/mg/ maths general

[Anonymous No.12266564]

Finnish school of function theory edition
Talk maths
Edellinen >>12243381

[Anonymous No.12266579]

How do you retain information? I'm taking precalc 1 which is essentially linear algebra and I'm having a hard time learning the material, but when I do the practice problems as I'm reading I understand the concepts enough to get the correct answer.
Anything you guys do to help learn math? First year at college and online classes are kind of kicking my ass.

[Anonymous No.12266603]

>>12266579
Just keep doing the exercises diligently.

[Anonymous No.12266607]

>>12266603
I'll try. I'm just feeling really demotivated because in high school I felt like I could learn new material fairly quickly.

[Anonymous No.12266619]

Is there a (reasonably simple) algebraic/trig function that converts x y coordinates to angle, for all pairs of xy? Or would I have to do piecewise stuff where I do "add theta if x is negative", since arctan spits mirroring values for negative x

[Anonymous No.12266623]

>>12266607
You've hit the wall of your natural talents. You're no longer able to effortlessly get along. Good, it was bound to happen eventually, now get over it.

[Anonymous No.12266642]

>>12266607
It's because online classes are a shite way to learn mate, dont kick yourself

[Anonymous No.12266671]

>>12266619
Perhaps you're looking for something like atan2.

[Anonymous No.12266677]

>>12266671
But how would you use both atan and atan2 in a single function, swapping between them when necessary without piecewiseness

[Anonymous No.12266697]

>>12266677
Why the piecewisenessphobia?

[Anonymous No.12266721]

>>12266564
Why not use >>12266268

[Anonymous No.12266757]

>>12266721
The absolute moron failed to write /mg/ in the title or even the post. He should never again try to make an edition.

[Anonymous No.12266761]

>>12266721
Shit image. Shit reddit text. Doesn't take you to the correct last /mg/. Doesn't say /mg/ in the title

[Anonymous No.12266955]

[math]\mathbb{Q}[/math] and [math]\mathbb{Q}^2 [/math] are homeomorphic as topological spaces (with the topologies induced from [math]\mathbb{R}[/math] and [math]\mathbb{R}^2 [/math], respectively).

[Anonymous No.12267039]

>>12266955
Yes, what's your point? Just because they exist it doesn't mean they're useful.

[Anonymous No.12267062]

>>12267039
i just found it surprising and i also got btfo'd by some related exercises

[Anonymous No.12267075]

You know the number [math]42[/math] has some interesting properties. It’s the 5’th Catalan number. It lies in the middle of a prime pair. And it is the he smallest perfect square that is the mean of two cubed twin primes. But I can’t help but wonder, for any generic property...

Should the subset [math] \big\{x\in \{42\} \mid P(x)\lor \neg P(x) \big\} [/math] of the singleton set [math] \{42\} [/math] even be finite, for every property [math] P [/math]?

Let’s settle this once and for all.

[Anonymous No.12267094]

>>12267075
You can think of infinitely many sequnce containing 42. Let [math]P[/math] be the property of appearing is said Sequence?

[Anonymous No.12267097]

>>12267094
I guess I don't know the formal definition of a property

[Anonymous No.12267112]

>>12267097
We'll get by by saying any expression involving [math] \land \lor \forall \exists \implies \bot = \in () [/math] and a finite collection of variables [math] x,y,z [/math].

For sure, if
[math] A := \big\{x\in \{42\} \mid P(x)\lor \neg P(x) \big\} [/math]
then
[math] (y\in A) \implies (y=42) [/math]

but that's only loosely related to the question.

[Anonymous No.12267113]

>>12267097
We'll get by by saying any expression involving
[math] \land, \lor, \forall, \exists, \implies, \bot, =, \in, () [/math]
and a finite collection of variables [math] x,y,z [/math].

For sure, with
[math] A := \big\{x\in \{42\} \mid P(x)\lor \neg P(x) \big\} [/math]
we have
[math] \forall y . \big( (y\in A) \implies (y=42)\big) [/math]
but that's only tangentially related to the question.

[Anonymous No.12267212]

>>12267075
Are you trying to say there are infinite properties of numbers? You can define property once, for every singleton set, therefore one set of N, R, Q of number 42, but properties, like being member of divisiors of some bigger number, is infinite set.
But for every property, there's just one x that is 42. For every negated property there's just x too, but there are infinite properties.

[Anonymous No.12267233]

>>12266955
Is this hard to prove? I'm thinking of why they would be and can't come up with anything.

