/sci/ - Science & Math

Früher: >>12668218

First for having your paper accepted into PRB

I hate life.

Prove this theorem:
anime=peedophilia

>>12692234
I figured out an equation to predict the possible sets and number of combinations but im tired Gn

>>12692672
REEEEEEEEEEEEEEEEEEEEEEEEEEE POST IT NIGGER

>>12692512
Are you sure? Maybe you just hate your current life. You could live diffrently, yknow

>>12692544
Neoteny but is only statistic also asians are more neotenous in general group minus 1

>>12692234
so now that we can reognize the unknot in polynomial time, does this mean that it is possible to build quantum supercomputers that would break blockchain encryption?

>>12692700
>reognize the unknot in polynomial time
What does this mean?

>>12692234
I like this proof

>>12692995
Definitions for the uninitiated

>>12693003
Heh antichain made me giggle

>>12692995
I dont understand this. It semes like k nmink and then meta subtracted, but idk how the first equation was gotten

>>12692234
>>12692995
based combinatorics

Using bayesian statistics, if youre drawing balls out of a bag, is the first ball you draw more likely to be more common? This could support the anthropic principle if true

>>12693192
This is like asking if the fact that I rolled a 6 on a die suggests its weighted towards rolling a 6. The answer depends entirely on the underlying probability of the die being weighted: if you saw your friend shaving off part of it, it's very likely. If you just did a 3d scan of it and the density is uniform and it's within a nanometer of a perfect cube, then it's very unlikely.

>>12693205
But if you have 2 worlds, one where a bag has 8 red 2 blue, one is 5 5. And in each world, a series of beings select a ball. In the 82 world, select a red, meaning red on the first try is more common. And cant bayesion inverse that to say more reds means red is more likely

>>12693229
Even in your example it's not so clear. What's the probability I'm in the 82 world vs the 55 world? If it's 50/50 then drawing a red on the first draw makes it more likely we're in the 82 world; if it's 1/99, drawing a red changes the likelihoods, but much less; but if it's 0/100 then drawing a red changes nothing. We can make no meaningful statements about the likelihood of being in either world without knowledge of the underlying distribution. The question you originally asked is
>Using bayesian statistics, if youre drawing balls out of a bag, is the first ball you draw more likely to be more common
This question is so broad it means close to nothing, especially in the context of the laws of physics and the reliability of human observation. In that context, the bag can be any size, the colors may be discreet or continuous, and there's no obvious probability distribution for which world we're in. We have, and it's probably impossible TO have, any knowledge of the underlying distribution.

Imagine you're a doctor and your patient has just tested positive for HIV. Even if I tell you that 5% of the time the machine outputs a false positive when it should have outputted a negative, this gives you *no information about whether this particular patient has HIV* because *you don't know the underlying distribution.* If I were to tell you that this patient has just had a 50-person all-HIV positive unprotected gangbang, then the chance she has it is waaay more than what Bays Theorem would tell you, and if I tell you she's a virgin and her parents don't have HIV then the chance is waaay less than what Bays would tell you. The probability she actually has HIV is independent of my observation; unless I know the probability she actually has HIV, my observation give me no real information.

how many possible permutations of /mg/ are there

>>12692386
>first
>third post in the thread
>posted fifty minutes after the second post

>>12693251
Just use the bag of marbles as a model. Im imagining it like one universe out of a set of unknown size, a bag with unknown marbles but maybe some hidden ratio.

>If it's 50/50 then drawing a red on the first draw makes it more likely we're in the 82 world
Why is this bad? If you see a bird first, you might first assume youre in a bird filled region, then update with more data

>>12693254
That function contains the syntax of english and german as a variable

>>12692234
I liked the cat edition a lot... this is lamer!

>>12693316
What's the character limit on posts

>>12692234
How many possible ways are there to arrange 5 men and 5 women in an orgy?

>>12693674
hmm.. what do you mean by arrange?
choosing heterosexual pairs is easy, but if we are taking arbitrary choices of positions with arbitrary people involved in each, the possibilities could be larger than omega.

>>12693693
>Using an ordinal infinity as a cardinality
Graduate high school and then come back here.

>>12693702
there's nothing wrong about using an ordinal in this context

why the fuck are epsilon delta proofs so difficult for my brain to comprehend? even the simplest ones, like showing that if a sequence converges it has only one limit, the moment i see an epsilon my brain fucking turns off immediately. i guess it has to be low iq? my first *online* iq test many years ago when i was 16 i got 133 and ive gotten that on every single online test ive ever taken since with startling precision

>>12693735
yeah it's normal. You really have to understand what the epsilon does and the delta does. On what they influence, ie either on the x antecedent or the f[x] ie the image.

you also have to pay attention to the quantifiers

no shit G = G. what kind of dumb question is this

>>12693735
>online test
I’m sorry to inform you that your IQ is too low for maths. Save yourself the trouble and give up now.

>>12693735
Read
https://mathoverflow.net/a/88599

Tim Gowers daughter came out as a lesbian and hes celebrating it on twitter lol

>>12693762
god he's such a cuck

>>12693791
Honestly I think caring about the reproductive future of the human race or any subset of it larger than a few people is the cuck position at this point. We aren't the future, either robots are or a charred planet of burning ash is.
So shut up and go back to enjoying math in the present.

>>12693674
each woman has 3 holes and 2 hands. each man has 1 dick. so that's 25 dick stations. so it's how many ways can you distribute 5 cocks on 25 dick stations, counting order. Ie it matters if tom is in saras pussy or if luke is. so that's p(25, 5) = 6 375 600. I think.

>>12693762
don't look up to mathematicians as role models on anything but mathematics... and get off twitar in any case

>>12693737
got et thank you

>>12693742
this might be true i am considering this but not without trying some more. i mention online iq not to smugly dab on anyone, but just to signify that perhaps i am not completely brain-dead since i predicted a response like yours and was hoping there would be some sort of explanation that wasn't just "you're dumb as fuck bro" but perhaps that's the case yeah

>>12693745
thank ya kindly that was a mind expanding read

>>12693836
men can fuck other men and you can put hands into anus/vagina

>>12693847
that's degenerate.

>>12692234
>tfw trying to count the number of partial orders on a 20-element set

>>12693857
not easy to count
https://oeis.org/A001035

Phi (and maybe all [math]\mathbb{Z} \pm [/math]phi) is the most irrational number based on a system for ranking irrational numbers based on how hard it is to approximate them with fractions.
Sure, I followed the proof, it makes sense.
Are there any real world applications of a ratio being difficult to approximate? Is phi used in noise cancelling headphones or something? Or is it interesting but useless?

>>12692234
Why is this picture not beautiful? Or am I not able to see the regularity.
The first column is fine but the rest has no simple system.

There are quadratic, cubic, quintic reciprocity laws etc. for all prime powers. Are there reciprocity laws for all positive integer powers?

