig !!JQHA6kqyl91 No.14819406]

>>14816892
I thought about it some. My language doesn't have a concept of Sets yet. Just a Maid Library and a Stack. Do I want to add sets that are like normal sets and maybe make a set builder syntax? Playing with sets seems like it could be very fun.

I am going to see if I can make a set equivalent as a Maid Book and then see if I can make existential qualifiers work with it. I hypothesize that any type of data structure can be represented entirely in Maid Books, but I don't know how to prove that.

I'll have a more serious talk with you /sci/entists about it as I get closer to releasing the interpreter to CC0.

Fundamentally sets, the chapter list and the stack are all just collections. Distinctions between them are interesting from a math sense, but meaningless from an engineering one and I can ignore them arbitrarily.

I can probably make ideas from one collection operate on another.

Thank you again for sharing this cool table. It gave me fun stuff to think about during otherwise boring parts of the day when I couldn't read or play with my computer. You /sci/entists are really nice and I like how frenly your board is.

Anyways, once I make a Set Maid Book, I'll post it in my randomness experiments thread and try to make an experiment with it.

I also have to figure out how to listen to a French guy who talks about logic. Unfortunately mostly in French. I need to figure out how to define new Maid Library Sections in terms of SLAM too. Right now if I want a new kind of Maid Library Section I just extend an abstract Maid Book class in Java 16, make up a section name, and file all the books using the new class into it. /Sci/entists who like reading about code can see the engineering here:

>>14819291

[Anonymous No.14819510]

Serious question. Why does math attract so many schizo's such as >>14819406 ?

[Anonymous No.14819531]

>>14819510
That guy doesn't sound like a schizo. He sounds like a regular tisticfriend who's got nothing to talk about except for what he's learning and working on.

[Anonymous No.14819661]

>>14819510
>>14819531
Autistic people with hobby projects should be cherished, they are kind souls who work on interesting things even if they're a little weird. Most people here have a lil bit of 'tism anyways.

[Anonymous No.14819673]

>>14818758
Have you been dropped on the head not just thrice, but many times as a little babby? I clearly talk about READING proofs.

[Anonymous No.14820071]

>>14819406
>Do I want to add sets
start from the top and add categories

[Anonymous No.14820075]

>>14819406
the only sane thing to do is reject LEM, Powerset, full Separation and keep your theory consistent with all functions N->N being recursive, making N^N subcountable. Adopt dependent choice if you must, but keep in mind that if you don't, you can make the Dedekind reals countable in some weird ass topos and that's cool in itself. Induction for N suffices for math, take a look at SOL arithmetic.

[Doctor Eli Selig !!JQHA6kqyl91 No.14820266]

>>14820075
I don't know what most of these words mean fren, but I appreciate the enthusiasm.

[Anonymous No.14820274]

>>14812147
>not taking all three
Ngmi

[Anonymous No.14820279]

>>14812780
Why not a rapper?

[Doctor Eli Selig !!JQHA6kqyl91 No.14820290]

>>14820279
If you become a rapper, you can also be a programmer. Most rap songs are easy to convert to stack machines. Before I made SLAM I made a DJ Assault themed stack language as a tech demo. It has an ASS N' TITTIES based number system.

Attached is an image of an Assault "Hello World".

[Anonymous No.14820318]

>>14819132
>It's a second order arithmetic set existence claim of x
fine but X can just be Y^c

[Anonymous No.14820703]

>read later Heidegger
>read Klein's Greek Mathematical Thought
>read Lachterman's Ethics of Greek Geometry
>realize that the Greeks had no concept of space or extension, only of division (khora) and place (topos)
>realize that we put words into the mouth of people like Euclid (e.g. "Euclidean spaces")
>realize that Plato was the first postmodern philosopher through his worship of number
>realize that arithmetic is individualism and geometry is fascism and a big clash between Plato and Aristotle
>realize that Descartes's unholy union of analytical geometry turns people and the world into undifferentiated mass, waiting to be divided into plots and consumed for industrial forces
>realize that infinity is completely bullshit and Wildberger is right
I have no idea what to do with this information except silently weep. But I thought you guys would love it.