[Anonymous No.12267238]

>>12267212
>Are you trying to say there are infinite properties of numbers?
No, that's not what I'm trying to say. I'm not trying to say much, really, I'm asking a question. In words:
>Should any subset of the singleton set {42} be a finite set?

There are, of course, infinitely many properties.
E.g. there's properties that are true for 42, e.g. [math]P(x)[/math] defined as [math] x > 17 [/math]. For this property, the subset is of course just [math]\{42\}[/math] itself there's a function [math]f\colon \{0\}\to \{42\}[/math] which counts it, i.e. it's a finite set.

I don't quite parse your other two sentences.

[Anonymous No.12267243]

>>12267212
>Are you trying to say there are infinite properties of numbers?
No, that's not what I'm trying to say. I'm not trying to say much, really, I'm asking a question. In words:
>Should any subset of the singleton set {42} be a finite set?

There are, of course, infinitely many properties.

E.g. there's some properties that are true for 42. E.g. we'd all agree that [math]P(x)[/math] defined as [math] x > 17 [/math] is such a one. For this property, the subset is of course just [math]\{42\}[/math] itself. Then there's a function [math]f\colon \{0\}\to \{42\}[/math] which counts it, i.e. it's a finite set.

I don't quite parse your other two sentences.

[Anonymous No.12267259]

>>12267212
>Are you trying to say there are infinite properties of numbers?
No, that's not what I'm trying to say. I'm not trying to say much, really, I'm asking a question:
>Should any subset of the singleton set {42} be a finite set?
Above I asked it for a more specific class of subsets, but this question is related.

There are, of course, infinitely many properties.
E.g. there's properties that are true for 42, e.g. [math]P(x)[/math] defined as [math] x > 17 [/math]. For this property, the subset is of course just [math]\{42\}[/math] itself. And there's a counting function [math]f\colon \{0\}\to \{42\}[/math]. In particular, it's a finite set.

I don't quite parse your other two sentences.

[Anonymous No.12267274]

Good intro book on functional analysis?

[Anonymous No.12267283]

>>12267075
Is this some intuitionist screeching? Looks trivial to me...

[Anonymous No.12267295]

>>12267233
see picrel for a more general statement
i'd say it's pretty hard

[Anonymous No.12267296]

>>12266697
I don't know, it just seems less aesthetic and more interesting to make the machinery rely on "base math". You could use fourier series to make that discontinuous function and use that somehow, probably, but that doesnt satisfy my simpleness desire.

[Anonymous No.12267306]

>>12267075
If we take property to mean boolean statement that references 42, either it will be true or false so 42 would either have P or not P

[Anonymous No.12267314]

>>12267306
>either it will be true or false so 42 would either have P or not P
How so?

[Anonymous No.12267359]

>>12267259
The answer is you don't get infinite set as subset of finite set?

[Anonymous No.12267367]

>>12267274
Lax.

[Anonymous No.12267429]

>>12267359
Says who?

[Anonymous No.12267466]

What is this book?

[Anonymous No.12267471]

>me yesterday
>lying in bed, thinking about random stuff
>Jesus blesses me with the solutions not just one, but two problems I've been cracking my head against for the past two days
>today
>solve another very hard question that's supposed to be above my weight
I wouldn't trade the feeling I have right now for sex even though I'm a virgin.

[Anonymous No.12267476]

>>12267471
Based and divinerevelationpilled

[Anonymous No.12267555]

>>12267471
Open your heart and your mind always follows

[Anonymous No.12267573]

>>12267471
Basted and readpilled.

[Anonymous No.12267640]

>>12267466
This? >>12267295
That's "Classical descriptive set theory" by A. Kechris.

[Anonymous No.12267678]

>>12267640
by any chance, if you know how to solve the second part of the problem, i'd be happy to hear a solution

[Anonymous No.12268503]

were there any news on mochizuki and IUT during the last few months?

[Anonymous No.12268689]

>>12267678
Sorry, I don't.

>>12268503
There was supposed to be an IUTeich conference earlier this year, but it has been postponed to next summer.
http://www.kurims.kyoto-u.ac.jp/~motizuki/project-2020-english.html
https://www.maths.nottingham.ac.uk/plp/pmzibf/files/May2020.html

[Anonymous No.12268701]

>>12268689
What is IUT even about? In the most vague sense, even. I see people talk about it a lot but never seen any reference to the math in it

[Anonymous No.12268710]

>>12268701
It's about Hodge theaters, étale theta functions and log-shells. Among other things.
Picture has what I believe are Scholze's latest words on the matter.