>>12693314
Okay, here it is with the bag of marbles: The "hidden ratio" you're talking about is the probability distribution of the contents of the bag. If either the number of colors a ball can be is unbounded, or the size of the bag is unbounded, this isn't really a "ratio" anymore: it's a probability density function (call it f) on a domain of countable size. We have no information about this f. It may be constant; It may be the Dirac delta function; It may be very erratic. There are many f's such that drawing a red gives us no new information: for instance it may be that f is zero for all bags with more than one red. And the probability distribution for f (that is, which f is true) IS the Dirac Delta. Only one f actually describes the bag; they are not all equally likely.

We can try to smooth this out with arbitrary constraints, but, to be clear, this is answering a different question: all Multi's hypothetical says is you draw a red ball out of a bag. Let's say that balls can be one of a finite number of colors that we know, and the size of the bag is known. Now f contains finite elements since there are finitely many possible bags, but that still says nothing about the nature of f. f still may be 1 at one value and 0 everywhere else, for example. Drawing a red tells us nothing unless we know more about f; it's not as though those f's from which we derive information are more likely than those from which we couldn't--since with some f's it would give us information and with some f's it wouldn't we can't derive any information with certainty.

>>12694524
We can impose the additional constraint that f must be >0 for all possible bags. Now, drawing a red does make it more likely that there are more reds in the bag, but there's no way of knowing how much more likely without knowing more about f. But this isn't the question Multi asked. His question is more like if a friend gave you a bag with a bunch of fruits and you draw a tomato, and asking about if it's likely for there to be more tomatoes in there. Maybe your friend hates tomatoes and put it in there as a consolation; maybe he loves them and it's chalk full of them; maybe he randomized them. It's impossible to know what the tomato tells us without more information about the friend.

>If you see a bird first, you might first assume youre in a bird filled region, then update with more data
If you flip a coin and get heads, you might assume the coin is weighted towards heads, then update with more data. But this assumption is unfounded because you don't know the underlying chance of the coin being weighted, and in which direction.

>>12693481
2000

Combinatorics is gay

>>12692995
oh, a combinatorics theorem? this kills the category theorist trannies

>>12694654
if you want to kill a category tranny... just ask him to solve a pde

>>12694654
nah, I think category theorists, algebraists, and combinatorialists are all friends at the end of the day, because of two core reasons:
1) they understand the importance of the aesthetics of terseness in their work. Combinatorialists in particular regularly present highly nontrivial ideas using only elementary structure.
2) reserve a certain hatred for analysis.

>>12694804
>category theorists
>terseness
My confusion is immeasurable.

Gotta say, I'm really enjoying the Viro elementary Topology book

If [math]T:X\to Y[/math] is a bounded linear map, then I get a unique linear map [math] S: X/N(T) \to Y[/math] where [math] N(T) = \{x: Tx = 0\}[/math] such that [math] T=S\circ \pi[/math]. I want to show [math] \|T\| = \|S\|[/math]. I have the inequality [math] \|T\|\leq \|S\| [/math] but I'm stuck on the other inequality [math] \|S\|\leq \|T\|[/math]. I know, by defn of infimum, that [math] \inf\{C: \|S(x+N(T))\| \leq C\|x+N(T)\|\} = \inf \{C: \|T(x)\| \leq C\|x+N(T)\|\}[/math] but I don't see how that implies it's [math] \leq \{C: \|T(x)\| \leq C\|x\|[/math]. What am I missing here?

>>12695001
For an arbitrary normed vector space [math]X[/math], we call the open unit ball centered around 0 [math]B_X[/math].
Then, as you'd remember, [math]||T||[/math] is the supremum of the norm function on the set [math]T(B)[/math].
Notice how [math]\pi (B_X) = B_{X / N(T)}[/math], hence [math]T(B_X) = S \circ \pi (B_X) = S(B_{X/N(T)})[/math].

uncountably many disjoint open balls in a finite interval of R with the usual topology

>>12693735
Yes they're hard at first.
The trick most of the time is to use triangle inequality. Most of the time you add and subtract a new term to get the triangle inequality e.g. |x-y| = |x -a +a - y| <= |x-a| + |y-a|
Also, you usually Impose a value on δ at the end, after deriving inequalities.

>>12694537
>Now, drawing a red does make it more likely that there are more reds in the bag, but there's no way of knowing how much more likely without knowing more about f
All possible F, so it supports anthropic?

>>12695095
What about closed balls?

>>12695206
what about them

>>12695095
uncountably based

>>12695204
No, because the part of my post you quote only holds if the two conditions I specified hold: the bag is a known size, there are finitely many colors, and the chance of any given bag occurring is >0. In the case of the multiverse, (a) the "bag" is an unknown, variable, and possibly infinite size, (b) the cardinality of the set of possible "colors" (values) a "ball" (universal constant/law) could be has the cardinality of the continuum, and (c) it's not at all obvious that all "bags" have a nonzero chance of occurring. I think in your head either all "bags" are equally likely to occur or you think each ball is a discrete random variable w/ a uniform distribution. Neither of those are necessarily true.

I don't know how else to get this across to you. Without any information about the underlying distribution of the possible bags, the first draw gives no useable information about the contents of the bag because there's nothing for the new information to modify. If I give you a bag and tell you it's 50/50 2 reds or 2 blues and you pull out a red ball, the only reason you gain information is because I already told you the distribution of the bags. If I give you a bag and you don't know how many balls are in it or how I'm picking the colors or even if I'm using a finite number of colors and you draw a red, it tells you nothing.
>but anon i drew red so more red probably in there!
Except unbeknownst to you I actually filled the bag with one red ball and 99 dildos.

>>12695301
What if the realm of possibility isnt continuum, what if its finite esque

Constructio ad absurdum

>>12695095
To be more specific, you need it to be an interval with two distinct points, for otherwise you could choose it to be a singleton. Then you have what you want.

>>12695314
dude, if you're going to tripfag you can't out yourself as a retard like this. if this whole thing has been bait it's perfect but otherwise i've tried every analogy possible to get you to understand the math of what you're describing. reread my posts, slowly.
>Without any information about the underlying distribution of the possible bags, the first draw gives no useable information about the contents of the bag because there's nothing for the new information to modify.

>>12695356
i dont remember asking

>>12694804
>reserve a certain hatred for analysis
>what is enumerative combinatorics

>>12694804
>reserve a certain hatred for analysis.
Lame.
Most geometers are the ones who deserve hatred, but it seems to me that combinatorialists just don't care about geometry in general.

>>12695875
>combinatorialists just don't care about metric geometry in general.
ftfy

>>12692234
I'm currently taking a highschool calculus class but I'm curious. Are there any other areas of math I can study alongside this? It does not necessarily have to be related to calculus.