[Anonymous No.14820704]

How did any of you decide on a field of research for your PhD? How did you decide on an advisor?
I'm pretty well set up for applications, but I really don't care what school I go to, who my advisor is, or even what I research. I simply don't know enough to make that decision.
What is a field with tons of low hanging fruit so I can just get the PhD out of the way? PDE's? Differential Geometry? Stochastic calculus?

[Anonymous No.14820711]

>>14820703

[Anonymous No.14820741]

>>14820075
>reject LEM, Powerset, full Separation
>"reject all fun"
lmao no

[Anonymous No.14820824]

Sorry for elementary question, but /sqt/ is leaving me dry.

How did he get (3(pi))/4 ?
Shouldn't the answer be -1(pi)/4

[Anonymous No.14820845]

>>14820824
Tan(theta)=-1 implies a triangle whose side lengths are equal, with opposite signs. Try drawing the possible triangles on a unit circle

[Doctor Eli Selig !!JQHA6kqyl91 No.14820850]

>>14819406
Should I add trigonometry to SLAM? Does anyone like playing with trigonometry?

[Anonymous No.14820854]

>>14820845
Oh I speed read your post. Tangent function only has a period of pi instead of 2pi like most other trig functions so your 2 answers are equal

[Anonymous No.14820882]

Is there any 3D plotting software like maple, sagemath, octave, but that has an automatic symbolic conversion for inputs (like symbolab)?

[Anonymous No.14820903]

>>14820882
geobra is the only one I can find.

[Anonymous No.14821012]

>>14820854
Thank you for your time, fren. Now it makes sense.

[Anonymous No.14821028]

Hello everyone, algebra is my absolute weakest subject. Can someone please tell me how to solve for X in this equation? I don't need the answer fed to me, just the steps to get the answer myself:

.001 x ((5,000 x X) / 200) = 750

[Anonymous No.14821040]

>>14820266
I assume by SOL he means second order logic, and LEM is the law of excluded middle. Constructive mathematics does without the LEM I believe.

[Anonymous No.14821041]

>>14821028
Divide by .001, multiply by 200, divide by 5000.

[Anonymous No.14821099]

>>14821041
I'm assuming I'm starting with 750. In which case I ended up with 30,000. Maybe I read your instructions wrong, cuz the answer is supposed to be 12,500 according to the practice side of my course. I know the answer is supposed to be 12,500, but i don't know how to get there. :/

[Anonymous No.14821118]

>>14821099
you either read the problem wrong or the solution given to you is wrong, the answer indeed should be 30,000 try plugging that value in the equation and see if it works

[Anonymous No.14821271]

>professor set Linear algebra II exams on webassign
>its another semester of failing every exam when submitting answers, feeling like a worthless subhuman, and getting credit for answers in submitted written work later that gets me a B.

I hate this. Just because I'm taking the class online due to scheduling issues doesn't mean professors just have to give zero fucks. Isn't it actually even MORE work for them to grade things twice, as opposed to just using regular printed exam proctoring test? They have to grade it by hand anyways. Never met anyone that actually passed webassign exams.

[Anonymous No.14821296]

>>14820703
realize meds pls

[Anonymous No.14821315]

>>14820075
kek, you copypasted my post from /lit/ 10 days ago or so.
But yes, I stand by all of this

>>14820318
In the formula \mathcal X and \mathcal Y (and their compliments) are general classes/predicates, while x is a set (as per this axiom)

[Anonymous No.14821354]

>>14821271
>Never met anyone that actually passed webassign exams
My students who ACTUALLY PAY ATTENTION IN CLASS do.
The ones that don't, get zeros.

[Anonymous No.14821567]

>>14816125

[Anonymous No.14821573]

>>14821354
>>14821271
Just follow the definitons

[Anonymous No.14821640]

>>14821354
>web assign bank question on topic X
>question on topic X that requires 30 minutes of long algebra computation

Maybe you look at the webassign shit that you put up, but ever time I've had exams on this shit software, its always shit like this. On written exams I can usually take something like a massive quotient derivative and treat like like a variable, not solve it, and show the rest of the work for the actual math.
Best class I had was a discrete math class where I was able to go the entire course without computing anything, I would just put it parenthesis and move it around as needed;
>largest n for which one can solve within some time an algo that requires f(n) perations in 10^-20 seconds with funcs p, q, r
>func p is log_2 n, my answer is floor function of 2^(10^-20)(required time) etc etc

cant do that on webassign, as the autistic graders want you to waste time on busy work.