[Anonymous No.12268711]

>>12268701
It's the mathgen of disciplines, it's not actually about anything.

[Anonymous No.12268726]

>>12268710
>What the fuck?

>>12268711
Seems so

[Anonymous No.12268731]

>>12268710
>deep into my heart
gay

[Anonymous No.12268733]

>>12267075
>And it is the he smallest perfect square that is the mean of two cubed twin primes
42 isn't a square number.

[El Arcón No.12268746]

>>12268710
First, note that the Hodge theater is my MCM unit cell. The "infinitely many copies" refers to my intention to construct a cosmological lattice from infinite many copies of Minkowski space H sandwiched between de Sitter and anti-de Sitter space. They way I want to add "something new" to the mathematical structure is to add lattice interference effects which would not be present if there was only one copy of H.

[Anonymous No.12268748]

>>12267113
> A:={x∈{42}∣P(x)∨¬P(x)}
Based I know how I'm defining everything in math from now on

[Anonymous No.12268750]

>>12268726
Oh, and it is also about Frobenioids. How could I forget Frobenioids? They're the key to all of this. The inter-universal samurai has made this helpful animation to illustrate IUTeich to us mere mortals:
http://www.kurims.kyoto-u.ac.jp/~motizuki/2020-01%20Computation%20of%20q-pilot%20(animation).mp4

[El Arcón No.12268753]

I am physicist and I have no idea what "anabelomorphy" is or even an "outer isomorphism." I understand calculus and analysis very well, but not so much when it comes to abstract algebra. Still, I am pretty sure that Mochi's Hodge theater is my unit cell. The Randall-Sundrum brane world models are quite similar to what I have done, pic related. In the MCM, the AdS and dS branes are placed infinitely far away and the Minkowski brane is snadwiched between them. It's a combination of RS1 and RS2. I only read about RS1 and RS2 later and I did not use their work in my research, or know about it.

[El Arcón No.12268757]

Everyone has heard of the AdS/CFT "holographic duality" by which physics on a bulk determines physics on a surface, and vice versa. My main new idea was to have a surface sandwiched between two bulks. Usually when they look at AdS/CFT, they just imagine a surface at the end of one bulk. This is reflected in what RS have done. Pic related, I said, "Let there be two semi-infinite 5D bulks with a 4D surface of tangency."

[El Arcón No.12268761]

I also showed the vibrational spectrum of the lattice I constructed is EXACTLY the particle spectrum of the standard model. I also had a lot of other outrageously confirming results.

[Anonymous No.12268767]

>>12268710
The only thing I'm confused about is why does he even care so much abou it? Either construct a conterexample/disproof/however you might want to call it or shut up, end of story. I have no doubt btw that every single person involved in this argument is anally autistic but Jesus Christ it's math, it's either right or wrong and most certainly it does not strike into anyones heart. Fuck me, seriously.

[El Arcón No.12268782]

Here is the gist of my lattice model. I added at 5th embedding dimension such that it is the perpendicular direction to the H brane. This allows us to write the 4-metric as a function of the 5th dimension. In GR, although the theory technically says that the whole 4-manifold has dynamical geometry, we usually say that the dynamical object is the 3-metric because we can write it as a function of the 4th dimension: time. As soon as you start trying to compute the 4-metric, GR pretty much stops working immediately. This is the utility of imposing a fifth embedding dimensions: it lets you write the real 4-metric as a function of the 5th dimension. Otherwise, you have to assume Lorentz frames exist and that, basically, time is only special relativistic while 3-space is generally relativistic. So, I hope, you can see the obvious reason why it is preferable to have a 5th dimension. However, there is a problem! It is easy to know what it means to have a 3-metric at some constant time, but it is not so easy to understand what it means to have a 4-metric at some constant 5th dimension. If the universe is 4D, then what is this 5th dimension? I have constructed it as an abstract lattice, but physics uses a 4D universe so the question remains: what is a slice of constant 5th dimension?