>>12696760
You might be interested in a book on 'Discrete Mathematics.' The topics they tend to cover are very broad: from graph theory to combinatorics to first order logic, but many of them don't require advanced (or sometimes any) calculus and cover many important topics in first-semester undergrad depth--it'll give you a good sampling of many fields and you'll be able to feel what resonates with you. The textbook the discrete math class I took in high school used was pic related. No idea if it's considered terrible but I found it highly adequate.

You could also take a course (or buy a book, or follow an OpenCourseWare thing, or watch 3B1B's series on YT, &c) on 'Linear Algebra'; it won't require calculus either but it's an important subject for various reasons, and it's good to learn because it'll acquaint you with concepts like vector spaces and group axioms.

Sorry for the perhaps basic question but is 3^2x = e^ln(3)2x? It seems correct to me but apparently something else is wanted, where the initial function is rewritten to be just ^x without the 2 there. How do I do that?

>>12693738

E and F are both subsets of G.

Professor claims that if I have a quadratic form [math] d : A \longrightarrow \mathbb{R}[/math] (meaning symmetric, and s.t. [math](a, b)\longmapsto d(a,b)-d(a)-d(b)[/math] is bilinear) that is positive definite, then the map given by halving that bilinear map gives an inner product that satisfies Cauchy-Schwarz inequality.
I've seen this in the context of linear algebra, but here [math]A[/math] is not a real vector space. I know how to prove the inequality if the image of [math]d[/math] is contained in [math]\mathbb{Z}[/math], but that doesn't need to be the case.
So I used tensor products to extended the inner product to [math]\langle \cdot, \cdot \rangle_2 : (A\otimes_{\mathbb{Z}} \mathbb{R})^2 \longrightarrow \mathbb{R}[/math] satisfying [math]\langle a\otimes x, b\otimes y\rangle_2 = xy \langle a, b\rangle[/math]. Since [math]A\otimes_\mathbb{Z} \mathbb{R}[/math] is a real vector space by extension of scalars, I have C-S for this inner product and then taking [math]x=y=1[/math] on that identity I get C-S for the original inner product.

Is there an easier or more elementary way to do this?

>>12696855
are you retarded?
go to >>12677060

note [math] 3^{(2x)}=9^x[/math]

>>12696988
Doesn't showing that d/2 is an inner product imply Cauchy - Schwarz?

>>12697084
I think you referred to the inner product I mentioned, which is [math](a, b)\longmapsto \frac{1}{2}( d(a+b)-d(a)-d(b))[/math]. (I typed [math]d(a, b)[/math] by mistake)
This is an inner product seeing [math]A[/math] as a [math]\mathbb{Z}[/math]-module, scalars being integers. I don't know if there is a standard proof of Cauchy-Schwarz in this case, the usual ones fail because we cannot say things like [math]d(b) a\in A[/math] for [math]a, b\in A[/math]. So I did like I explained.

>>12695095
Not possible

Did you guys ever experienced a teacher pushing into certain path/branch?
Like a teacher telling you to work on certain subjects with him or asking you to work/attend certain seminars.
Dunno if I could make my point clear.

Are there any interesting irrational approximations of [math]\pi[/math]?

>>12692234
How to find good *introductory* books on various topics in math?
Looking for textbooks on Probability, Statistics, ODEs, PDEs, and Complex Analysis.
And by introductory, I mean not choke-full of autism-tier formalism.

>>12696988
Managed to get a more elementary & analytic approach:
It is enough to show that [math] f : t\longmapsto \langle a, a\rangle + 2 \langle a, b \rangle t + \langle b, b\rangle t^2 [/math] is nonnegative on any real number. We know it is on integers, and by density it suffices to show it is on rationals.
Let [math]m, n \in \mathbb{Z}[/math] with [math]n > 0[/math], then
[math]n^2 f(m/n) = \langle na+mb, na+mb\rangle \ge 0[/math], so we're done.

>>12697837
Ramanujan gave a false algebraic value for pi which is pretty accurate.

>>12697697
prove it without a contradiction argument

Kind of a retarded question but is there a number with no digits?

>>12698170
yes, its

Yes, infinity is a number represented by a symbol, not a digit.

>>12698225
>infinity is a number
???

>>12693839
Except Uncle Ted
He's my hero

>>12698225
Infinity Is a Dangerous Thing for a Grad Student Like Me to Have – but I Have It

>>12695380
>Without any information about the underlying distribution of the possible bags
Right and Im just positing that what if we do have usble information, what if we somehow know that the realm of possible universes is either finite or countable, such as by plank distance

>>12698477
Is this a death grips reference

>>12693839
>twitar
Based spelling reminds me of Dune

>>12698252
>>12698225
https://www.youtube.com/watch?v=kq5l0MT_Ivg

Infinitz is a place u will wait for the reast f zour life
Drunk srzy

I'm learning about polynomial division in self-study. How do I choose a divisor to have a remainder of zero? Google isnt helping

>>12698584
Find two that multiply into the target

>>12698584
do you mean factorising?
find a value or two that give the polynomial a value of 0

>>12692234
retard here
how do i read this expression: I(ν, T)dν
and how do i read the "dν" in the following excerpt: "in the frequency range between ν and ν + dν"
context: https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#Derivation_from_Planck's_law

How can I document, or otherwise legitimize, my personal studies?
I'm doing real analysis now.

>>12699670
Type up your solutions to exercises in LaTeX.

>>12699670
To add proof for a resume? Take open certified exams

>>12699670
your picture is very cute

How's this for a proof of the Archimedean principle?

We only need to prove this for positive numbers. Assume that there's some number [math]x[/math] with [math]|x| < \frac{1}{n}, \forall n \in N[/math]. This gives us:
[eqn]
|x| < 1/n\\
\rightarrow x < 1/n\\
\rightarrow x - 1/n < 0\\
\rightarrow |x - 1/n| < 0, \forall n \in N
[/eqn]

And [math] x = 0 [\math].

Did I violate any real analysis principles here?

https://www.pagat.com/domino/math.html
>The number of tiles in a set of [n-n] dominoes is given by the formula ((n2+ 3n + 2)/ 2). For example the number tiles in a [18-18] set is (18*18 + 3*18 + 2)/2 = 190.
Where does this formula come from? I thought that it comes from ((n+1)^2+(n+1))/2 because a [n-n] has n+1 different numbers but I have no idea why +(n+1) or /2.

Just got a banned IP from my mobile carrier. Scawy.
Anyways, thinking of going deeper into diff eq and dynamical systems.

>>12692386
>PRB
published there as an undergrad.
try pnas small fry

>>12699754
last inequality may be wrong

>>12699754
>>12700391
last inequality is definitely wrong.