[Anonymous No.14821649]

>>14819027
I don't know how much of it is surprising but for one, I don't really get how it all fits together mechanically, how you can "use" a formula/axiom, or why you can go from the binary relation specifying a function to using that function to transform something.. I could say more of what I don't get but I don't know if it's necessary.

[Anonymous No.14821720]

>The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true ( https://en.wikipedia.org/wiki/Consistency#Definition))
Let's say you have a set of formulas S and it is semantically consistent, so there is an interpretation under which all of its formulas are simultaneously true. What happens if you add something that isn't a formula to that set? You still have an interpretation under which all of its formulas are simultaneously true, since what you added wasn't a formula. Can you still call this extended set consistent?

[Anonymous No.14821775]

>>14821720
isnt a theory supposed to be partly defined as being a set of just formulas

[Anonymous No.14821801]

>>14821775
I believe you are right

[Anonymous No.14821912]

>>14821720
I've never seen someone mixing objects when discussing a theory as a set of formulas.

In fact I've never seen anybody doing formal set theory when discussing theories like that either.
Unless you explicitly study the metatheory as well, the set theory in model theory is also broad and vague with little regard to size etc.
This is evidenced by the fact that famous common knowledge like

https://en.wikipedia.org/wiki/Lindenbaum%27s_lemma

casually uses choice to prove it

[Anonymous No.14822043]

>>14819116
is the nero worth it over the standard orenz .2mm?

[Anonymous No.14822053]

Is it possible that some open questions in mathematics unlock supernatural powers when solved? (not schizo larper just interesting to think about)
>>14813855
This is the easiest way to make sure you will never go anywhere in math
>>14815208
How many times are you going to post before you understand that no one gives a shit about your faggy vanity project also ywnbaw
>>14819661
No they should be imprisoned
>>14818164
I like the maruman spiral notebooks but these are good too though a little too small for me. orenz is great, love small diameter lead
>>14820703
Didn't larouche write about this
>>14820711
onions rotator
>>14812993
is there anyone good on math twitter btw

[Anonymous No.14822304]

>>14821315
>In the formula \mathcal X and \mathcal Y (and their compliments) are general classes/predicates
sure, that is the context was needed. weird thing about this theorem is one direction needs induction but the other one doesnt. like whats going on there what does that mean? idk

[Anonymous No.14822309]

>>14822043
Yes, I wouldn't use .2mm with anything other than the Nero. 0.2mm breaks so incredibly fast if you stick out anything but the most minuscule amount. As the nero is automatic, every time you pick up the pencil, it pushes the lead out a bit for you. With any regular 0.2mm mechanical pencil, you'd be clicking constantly to the point of unsuitability. I use the Orenz nero 0.2mm like a pen, I click one and start writing, never click again.
Also you should know that the only 0.2mm lead you are likely to find is pentel ain stein. I recommend the 2B, as its darker but not too soft.

[Anonymous No.14822316]

>>14822053
>This is the easiest way to make sure you will never go anywhere in math.

I don't need to get that far to be satisfied. Three of the springer TAM books are recommended as the definitive study texts for prelims at my school, and the rest are interesting or I expect to be of interest later. Rather get them now at my leisure while they're cheap.

>>14822053
>is there anyone good on math twitter btw
Twitter is designed to push you into making inane comments, and forcing you to posture and praise whatever political opinion is expected that day. A giant techno-political commissar. They don't delete your posts, that would be censorship. Instead, you are banned until you delete your own posts.

[Anonymous No.14822347]

>>14822316
>I don't need to get that far to be satisfied.
This made me sad
>Twitter is designed to push you into making inane comments, and forcing you to posture and praise whatever political opinion is expected that day. A giant techno-political commissar. They don't delete your posts, that would be censorship. Instead, you are banned until you delete your own posts.
did I ask for a muh free speech npc dialogue response?