[El Arcón No.12268805]

Here, my idea is to make the connection to quantum theory. I put a periodic condition on the fifth dimension so that H is the branch cut. Then, I tie the periodicity of the fifth dimension to quantum measurement. Measurements are made in H. the 5th dimensions is an abstract psychological dimension with period Phi such that Phi amount of 5th dimension proceeds between successive measurements. Wavefunctions diffuse in Sigma+ and Sigma- between measurements, and then they collapse again on H. I have some work left to make the connection to the quantum theory but the formal unification of gravity and EM was achieved in 2013. That's we we suddenly got all these new "hypersonic missiles" that no one was talking about in 2012 but were suddenly all over the place by 2016. So, now I hope you understand what it means for each 4-space H to have a Hilbert space H' attached. If we have a quantum system with some space of eigenstates, and then we make repeated measurements on them, the Hilbert space spanned by those states remains the same across any number of H. So, every Hilbert space is "isomorphic." However, the domain of the functions in the Hilbert space does not stay the same. For instance, when doing a measurement at t1, we will sample a Hilbert space whose functions have a their domain as a slice of constant time in H, which is a 3-space. We say "time doesn't exist in quantum mechanics" because states in Hilbert space are functions of space but not time. Quantum theory uses repeated measurement for things like building up the double slit interference pattern from a series of random scintillations, for example. This means later measurements will sample from Hilbert space whose functions have a different 3-space as their domain because the domain is a slice of 4-space at t2 instead of t1.

[Anonymous No.12268811]

>>12268733
I meant the square of [math] 42[/math] ,

[math] 42^2 = 11^3 + 433 = 13^3 - 433 [/math]

I was just shitposting, though, I got those facts from some website.

>>12268748
These go along the lines of what's called Brouwerian Counterexamples, but their pedagogical value is argued about. The idea is to show ickyness of mathematical principles by coupling something simple with something hard.

E.g. to for a set [math] X [/math] to be finite is for there to exist a bijective function between the canonical [math]n[/math]-element set [math]\{0,1,2,\dots,n-2,n-1\}[/math] and [math] X [/math] , where [math] 0 [/math] denotes [math] \{\} [/math] and the successor set of a set [math] y [/math] being [math]y \cup \{y\} [/math]. E.g. the set [math] \{6, 7, x\mapsto x^2, {\mathbb N}\} [/math] is countable because there's a bijection [math] f\colon \{0,1,2,3\} \to \{6, 7, x\mapsto x^2, {\mathbb N}\} [/math].

The empty set is finite via the empty function on the empty set. Any singleton set [math] \{a\} [/math] is finite via the unique function [math] g\colon \{0\}\to\{a\} [/math].

Now define a subset of [math] C\subset \{0\} [/math] by the set which holds 0 if the Continuum Hypothesis is true and holding nothing if it's false. Now it's suddenly undecidable which function counts [math] C [/math] .

[math] {\mathsf{ZFC}} [/math] can't prove give use the counting function, but still wants to claim that either the identity on [math]\{\}[/math] or the identity on [math]\{0\}[/math] counts it, i.e. makes [math] C [/math] finite.

[Anonymous No.12268813]

>>12268767
Well, right now the abc conjecture is a theorem in Kyoto and conjecture elsewhere. IUTeich people should write a clearer proof. It's all very embarrassing so I understand Scholze here.

[Anonymous No.12268815]

>>12268750
But what does any of that mean? The most I know is some analysis and topology.

[Anonymous No.12268814]

>>12268733
I meant the square of [math] 42[/math] ,
[math] 42^2 = 11^3 + 433 = 13^3 - 433 [/math]
I was just shitposting, though, I got those facts from some website.

>>12268748
These go along the lines of what's called Brouwerian Counterexamples, but their pedagogical value is argued about. The idea is to show ickyness of mathematical principles by coupling something simple with something hard.

E.g. to for a set [math] X [/math] to be finite is for there to exist a bijective function between the canonical [math]n[/math]-element set [math] \{0,1,2,\dots,n-2,n-1 \} [/math] and [math] X [/math] , where [math] 0 [/math] denotes [math] \{\} [/math] and the successor set of a set [math] y [/math] being [math]y \cup \{y\} [/math].
E.g. the set [math] \{6, 7, x\mapsto x^2, {\mathbb N}\} [/math] is countable because there's a bijection [math] f\colon \{0,1,2,3\} \to \{6, 7, x\mapsto x^2, {\mathbb N}\} [/math].
The empty set is finite via the empty function on the empty set. Any singleton set [math] \{a\} [/math] is finite via the unique function [math] g\colon \{0\}\to\{a\} [/math].

Now define a subset of [math] C\subset \{0\} [/math] by the set which holds 0 if the Continuum Hypothesis is true and holding nothing if it's false. Now it's suddenly undecidable which function counts [math] C [/math] .
[math] {\mathsf{ZFC}} [/math] can't give us the counting function, but still wants to claim that either the identity on [math]\{\}[/math] or the identity on [math]\{0\}[/math] counts it, i.e. makes [math] C [/math] finite.