-2 < 0
but |-2| > 0

>>12700391
>>12700675
1/n has to be positive, so youre always removing more than x

>>12700911
Nevermind Im retarded

So if arithmetic isn't a decidable theory, then how come "natural numbers with addition but no multiplication" is? when you can just unavoidably define multiplication in terms of addition.

What is the most important negative mathematical constant?

>>12701032
your life lmao

>namefag cant even into directed numbers
top wew

>>12701103
Im running an unusual algorithm, just bear with me

>>12692700
wait, we can? sauce?

>>12701032
-1

>>12700943
Wot

>>12698129
trivial, take a rational from every open interval, thus we get an injective function into the naturals.

alri lads, what prerequisites do I need to study moonshine theory and vertex algebras?
Group theory, representation theory, complex functions, galois theory?

>>12701236
Bzzt, that needs choice and choice implies third removed, try again.

>>12701415
So? nobody other than set theorists and logicians gives a fuck about any system besides ZFC. Analysis doesn't even work without choice.

>>12701437
>Analysis doesn't even work without choice.
it does if you don't use "real" "numbers".

Hey anons, I got to do this for my homework, do you have any insights ?

this nigga deadass just took a screenshot of wikipedia baka

>>12701447
original meme bro lol out loud
but seriously, choice is assumed always, end of story

>>12701415
you got what you asked for, seethe more

>>12699980
>PNAS

>>12693702
Actual infinity doesn't exist, anyway

>>12693735
>why the fuck are epsilon delta proofs so difficult for my brain to comprehend?
Because it is fake judeo-math.
Your brain is telling you that Analysis is trash. It is functioning correctly.

roll 2 dice
find P( at least 1 die lands on 6 | dice show different #'s )

if first dice is 1 , P = 1/5
if first dice is 2 , P = 1/5
if first dice is 3 , P = 1/5
if first dice is 4 , P = 1/5
if first dice is 5 , P = 1/5
if first dice is 6 , P = 1

thus P = 5( 1/6 * 1/5 ) + 1/6 = 1/3
P( at least 1 die lands on 6 | dice show different #'s ) = 1/3 .

>>12701615
OR ,

P( at least 1 die lands on 6 | dice show different #'s )
= P ( at least 1 die lands on 6 AND dice show different #'s ) / P ( dice show different #'s )
= ( 10/36 ) / ( 30/36 ) = 1/3 .

>>12699660
>"dν"
deevee

I'm trying to figure out a lower bound on the permutations of a matrix: i.e the of the number of ways you can arrange elements in all matrix diagonals. The permutations will always be the product of each diagonal's permutations (i.e for a 2x2, we have 1! * 2! * 1!, a 3x3 we have 1! * 2! * 3! * 2! * 1!). I know it's bounded by some n^(an) but I don't know how to prove it.

>>12701870
well even n! is bounded below by n^(n/2) or something

>>12702009
yeah but it's sqrt(n) at the longest diagonal, n is number of elements in the matrix

>>12701032
-1/12 (sum of all natural numbers)

Took my first probability exam, couldn't answer a single question in its entirety. He curves, but I feel retarded. Any ideas I had in my head about how to solve the problem, I couldn't get to work because of some combinatorics issue or some other stupid setback. I know it's not necessarily hard, but it requires a lot of intuition imo, something I'm lacking in this case.

Animefag did you die?

>>12701032
-1

>>12702476
1. think about probability that the two died DID work for the same capitano
b) think about when they both go through and when one goes through and when the other goes through
iii) draw a probability tree

Is the function [math]e^{1.01x}[/math] exponentially larger than [math]e^{x}[/math]?

>>12701236
>picking a rational from an open interval requires choice
lol youre a dingus

>>12703061
Meant>>12701415

>>12703039
ratio of the two functions

>>12703039
exp(1.01 x) = exp(0.01 x) exp(x)

Any recommendations for a good analysis textbook with a solution manual? I'm trying to read through 'The Way of Analysis' but I don't have much confidence in my answers, and the lack of solutions is just making things worse.

I found a probably useless method of multiplication that works best with double digits and I need someone to tell me if I’m just being autistic. Let’s take 33*21. Put 21 into 2 single digits like 2 and 1. Multiply each by 33 and you get 66 and 33. Add the last digit of 66 and the first of 33 like 3+6 and you get 9; the middle digit of the number. Put the first digit from 66 in the front and the last digit of 33 at the end and sandwich 9 in the middle and you get 693; the same as you would get multiplying normally. The larger the variant, the more digits you need to work with but I’ve found methods all the way into the hundreds so far because I’m too lazy to look further

>>12703180
Yes because powers of ten 60+6 gleich 66

>>12700943
You... can't just do that?
You can add n to itself, but how do you define "add n to itself m times"? what is "m times" in the formal language?

Why is human architecture filled with unknots

>>12703207
Given M, find a set with its cardinality, and make a bijective function of +n symbols with its elements, use indexes if you must

>>12695759
I think you mean external theory lol

>>12695759
I think you mean extremal theory lol

>>12695875
Lmao what? Combinatorial geometry is huge, especially in computational problems. Also LP duality
>what is the the matching polytope

>>12703190
I guess I don’t follow what you meant. It also works with any combination of # I just chose those I can draw it if you want me to

>>12703224
I know, the reason it works is because multiplying 66 and 30 is the same as multiplying 66 by 3 by 10, so it shifts it over one place, as you observed

>>12703061
If you're picking one for each interval from an infinite collection of intervals then yes, you're using choice, retard

>>12703283
Isnt that only when you lack relevant info on the set? Otherwise you can create a recursive function to get zahls

>>12703283
Actually we can explicitly well-order the rationals and use that well-ordering to pick the rational from each open set, I originally called anon out on using choice because I was pretty sure he couldn't go around it.

>>12703223
Most combinatorialists don't care, and most of the ones who do work on combinatorial geometry don't care about traditional geometry areas

>>12693963
by column:
no pairs;
those pairs which are adjacent;
those pairs which are one away (showing that 5C2 = 10);
those triples for which their complement aren't adjacent;
those triples for which their complement are adjacent (5C3 = 10);
The next 15 graphs are the ways which you can choose 2 (exclusive) pairs from 5, which (as you see from the ordering in the picture) amounts to the amount of ways you can choose 2 pairs from 4, times 5. Note that the unpaired dot is in the same place in each row. The column of red drives this point home.
The last 2 columns of 5 illustrate that (n choose k) is the same as (n choose n-k) by illustrating that every time you choose k from n, the ones you aren't choosing amount to n-k.

>>12701578
based

>>12693735
Afaik, epsilon is just a way of saying For Any Number, Any N greater than 0 works, all positives work.

>>12703268
Ahhh i understand now, thank you

>>12702476
>pirates
The squads are mutually exclusive and so, this enumerates all the pairings between different squads...
(6*7+7*4+4*6)
divided by all possible pairings...
(17*16/2) i.e. 17 choose 2 i.e. 17 pirates, each with 16 left to pair with (NB: in finding pairs from the same group rather than bipartite matchings as we did first, we must divide by 2, since otherwise we count the same pairs twice)
and you get 94/136 = 0.3455...