[Anonymous No.14822357]

>>14822316
>Twitter is designed to push you into making inane comments, and forcing you to posture and praise whatever political opinion is expected that day.
I don’t think this was the goal at any point in the system’s design, but it seems to sum up the result. Social media should be banned under the Nuremberg codes unless some minimally damaging version can be identified and implemented - if I had to guess, just traditional smallish-scale forums and chatrooms with no “algorithm” to speak of
They don't delete your posts, that would be censorship. Instead, you are banned until you delete your own posts.
This part is in-your-face menacing lol

[Anonymous No.14822359]

>>14822316
>Twitter is designed to push you into making inane comments, and forcing you to posture and praise whatever political opinion is expected that day.
I don’t think this was the goal at any point in the system’s design, but it seems to sum up the result. Social media should be banned under the Nuremberg codes unless some minimally damaging version can be identified and implemented - if I had to guess, just traditional smallish-scale forums and chatrooms with no “algorithm” to speak of
>They don't delete your posts, that would be censorship. Instead, you are banned until you delete your own posts.
This part is in-your-face menacing lol
>>14822347
>tranny roid rage engages
go cry about it on twitter sir

[Anonymous No.14822705]

>>14807136
omicron (nice try distinguishing it from roman o)

[Anonymous No.14822714]

If 100g of bacon is 265 calories, and I've just put 64g into the pan, how many calories is that?

Thank you

[Anonymous No.14822719]

>>14810348
https://duckduckgo.com/?q=collections+of+math+formulas+in+LaTeX
gives
https://equplus.net/

[Anonymous No.14822720]

>>14822714
11, like your iq & age

[Doctor Eli Selig !!JQHA6kqyl91 No.14822721]

>>14822053
I'm going to post in every math general, post in my own threads, and occasionally post in /sqt/.

If you don't like it, just filter my trip? That's what it's turned on for. If you're reading my posts, you're the one who decided to do that, since they are all plainly marked.

If you don't filter me, then I hope you like maids, because you're gonna see a lot of them.

Anyways, I'm demoing some stack operators I made up in my thread if you wanna watch.

>>14812629

Current question is if I should make an abstract Exodia or not, and if I should make more operators.

[Anonymous No.14822723]

>>14822720
This is incorrect but thank you for trying

[Anonymous No.14822782]

>>14822714
This is how I solve these things mentally:
>64 is about 2/3
>265 is about 270
>so about 180, actually a little less
Then refine it a bit as necessary, e.g. to use 264 instead of 270 we subtract 4 from the answer

[Anonymous No.14822817]

>student comes to me
>says he didn't see the email announcement I sent (was for a quiz or something)
>turns out it's because he muted his email notifications, because some professor sends way too many announcements
So wtf does he want me to do? I did what's required of me. Am I supposed to come knocking on his house and notify his majesty personally? His problem is with that professor, so why bitch to me? What does he even expect from me?

I hate having to deal with stupid people.

[Anonymous No.14822833]

>>14821649
any answer to this? the concept of a group makes more sense. but even then, i don't have a sturdy idea of what "concept" would mean there

[Anonymous No.14822845]

>>14822817
Tell him to filter his other professor's announcements as spam. Either that, or inform students about quizzes at least one class before.

[Anonymous No.14822899]

>>14822782
thank you very much

[Anonymous No.14823021]

>Just finished the semester.

[Anonymous No.14823047]

>>14822817
>email announcement
depends what the consequences were desu

if he literally missed a final exam getting 0/100 consider something merciful

if he says he just showed up and got a low stakes unexpected quiz, then I wouldnt worry too much, absent powerful confounding factors

[Anonymous No.14823062]

>>14822817
Grades in university are very high stakes.
What if a credit lender sent you a notice by email but you didn't check, because you get so much spam, is it their fault that your credit score tanked and now you owe more in late fees? After all, you were notified. Are they supposed to come to your house and notify your majesty personally?

[Anonymous No.14823072]

>>14821649
An important piece of context here is that a “relation” here just means a set, and that “binary” here applies only to functions of the form f(x)=y. For functions like x+y=z, you would use a ternary relation that contains ordered triples such as
>(1,7,8)
>(15,16,31)
>(8,-1,7)
>(7,0,7)
representing (x,y,z) respectively.