[Anonymous No.12268818]

>>12268750
Also that video may be the single most autistic video I've ever seen

[Anonymous No.12268820]

Is the Continuum Hypothesis either true or false?

[El Arcón No.12268825]

In abstract Minkowski space, the 3-spaces are all the same simply with different labels. However, in a physical 4-space with perturbations, the metric of the 3-space domain of the Hilbert space functions will not be a constant, and then the probabilities associated with the wave functions will change. So, note well: even though the functions Psi_n in each Hilbert space are the same, the actual values |Psi_n(x)|^2 will change depending on the metric of the 3-space which was the domain of the functions in the Hilbert space. Then, because quantum mechanics relies fundamentally, in my opinion on the psychological process of measurement, I would like to set up some kind of "Dirac comb" potential for a "cosmological state space" containing all H' such that each instance of H' in an H holds states in an "infinite well" but tunneling allows states in one Dirac well to interact with states with another Dirac well.

Essentially, since all quantum effects are modeled as power series in one thing or another, often the fine structure constant, I would like the associate each increasing power term with the next adjacent instance of H' in the next adjacent instance of H. So, you see, then, that I would like to say, "The [math]\mathcal{O}(\lambda^3)[/math] terms come from tunneling from this third brane off to the side over there, or maybe from simultaneous contributions from the third adjacent forward and backward branes simultaneously."

Overall, even if I have infinitely many copies of the same Hilbert space, meaning that the states of my double slit experiment are the same states no matter how much data I collect, the Hilbert spaces are distinct because their domains are distinct 3-space slices of H at different times. In pure Minkowski space, the domains are isomorphic as well and only differ in their label, but in a physical manifold the perturbations on Minkowski space make the domains of the isomorphic Hilbert spaces not isomorphic at all.

[Anonymous No.12268859]

The wikipedia article says that perturbation theory has breakthroughs via Feynman diagrams, i.e., the writing out of differential equations and all their different terms and little epsilon order corrections is somehow made easier by a Feynman diagram. Obviously Feynman diagrams are useful insofar as computing subatomic particles, but could someone explain to me how you might use it in the context of say, an epidemiological model, or a fishery model?

[Anonymous No.12268860]

Hi friends. Not math, but I wrote an important essay on pragmatic reorganization of society and would appreciate if you considered it! After all, how can we do math after the apocalypse?

>>>/lit/16645189

[El Arcón No.12268871]

Case in point, here's Mochi making fun of the tension in my neck and shoulders on his faculty page.

[El Arcón No.12268873]

Right now, I have begun conducting a survey of quantum theory so I can write in my next paper, or an upcoming one, exactly what the details of the quantum connection are, or at least improve my statement of what remains to be done. However, since my solution to classical electrogravity, which is UFO tech basically, got swept under the rug when I fully solved the problem, I have been procrastinating studying the connection to quantum theory. It looks like I might need to solve the 5D heat and/or wave equation in curved spacetime, and I do not really want to do that in isolation when I hope to have collaborators in the future.

Right now in quantum theory, the anti-symmetry of the fermionic wavefunction is an empirical constraint not motivated from first principles. I have the goal to show that fermions have anti-symmetric wavefunctions due to what is essentially a specular reflection of probability current off of a singularity joining Sigma+ to rightward Sigma-. I have joined Sigma- to rightward Sigma+ across H at 0 curvature (Minkowski space) but I join Sigma+ at large positive curvature to Sigma- at large negative curvature but letting the curvature go to infinity. Infinite curvature is a GR singularity and I need to solve the T and R coefficient problem (transmission and reflection) at the interface there hopefully to come up with a good reason for the anti-symmetric wave function.

I have a lot of good ideas I still havent written papers about. I kind of just go with whatever seems easy, like solving RH, but I think I have finally come to the point where I need to push my physics research program past the 1920s at least up to the 1940s. Things got a lot more complicated in that time and I have been hoping to wait to do that stuff after I get out of isolation. However, I've begun the survey of the new developments in that time and hopefully I see something to write about.

[El Arcón No.12268877]

>>12268761
>the particle spectrum of the standard model

[Anonymous No.12268901]

>>12268859
Some broad strokes...