>>12702985 is right in that you can also count how many ways those that are in the same squad can pair:
(6*5/2+7*6/2+4*3/2) [be sure to factor the 1/2 out for a less labourious calculation] = 42 ways two squadmates can both die. 1 - 42/136 = 94/136, as above.

>>12703481
I may have used the term "matching" improperly here so take it as a layman would; it's been a while since I've done graph theory

>>12702698
she had some mental breakdown a few threads ago

The integers are not simply ordered Proof
>the sum of all natural numbers is greater than any natural, because for any natural, the sum of all contains it plus another term
>thus any natural is less than -1/12
>but any natural is greater than -1/12

>>12703514
Rationals not integers

>>12703514
Stop changing your name field to make it harder for people to filter you.
If you don't want to be filtered just make good posts.

How the fuck do I solve for x in terms of y?
[eqn]y=\frac{1}{8}\left(x^2 - x + \frac{600\left(2^{\frac{x}{7}}-2^{\frac{1}{7}}\right)}{2^{\frac{1}{7}}-1}\right)[/eqn]

Multiple each side by 8 is easy, but I'm not sure what to do about the mess afterwards.I was tempted to use the quadratic formula, but the third term isn't a constant.

>>12703554
I ended up with 8y = x^13 - x^7 + (constant) - Xrootof2

I didn't know what to do after that for you though, it's pretty clear you just distribute the 7/x exponent though.

>>12703522
無

Can every mathematical entity be expressed as some cartesian product in a system that operates on cartesian products

I'm 4 months away from getting my PhD in mathematics, and I want out. Academic mathematicians are just such a shit, self-important, virtueless bunch of people.
What the fuck do I do?

>>12704407
find a job shoveling shit
or get your forklift operator qualifications
idk what you want from your life

>>12703292
Well, if the first answer didn't read like some ultrafinitist shitpost, I would"ve thought about it at least a little, but you're right, most probably wouldn't have come up with this answer, that 1 set theory class I took was long ago.

all i want is 2b 1/x

>>12704473
i guess this doesn't really work does it. oh well, so much for my only sci post

>>12704233
every object is the first cartesian power of itself

>>12704473
>>12704476
bro... happy valentines day...

>>12704473

>>12704479
Oops I meant to say the elements had to be tally marks or voids

>>12704473
My ex who I met on 4chan emailed me

Why is the space [math]\prod_{n=1}^\infty [n, \infty)[/math] so unintuitive?

>>12704848
What's unintuitive about it?

>>12703216
can you even do that in PA without multiplication?

>>12704848
seems pretty straightforward to me

>>12704407
Have you considered the possibility that most people are like that? Do you think industry or even unskilled work would be any different? At least math people are all smart. And in fact, I would hardly call them virtueless - this post reeks of /pol/ brainwashing.
In any case, if you never took the time to study some numerical mathematics and some computer science, then you must be a real dunce. Always set up a plan B. Maybe the other people aren't self-important at all, maybe they just make you feel insecure.

Are there interestings results about [math]\mathbb{H}[X][/math]?

>>12704407
it's the same in the industry, but you dont have the freedom of working hours

>>12705224
quaternion polynomials in one variable?

>>12704407
Fellow PhD anon here. I'm gonna be honest with you, 4 months is a little late to realize you don't want to stay in academia. Do you have any other work experience or projects you could put on a resume? What area is your dissertation in?

>>12704894
>At least math people are all smart.
This is blatantly false, and this stereotype needs to end. Academia, like anywhere else, is filled with midwits who think they're geniuses because they work hard to please their supervisors. Speaking of my own department, almost none of the grad students have any plans for the future aside from keeping their heads down and hoping they can land a teaching job after their final year. At least they're smart enough to realize they'll never get that cushy professor job, unlike every wide-eyed undergrad. The professors themselves got their jobs so many years ago and are so detached from reality, they can't give you any advice worth a damn that's not related to their research.

>>12705389
yes that's what [math]\mathbb{H}[X][/math] is.

So my goal is to study mirror symmetry, and some of the other mathematical upshots of string theory. I have an undergrad math degree where I took algebraic geometry, topology, real and complex, algebra, advanced linear and graph theory. I am not sufficiently versed in the areas of knot theory, homological algebra, category theory and differential geometry.

Should I just begin self-studying a basic graduate track, or is there a path that could expedite my learning this subject? For example, I feel like I can skip most of real analysis, but I'm not 100% sure. Anyone here studying mirror symmetry?

>>12705402
"Smart" and "good at planning" are not synonymous. Plenty of idiots are good at planning. Intelligence is a love for pursuing knowledge without the promise of wealth. If you're such a practical person, go paint houses or something.

I'm trying to prove a certain problem from Folland. If [math]T: X\to \mathbb{F}[/math] is a linear functional such that [math]\ker(f)[/math] is closed, prove that [math] f[/math] is bounded. I understand so far that the kernel is a closed subspace of X which implies that [math] \|x+\ker(f)\| \geq 1-\epsilon[/math] for any [math] \epsilon >0[/math] but I'm not seeing how this helps me get boundedness at all. Any help?

>>12705861
Suppose T is unbounded. Then for each n there exists a vector x_n such that T(x_n) >= n and ||x_n|| = 1.
Now write y_n = x_n / T(x_n). ||y_n|| goes to 0 as n goes to infinity. Also, T(y_n) = 1 for all n.
Well this isn't what we want, we want things in T^{-1}(0), not things in T^{-1}(1). But we just shift. Let z_n = y_n - y_1. Then T(z_n) = 0 for all n, so z_n is in the kernel of T. But z_n converges to -y_1 as n goes to infinity, and T(-y_1) = -1. So -y_1 is not in the kernel of T. Hence ker T is not closed.
TL;DR: use unboundedness, divide to get a bad sequence which is always 1 under T, then translate.

I work with stochastic processes/SDEs and probability in my research sometimes. I'd like to get a good enough handle on measure/lebesgue integration to read, for example, Probability with Martingales or a book on SDEs. What would be a relatively quick way to do so?
I'd like to avoid taking a class' worth of material, if possible. Is the first 3 chapters of big Rudin the way to go? My background in analysis is baby Rudin and a class on Kreyszig's functional analysis text.

>>12706247
big rudin is a piece of fucking shit. read like chapter 6 of pugh's real analysis book or part of folland or something.

>>12704884
Whats PA

>>12703216
There are no sets in arithmetic, unless you use tricks like coding a set as the product of nth primes for n in the set, or the binary number with nth digit nonzero if n is in the set, both of which use multiplication and can't be done with only addition.
>>12706643
Peano Arithmetic

>>12706660
Why is set theory not allowed? Does it require multiplication?