[Anonymous No.14823081]

>>14822833
Your lost In the sauce. There math came before the axiomatic system, you should lessen more math before you start trying to build it from the ground up. You need to motivate your concepts

[Anonymous No.14823104]

>>14823062
>>14823047
>>14822845
I don't remember what it was, this was a while ago, but it was probably a quiz, since that's just about the only thing I send announcements for.
There's a quiz every two weeks, and I announce the material covered a week ahead (not that they need an announcement for that; it's just whatever we covered and haven't had a quiz for).
They know we have a quiz every two weeks because I told them that in the beginning of the semester. And I remind them in class the week before a quiz.
The quizzes are open book, and require programming. They don't take more than 3 minutes if they know what they're doing, and we give them 10 minutes. We have our own manual where every topic is like 3-4 pages long (2-3 topics per quiz). Yet still most get zeros.

One time a student asked me how to do a certain thing (like rounding a number or something) WHILE HE HAD THE PAGE FOR THAT COMMAND OPEN IN THE MANUAL.
Like holy shit just fucking read. Ctrl+F if you have to.
One guy didn't know how to copy so I had to show him how to Ctrl+C/V.
One guy came to the quiz and didn't know which program we're using.

Teenagers are fucking stupid.

[Anonymous No.14823111]

>>14823104
Oh, well now that you elaborated, I think you're in the right. Is this a high school class? Doesn't seem like you can make it any simpler.
Concerning the CTRL+F /C/V issue, you should see if a short course on computer basics could be introduced. Frightening how poorly students work computers these days compared to when we were young in the late 90s and early 2000s. I know its a requirement for anyone that wishes to enroll in online courses where I teach(community college), to prevent issues like that.

[Anonymous No.14823113]

>>14823111
University.
And they do take a computer basics course.

[Anonymous No.14823124]

>>14823072
i see how you could specify n-ary functions using this, but how do you "use" the functions or axioms; when can they be used for what in a "system"

[Anonymous No.14823189]

>>14823124
Here's one way: take the intuitive definitions of injective, surjective and bijective, and prove that being both injective and surjective is logically equivalent to being bijective. Is this the kind of 'use' you are looking for, and do you feel the formal system is still insufficient to prove this?

[Anonymous No.14823200]

>>14823124
>how do you "use" the functions or axioms; when can they be used for what in a "system"
These equivalences are pretty flexible in that they work in a lot of systems. But there are also systems where the two notions (functions that transform x to y, and sets of tuples satisfying the vertical line test) are not quite equivalent. But usually there is no deep philosophical reasoning behind it: you kinda accept the equivalence, and use the characterization that is easier to write down. When you study real analysis you will encounter this kind of decision a lot.

But if you REALLY need an axiomatic system to anchor this, try to formulate a function in ZFC set theory. Since everything has to be a set, you actually have no choice but to express your functions in terms of sets; and this is, as far as we know, the least crazy way of doing that.

[Anonymous No.14823213]

>>14823021
season 3 when

[Anonymous No.14823238]

Here's a question:

Suppose you made a perfectly symmetrical coin. Not loaded, and perfectly fair.
Flipping it gives only two outcomes with equal probability: Heads or tails. Nothing out of the ordinary.

Now suppose you flip it 5 times and you get all tails. That's valid. Each flip has the possibility to give tails.
You flip it 10 more times and it's all tails. Still valid, but now you're getting suspicious. Flip it 100 more times and still all tails.

Math tells you that it's possible. It even tells you that every finite sequence of heads/tails will eventually show up, so it's valid that every flip so far gave you tails. But at the same time, every fiber of your being tells you this is not right.
You flip it a million more times and still all tails.

Sure, the probability of getting a million tails in a row is nearly zero, but every other sequence of a million flips, no matter how much "more random" it looks, has the exact same probability (assuming it's a fair coin).

So what are the actual odds of heads and tails for this coin?

[Anonymous No.14823279]

How do you prime-check a number greater than 15k digits long? I've got two machines running Miller Rabin. I'm guessing a million digit long number would take months at this rate.
I have three numbers already rejected, but this one is taking a long time.

[Anonymous No.14823325]

>>14823279
First you need to find the function that defines all primes. The rest is easy.