>>12706247

axler's book on measure theory is quite good. I used it as a supplement to folland.

>>12706247
1) Ch. 1-2 of Stein & Shakarchi III
2) Durrett Probability
3) Oksendal SDEs
4) Karatzas & Shreve Brownian Motion and Stochastic Calculus

I went through the above in that order and it worked out well. You probably can skip the Oksendal text but I found Karatzas and Shreve's book pretty hard and needed something easier to start. Also if you want to go as quick as possible you might be able to jump directly into Durrett.

>>12698584
The divisors that have a remainder of 0 are also divisors of the constant term. For example if c was 6, you would try +- f(1), f(2), f(3), and you'll find a factor in one of those.

Would a letter of recommendation from Ted Kaczynski be good to put on grad school applications?
I know he doesn't approve of studying math anymore but suppose we were in good correspondence and I somehow convinced him that studying math was something worthwhile for my life. Would a letter from him get you into a better school? He is one of the most famous mathematicians of all time, after all.

guys i need some algebra (boy) pussy

>>12707111
Trips of truth say yes

>>12707405
>>12707111
go for it, Ted Kaczynski loved trannies and gays, before they were trendy in academia

>>12707552
>that usage of the word pink
He wouldve been happier if the internet existed because then he couldve posted on mg with fellow autists

can a function be continious in only a single point?

>>12708374
yes
proof: think

>>12707552
>Got fucked by his friends

>>12708397
fuck thinking I just googled it

I'm sorry for a stupid question, but what would [math]D^2X[/math] mean?

>>12707111
It would be epic.

>>12708528
The derivative of derivative of x.

>>12708528
Second central moment, perhaps?

>>12706699
you don't understand mathematical logic at all, do you? read a fucking book on the subject instead of haranguing us with idiotic questions.
PA IS A COLLECTION OF AXIOMS. YOU CAN ONLY DO THINGS WITH THOSE AXIOMS. YOU CAN'T JUST MAKE UP RANDOM SHIT THAT YOU GET IN NORMAL ZFC-BASED MATHEMATICS.

>>12708528
completely and entirely depends on the context. what is X?

>>12708657
>replying to the room temp iq namefag

>>12708662
Baby don't hurt me.

>>12708689
Hahahahahahahahahaha! Good one!

>>12708696
Man, that reaction image takes me way back to the days when I was a twelve year-old browsing 9gag.

Diff geo is properly filtering me bros.

I want to prove [math] S = \{(x,y,z)| f(x,y) + z^2 =0 \} [/math] is a surface. (given [math]f(x,y) [/math] smooth and s.t. when [math]f(x,y) = 0, \ f'(x,y) \neq 0 [/math])

My thought is maybe I can split this into the case where [math]z[/math] positive and negative, then apply the implicit function theroem. My issue is that the derivatives aren't really making sense to me.
The other option is the Rank Theorem, but I'm once again stuck with taking [math] \frac{\partial f(x,y)}{\partial x}[/math].

>>12708738
> I'm once again stuck with taking
Nigger how stupid can you possibly be. If z is non-zero, that component of the derivative is non-zero. When z zeroes, f(x, y) zeroes, f' isn't zero (as is stated explicitly on the question).

>>12708760
Oh, I see now. Sorry, I'll go be profoundly retarded elsewhere.

>>12708738
the surface is the level set [math]F(x,y,z) = 0[/math] of [math]F(x,y,z) = f(x,y) + z^2[/math]. let [math](x,y,z)[/math] be a point lying in this level set. if [math]z \neq 0[/math], then [math]\frac{\partial F}{\partial z} = 2z \neq 0[/math] and implicit function theorem applies. your assumption tells you that if [math]f(x,y) = 0[/math], then the differential of [math]f[/math] is non-vanishing. therefore if [math](x,y,z) = (x,y,0)[/math], then [math]0 = F(x,y,z) = F(x,y,0) = f(x,y)[/math] and so by this assumption [math]dF = df + 2z\, dz = df \neq 0[/math] at this point. and implicit function theorem also applies.

Hey /mg/, have you ever actually wondered about how we know what molecules actually look like? I don't know chemistry beyond high-school leve, but I remember that before I studied mathematics I never questioned how we actually know the structure of molecules.
I assume the process goes something like this: A lot of measurements are made and information is collected about the molecule. But then someone has to make an argument to nail down the structure of the molecule from this information.
Now my point is that with a mathematical view regarding rigor and completeness this seems like quite a daunting task, with endless amounts of cases.
Like if there is a methyl-group here then there cant be a nitrogen over there because it doesnt match up with measurement X.
Suppose this arm is oriented to the left. Then it must be the case that....
stuff like that.
Seems like a nightmare. Does anyone have any insight if chemists write arguments of this fashion? Do they not really "prove" that only this structure can be the molecule but just demonstrate it's the only reasonable one really?

>>12708916
theyre cubes not hexagons

Is it possible to elegantly expand [math]asin(sin(x))[/math]?

>>12708916
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Lewis_Theory_of_Bonding/Geometry_of_Molecules

tl;dr once you know what atoms are in a molecule (easy to figure out), how they roughly fit together (less easy to figure our, but can be reasoned through based on how it got made), determining geometry is just a matter of considering some basic cases, built off the assumption that things minimize potential energy, and playing legos with them.

>>12706365
>>12706710
>>12707013
Thanks everyone. I'll check out the Stein/Shakarchi and the axler and then probably move on to Durrett or Prob w/ martingales. The Stein books seem like a great series in general.

>>12709095
[math]-ax(ns)^2[/math]

>>12703207
[math]m(a,1) = a[/math]
[math]m(a,b+1) = a + m(a,b)[/math]

>>12708916
we did some molecular angles, mainly hydrocarbons iirc in lower 6th chem (two years before university in bongland)
you should be seeing basic strucural representations by 7-8th grade

>like 10 REUs are done at midnight
>emailed professor a month ago for recc letter, he said yes
>remind him weekly
>still hasn't uploaded letter

who
>skipped grades
?

I was placed in an experimental math education program in 1st grade, then I started my high school courses in 6th grade. I finished my math requirements my freshman year of high school. Then I was bored so I spent the rest of high school smoking weed and now I'm retarded kek

When I started college I was placed in remedial algebra class. Did okay in calculus and linear algebra but failed numerical analysis. Finally picked up the baton again this year, working through a proof book and wondering what could have been. le sigh

>>12710019
Godspeed REUtard.
I took the finance-pill instead and got an internship with some quants

>>12710071
How do you take the finance-pill? Do you just look up quant internships and send in an application? I've taken grad math classes and like 5 or so CS courses. Is that enough or do I need something more?

>>12710019
Who else did you ask?

>>12710154
I already have one recc letter. I'm just waiting on the second one. I should've asked a third one just as a back-up desu this is kinda my fault.

>>12710065
Holy fuck this must be American public school education. How can you do everything before calc by age 14 and then bail and become retarded? I didn't learn calculus until I was 15 and I'm like the special ed kid in my PhD program.

If I label the edges of a polygon instead of its vertices, does the [math]D_n[/math] group still describe all the actions I can take on it perfectly? Or do I need to change my permutations?

>>12696808
Thanks, this book is just what I was looking for.

>>12710549
Why wouldn't it?

>>12692234
what the actual fuck are you studying when you study topology?
>Calculus: you study how things change
>Analysis: you study the formal, theoretical underlyings of calculus
>Algebra: you study systems using linear maps, as well as the theory behind it all
>Geometry: you study shapes and how they relate
>Topology: ???

What's 2+2?

https://sites.google.com/view/hhs2021-opening/videos

>>12710638
Continuous change of shapes.

>>12710641
I don't know. I'm an algebraist.

>>12710638
Itty bitty brained post.

>our big calc 2 integration techniques test told you what technique to use on every problem

what the fuck is this shit

>>12710817
>>our big calc 2 integration techniques test told you what technique to use on every problem
I wish that was me during calc 2, sounds comfy.

>>/sci/thread/S12668218#p12682819
Well anon? Are ya gonna do it anytime soon?

>>12708721
Precisely why I have it saved.

>>12710159
You should know that something similar happened with my professor and she told me later not to worry and that usually they don't mind if they prof's letter is in a few days late since they don't review them immediately. Sure enough I got into a few REUs just fine. But you do want to set earlier deadlines than the actual deadline when it comes to grad school apps.

>>12710638
geometry is the study of rigid shapes, topology is the study of nonrigid shapes.

>>12708657
https://www.youtube.com/watch?v=cXpNZGDxMEc

Obey ZFC.

>>12708681
I got shot in a metal tube across a continent today. How can I be retarded if I know how to fly?

>>12711298
Thank you for telling me this. That makes me feel a lot better. Also thanks for the extra tip about recc letter deadlines for grad school apps.

>>12710893
I don't use discord, nor do I plan to do so. Sorry.

>>12711415
I can second the more flexible dates with the letters, at least in the Old World.

How do I work out the odds of rolling two dice that are >4 when using 3/4/5/x dice?

what about 3 odd numbers using 4/5/6 dice?

>>12710638
That's a very good question. Historically topology was developed of fringes of mathematics then one day certain results were put into one handbook and thst handbook was labelled 'topology'. Topology is mostly a study of continuous fuctions and their invariants (like compactness or connection).

>>12710638
same as geometry, but different flavor

>>12710116
Yeah, I'm euro so it's slightly different here.
Prop shops tend to look for strong math undergrads with some programming knowledge. Most of the time you apply online and get sent an automated test that goes over basic probability just to make sure you aren't completely retarded.

Is there anything like elementary diffeomorphism such that there is a unique/minimal decomposition etc?

>>12710638
continuity

>>12711355
Pretty sure someone else (or several thousand other people) knew how to fly and built/piloted that metal tube.

>>12711415
I mean maybe take the opportunity to put on a little pressure and make them feel a little bad if they still haven't submitted it (extremely politely of course). When was the last time you reminded them? If it was more than a few days ago I would send something today as soon as you get a chance.

>>12712205
No one has any clue what you're talking about. Be more descriptive. What is an "elementary" diffeomorphism? What decomposition are you talking about?

>>12712301

the derivative is an elementary matrix

I guess the answer is yes but only to the first order.

>>12712205
>Is there anything like elementary diffeomorphism
>the derivative is an elementary matrix
yes, for example every invertible linear map given by an elementary matrix

>>12712459

exactly, the point is if there is an equivalent statement for smooth maps

>>12712469
are you asking if there exists some kind of classification of diffeomorphisms in the sense that there's some list of simple and well understood diffeomorphisms such that every other diffeomorphism can be written as their composition? if that's your question, then no, and if you manage to do such a thing, you're guaranteed to get the Fields medal and worldwide recognition.

How do I handwrite q, g and 9 to avoid confusion, they look so similar

>>12712507
q has a straight line
9 has a curvy line
g has a very curvy line which connects back to itself, as in [math]\mathbf{g}[/math]

>>12712507
Put a line through the stick in q. Also, put a line through the diagonal part of z to distinguish between z and 2. Write your 9 as a proud and big boy standing tall while your g is down there, partially underground.

>>12712507
O|
...|/
for q
O|
_/
more curly tail for g
O|
...|
straight line only for 9

>>12712507

>>12712507
anything other than this standard is barbarism

>>12712535
>put a line through the diagonal part of z to distinguish between z and 2
based

>loops on g
>curly tail on nine
>no flick on q
imagine doing any of these things

>>12712507
duh

What about absolute value bar and lower-case l? Do a cursive l?

>>12712567
Thanks! Although, who even uses 2 for anything? ~oddprimegang~

>>12712342
Ah, I see. That's an interesting question. I doubt in general you can extend that beyond first order.

>>12712575
i use 2 to write down the number of genders in this world you fucking tranny

>>12712575
I thought you killed yourself. Or hoped.

>>12713073
Rude but redpilled.

>>12712573
absolute value bar is a straight line
[math]l[/math] is curved at the bottom

>>12710638
I think in most university courses general topology happens before any algebraic or differential topology.

If you like, general topology is like real analysis but you get rid of the notion of "distance," or precisely a metric. You still have open intervals, but now they're open sets, and the definition of a continous function no longer relies on epsilons and deltas but on the preimage of open sets being open. It's very flabby, but fully equivalent to what was done before.

It was essentially finished like 50 years ago, although other modern branches developed before, during, and after general topology, despite being technically dependent on it.

Usually in anything called topology, you're studying something that looks geometric while simultaneously ignoring that different points may have different distances between them. Distances matter sometimes but rarely and usually on not any particular distance. Maybe this helps.

I'm trying to prove the version of the splitting lemma for chain complexes. I have a proof where I explicitly construct a map [math] q: C\to B[/math] given a map [math]r: B\to A[/math] such that [math]rf = 1[/math] where [math] f:A\to B, g: B\to C[/math] are the chain maps in the short exact sequence. I want to know if I can prove the splitting lemma for chain complexes directly from the splitting lemma for modules. As in, for each n, there exists a map [math]q_n: B\to A[/math] such that [math] g_nq_n = 1[/math], can I show the commutativity [math] q_n d_n = q_{n-1}d_n [/math] ? I've been toying around with it for a few hours and haven't had any luck.

I still don't really get what a semiring is. All I really understand is that rings, semirings, fields, and their sigma versions are just sets with defined properties that have useful applications. Most of these classes have logical enough properties (being closed under X operation) but how in the hell does anyone just decide that they'll make a class called a semiring and say "alright this one will be closed under intersection and also let's have the proper difference of any two subsets be able to equal the countable union of a sequence of disjoint subsets."