[Anonymous No.14823340]

>>14823325
I sorta have. That's what I'm trying to prove with an informationless proof.
I can generate new primes using primes.
Small primes are easy. 11 and 103 generate a lot together for example.

[Anonymous No.14823362]

>>14823340
not possible, because I've found a nontrivial zero of the zeta function off of the 1/2 line

[Anonymous No.14823370]

>>14822719
>https://equplus.net/
thank you bro

[Anonymous No.14823373]

>>14823362
lol
Seriously though. What's an informationless proof for my claim? There should be one as there is an informationless proof for everything mathematical.

[Anonymous No.14823405]

>>14822714
what she on?

>>14822304
Not sure what you mean by the induction comment.
>weird thing about this theorem
It's an axiom.

>like whats going on there what does that mean? idk
It says that if you got two classes (A,B) which are apart from each other, then there exists as set (X) that contains the one class (A) but doesn't intersect with the other (B).
I drew ya a Venn diagram type pic.
Of course it's not an interesting postulate if you got some theory with the full separaiton axiom, since then a subclass A of N is of course a set already

[Anonymous No.14823483]

>>14823373
what is your claim

[Doctor Eli Selig !!JQHA6kqyl91 No.14823486]

>>14823279
Is this a task math /sci/entists frequently do? Find a big prime with their computers? Is it fun?

I know what primes are, but I don't know what a Miller Rabin is. Why do you want a 15k+ digit long prime number?

[Anonymous No.14823511]

It's been nearly a decade since I took a course in linear algebra or statistic, and this is making me feel like a brainlet.
I'm getting tempted to just install something like python and brute-force it.

[Anonymous No.14823515]

It's been nearly a decade since I took a course in linear algebra or statistics, and this is making me feel like a brainlet.
I'm getting tempted to just install something like python and write a program to brute-force it.

[Anonymous No.14823663]

If [math]P[/math] is the matrix in your pic with the last column changes as written next to it then the expected hitting times are the minimal positive solution [math]x[/math] of the system

[eqn]x(I - P) = (1,1,1,1,1,1,1,1,0)[/eqn]
Most imporantly the first entry of the vector [math]x[/math] is what you're looking for.

[Anonymous No.14823676]

>>14823483
That I can make bigger primes using primes.
It's okay though, I think I figured it out.
>>14823486
>Is this a task math /sci/entists frequently do? Find a big prime with their computers? Is it fun?
Is fun the right word? It's satisfying in an odd way.
>I know what primes are, but I don't know what a Miller Rabin is. Why do you want a 15k+ digit long prime number?
Miller Rabin is a test to see if a number is composite or not. That is to say, whether or not it has prime factors other than itself and 1. It doesn't directly test for primes, but if you do it with enough repetitions that don't say the number is composite, you can assure yourself that the number tested is probably prime.
It's something computers can do fairly easily as it's mod with bonkers long powers. But once you get into the thousand of digits range it's slow. Unless you have a bank of crypto mining computers and even then it's probably slow.

[Anonymous No.14823798]

>one year of continuous undergrad math
>suddenly, can read and visualize textbooks at a steady pace vice constant stopping and head scratching

Is this what mathematical maturity means? I'm at the point where I enjoy reading the books more than watching lectures.

[Anonymous No.14823807]

>>14823676
I can make a prime using primes. [math]2^n-1[/math]

[Anonymous No.14823875]

>6 weeks till stokes theorem and final exam

[Anonymous No.14823954]

>>14823515
let Q be your matrix with the last row and column both removed. Find [math](I-Q)^-1[/math] and the sum of the first column should be your answer

[Anonymous No.14823994]

>>14823515
You're looking for the term "Markov Chains"

[Anonymous No.14824012]

>>14823954
Thank you!
I'm getting 390, which is higher than I expected, but that seems like a realistic number, and I am a brainlet.

[Anonymous No.14824134]

>>14823405
>Not sure what you mean by the induction comment.
to proof wkl from pi1 reduction requires use of induction, but the other direction does not

[Anonymous No.14824240]

Bump >>14823238

[Anonymous No.14824257]

>>14823238
In that system it would still be 50% because you defined it as that. But one model that could be more like how you would look at it in real life would be using Bayesian statistics. I don't know the specifics but you could start with a 1% chance (prior) it's rigged but if you get outcomes that are more of one side than the other then it could increase your chance it's rigged. Also you may want to use /sqt/

[Anonymous No.14824577]

>>14823807
I like 5x^2 + 5x + 1.