And then sigma ring generated from the set of all intervals, which is "clearly" a semiring, is somehow the Borel Algebra. I'm tired of being a brainlet, anons.

>>12714406
Take any [math]c\in C_n[/math] and consider the element [math]b = (\partial_n \circ q_n)(c) - (q_{n-1} \circ d_n)(c)[/math], where [math]\partial_*, d_*[/math] are the differentials of [math]B_*, C_*[/math], respectively. Since [math]g_{n-1}(b) = 0[/math], exactness will imply that [math]b[/math] is in the other summand. However, the important part is to notice that it will also be in the summand corresponding to [math]C_{n-1}[/math], and hence lie in their intersection. Since this intersection is trivial, [math]b = 0[/math], as desired.

>>12714560
Dumb frogposter.

>>12714661
Ah, is this one of those generals where only anime reaction images are accepted? Very well.

>>12714675
Oh no, people complain about both here.

>>12714691
That's cool and all but I still don't know what a semiring is. I will keep everyone posted.

>>12714640
can you elaborate what you mean by "exactness will imply that b is in the other summand and that it will also be in the summand corresponding to C_{n-1}"

>>12714821
Okay. So you have the split exact sequences [math]0 \to A_n \xrightarrow{f_n} B_n \xrightarrow{g_n} C_n \to 0[/math], for every [math]n\ge0[/math]. Since they split, you may write [math]B_n = A'_n \oplus C'_n[/math] with [math]A'_n \cong A_n, C'_n\cong C_n[/math], and you know that [math]A'_n = f_n(A_n) = \ker(g_n)[/math]. Since [math]b\in C'_{n-1}[/math] by checking where [math]q_{n-1}(d_n(c)), \partial_n(q_n(c))[/math] land, the question is, where is their difference. Well, obviously, [math]b \in C'_{n-1}[/math] as that is a submodule, but [math]g_{n-1}(b) = 0[/math] implies that [math]b \in \ker(g_{n-1}) = A'_{n-1}[/math]. Hence [math]b \in A'_{n-1} \cap C'_{n-1} = 0[/math]. That [math]\partial_n(q_n(c)) \in C'_{n-1}[/math] follows from the fact that [math]g_*\colon B_* \to C_*[/math] is a chain map, and so the differential restricts to [math]\partial_n^C \colon C'_n \to C'_{n-1}[/math] (can you see why?), and [math]q_{n-1}(x) \in C'_{n-1}[/math] for any [math]x\in C_{n-1}[/math].

>>12714874
The wording is a bit dumb, but being a split exact sequence of complexes splits the differential of the middle one like that. Sorry it's morning and I haven't slept.

>>12714874
The only part I am not clear on is your claim that [math] \partial_n (q_n(c)) \in C_{n-1} = Im(q_{n-1})[/math]. It doesn't seem to be immediately obvious that a chain map should behave that way because it seems like your just making the claim that [math] \partial_n(Im(q_{n-1}) = Im(q_n)[/math]. This doesn't need to be true in general, no? Other than that, everything seem to be crystal clear.

>>12714946
I know my claim is true, but I'm starting to lean towards it being a consequence more than a part of what you are trying to prove. If we knew that [math]q_*[/math] is a chain map, we could define [math]\partial_n^C (x) = (q_{n-1} \circ d_n \circ g_n)(x)[/math]. Sorry. I'll go for a walk and see if I can get it done after that.

There are 3 relevant subgroups of Group God after Gödel.
The first is the known and living world. Here, the God elements vary under operation, each morphing into another given varying U-coordinates. All elements carry some God1 intersection points.
God2 is much less understood. A few examples have been found, and all such have been isomorphic under some unknown isomorphism. Proof of unprovability seems impossible, although no proof dabei has been found. The earliest discovered element can be accredited to the Romans or Greeks, their God2 Janus.

Finally, God3 remains impenetrable and ever present. It vaguely resembles the Universal Open Topology.

>>12714874
Nonsensical argument

>>12714560
If you know some programming look at how a semiring or a magma are defined in the Haskell programming language. Seeing it written like that makes it very simple to understand. It's a very basic concept really.

Absorptive property accepts sentience free definitions of existence

https://www.youtube.com/watch?v=aSxiNnWbJOE

Is it hard to prove that integers aren't closed under division? Do I need to know abstract algebra first?

>>12715208
Can you post it cause Im cur-i-ous

>>12715208
That drawing of Trudeau is legitimately creepy you shoudlt use such potent psyops. Try mountain photos

>>12715199
I know.

>>12715164
I did some more thinking/googling and I don't think the splitting lemma holds for chain complexes. This is confusing though because the category of chain complexes is abelian is abelian and I believe I was told that the splitting lemma holds in any abelian category. So?????????????????????????????

>>12715216
https://lukajcb.github.io/blog/functional/2018/11/02/a-tale-of-semirings.html

Even if you're not a programmer you can probably grok the whole thing. Haskell syntax is easy for mathematicians. See also

https://hackage.haskell.org/package/semiring-simple-1.0.0.1/docs/Data-Semiring.html

https://typeclasses.com/semiring

>>12715216
>>12715218
or perhaps he's wondering why someone would take acid before shitposting on /sci/

no one cared who i was until i posted higher order languages

>>12715214
is 3/2 an integer anon? or did i succumb to some sort of b8

>>12715239
I mean prove that all integers are not closed under division. 3/2 is just an example, right?

>>12715254
3/2 = 1.5 is a counterexample to the claim that the integers are closed under addition. you just need one counterexample to disprove closure of a set under an operation.

>>12715260
Cool, thanks!

>>12715244
Neuer

>>12715220
Whenever you some diagram result that you can express using commutativity and exactness, and it holds for all module categories, then it holds for all abelian categories. Can you formulate splitting using only those two? Yes you can, actually. It is just a commutative triangle in which one side is the identity. However, this would require two separate diagrams whereas the 5-lemma would be one commutative diagram and several exact sequences. This is probably the reason why it doesn't have to hold, too many diagrams at once! It would probably work if [math]A_*[/math] was acyclic. Assuming that [math]\partial_n(b) \in A'_{n-1}[/math] would then give you an [math]a \in A_n[/math] such that [math]f_n(a) = b[/math]. If then [math]b = q_n(c)[/math], this forces [math]c = 0[/math]. Then my dumb idea would actually work out as you would always have [math]\partial_n(c) \in C'_{n-1}[/math]. Sorry about that.

>>12715287
Actually, no. It wouldn't even in that case. Forget my ramblings.

>>12715208
I will definitely do that, sounds like an interesting way to look at it, thanks

>>12715271
TITS OR GTFO