[Anonymous No.14824583]

>>14806986
Numbers are the work of the devil. I do not believe in them.

[Anonymous No.14824912]

Why do cute girls never do math?

[Anonymous No.14824940]

Fun problem I got asked once in undergrad for you, /mg/.

Is it possible to rig a pair of dice in order that when rolling both of them and taking the sum, one gets results from 2 to 12 with uniform probabilities?

Precisions: We assume that you are able to produce any random variable with values in {1;2;3;4;5;6}. This is what we call a die. Can you produce two such variables X and Y, such that the random variable X+Y is uniform in [[2;12]]. ?

[Anonymous No.14825148]

>>14824912
https://www.youtube.com/watch?v=7DHE8RnsCQ8

[Anonymous No.14825210]

>>14824940
No.

I've seen something similar to this, where we use unique factorization of polynomials in R[x] to find a different set of die that have the same distribution for X+Y as two regular die.

Anyways, the solution goes like this: Define the ordinary generating functions for the distributions of both X and Y. These are polynomials p(x) and q(x), where each one's coefficients are the probabilities of X and Y, respectively (so the coefficient of x^n in p(x) is the probability of rolling n with X). Clearly there is no x^0 term in both, so both are divisible by the polynomial x.
To get the generating function for X+Y, it is just p(x)q(x). (if the reader is unsure of this, multiply them through to see that they indeed give the desired result)

So to have this polynomial give a uniform distribution, we need p(x)q(x) = (x^2+x^3+...+x^12)/11.
Equivalently, 11(p(x)/x)(q(x)/x) = (1+x+x^2+...+x^10), where p(x)/x and q(x)/x are still polynomials.
(1+x+x^2+...+x^10) has no real solutions (only complex roots of unity), so it can only be factored into a product of five degree 2 polynomials. So to find p(x)/x and q(x)/x, we need to distribute these factors between the two. (using unique factorization here)

But here's the issue: p(x)/x and q(x)/x are degree 5 polynomials. So there's no way to multiply a bunch of degree 2 polynomials to get a degree 5. So it is impossible to find such die.

[Anonymous No.14825225]

I have a question about probability theory / statistics. It's pretty basic but I haven't worked with these ideas for fucking years.

I have some random variable [math]X[/math] that depends on another one, [math]Y[/math]. [math]Y[/math] takes only 3 possible values but [math]X[/math] takes more. I then know the value of the following: for a fixed [math]Y = y_i[/math] where [math]i \in \{1,2,3\}[/math], and given that [math]X[/math] is one of [math]x_1, x_2, x_3[/math], what is the probability that [math]X = x_i[/math]? What I mean specifically is this:
[math]\frac{P(X = x_i | Y = y_i)}{P(X = x_1 | Y = y_i) + P(X = x_2 | Y = y_i) + P(X = x_3 | Y = y_i)}[/math]
This value is known for the problem I have.

What I want to know is: how do I average this expression over [math]Y[/math]? If I just take an expectation value as normal, I get something like
[eqn]\sum_{i=1}^3 P(Y = y_i) \frac{P(X = x_i | Y = y_i)}{P(X = x_1 | Y = y_i) + P(X = x_2 | Y = y_i) + P(X = x_3 | Y = y_i)}[/eqn]
but I feel uneasy about this because we have [math]y_i[/math] in both the numerator and denominator.
Would it make more sense to do something like
[eqn] \frac{\sum_{i=1}^3 P(Y = y_i) P(X = x_i | Y = y_i)}{\sum_{i=1}^3 P(Y = y_i) \left[ P(X = x_1 | Y = y_i) + P(X = x_2 | Y = y_i) + P(X = x_3 | Y = y_i) \right]}[/eqn]
? Does either of these "averages" even make sense?

[Anonymous No.14825328]

>>14825210
Nice

[Anonymous No.14825508]

New thread
>>14825203
>>14825203
>>14825203