If [math] f(t) = f_0 + f_1 t + f_2 t^2 + \cdots [/math] is an analytic function, then [math]\left(\frac{d}{dt}\right)^n_{t=0} = f_n[/math].
If you got a random variable [math] X [/math] and all [math]f_k[/math]'s are nonzero, then [math]E[f(t X)][/math] already encodes all moments of the distribution, and it depends on both f and the distribution p underlying X. Think characteristic function
https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)#Definition

Roughly, Feynman diagrams are a means to compute such expressions. Big integrals encoding all transition probabilities.
Looking like
https://en.wikipedia.org/wiki/Path_integral_formulation#Expectation_values
And QFT has some Hilbert space'ish framework in the background, defining E[], and of course it spends a lot of time on regularization.

[Anonymous No.12268907]

(d/dt)^n|_{t=0} of f(t),
of course

[Anonymous No.12268941]

>>12268901
Ah, that does help a bit. Wish I had taken more physics courses, just to be more familiar with the notation

[not sketchy at all No.12268961]

>>12268941


I can't find a good Wikipedia page wrapping it up nicely, but how it plays out for QFT goes something like this:

You'll believe that

[math] z_a:=\int_{ -\infty}^\infty{\mathrm e}^{ -\tfrac{1}{2}a\,\phi^2}\mathrm d\phi =(2\pi)^{1/2}a^{ -1/2} [/math]

and

[math] \int_{ -\infty}^\infty\mathrm e^{ -\tfrac{1}{2}a\,\phi^2+i\,\phi\,j}\mathrm d\phi = z_a\cdot\mathrm e^{ -\tfrac{1}{2}j^2\,a^{ -1}} [/math]

And then, much more broadly
When
[math] A_\varepsilon [/math] a matrix with [math] \lim_{\varepsilon\to 0}A_\varepsilon = A [/math] in some sense.

And the info of the system is encoded in a big sketch

[math] Z_f(J):=\lim_{\varepsilon\to 0}\int_{ -\infty}^\infty\,f(\phi)\,\mathrm e^{\frac{1}{2} \left\langle\phi\left|\,A_\varepsilon\,\right|\phi\right\rangle +i\,\left\langle\phi\left|\right.J\right\rangle}\prod_{i=1}^m \mathrm d\phi_i [/math]

which is what you want to get at.
(You can think of the exp being introduced as the flow on a Lie group or coming from the Schrödinger equation v'=iH·v that's solved by v=exp(tH).)

So firstly, f the constant function 1 gives
[math] Z_1(0):=\int_{ -\infty}^\infty \mathrm e^{ -\tfrac{1}{2}\left\langle\phi\left|\,A\,\right|\phi\right\rangle} \prod_{i=1}^m \mathrm d\phi_i = (2\pi)^{m/2}(\det A)^{ -1/2} [/math]

and more broadly this gets to
[math] Z_1(J):=\int_{ -\infty}^\infty \mathrm e^{ -\tfrac{1}{2}\left\langle\phi\left|\,A\,\right|\phi\right\rangle +i\,\left\langle\phi\left|\right.J\right\rangle}\prod_{i=1}^m\mathrm d\phi_i = Z_1(0)\cdot\mathrm e^{ -\frac{1}{2}\left\langle J\left|\,A^{ -1}\,\right|J\right\rangle } [/math]

And finally, with some effort,

[math] Z_f(J) = Z_1(0)\ f\left(-i\frac{\partial}{\partial J}\right)\,\mathrm e^{ -\frac{1}{2}\left\langle J\left|\,A^{ -1/2}\,\right|J\right\rangle } [/math]

You hope that f can be expanded and thus you can compute the big Z component wise. Combinatorics makes those components representable by diagrams (in fact, you can replace computations by drawing)

[Anonymous No.12268996]

The point being that you turned a huge expectation value integral over a lot of smaller ones, over an auxiliary J "parameter" called external source field

https://en.wikipedia.org/wiki/Source_field

But the derivatives are with respect to that field, so at this point you're already deep into functional analysis.

But nevertheless, the generating function Z is "something like" a characteristic function

[Anonymous No.12269062]

>>12268961
>>12268996
Unfortunately this might be a bit out my depth at this point. Still in undergrad and was just wondering about perturbation theory since my prof for 3rd year differential equations mentioned it. I'll look into it though, it's all a matter of getting a feel for some computations you can do, right?

[Anonymous No.12269139]

>>12268814
So they were basically just Brouwer showing that formalism is silly?

[Anonymous No.12269144]

>>12269062
I don't have good examples for plain differential equations.
But for a related tie between the fields, see
https://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula

>>12269139
who's they?

[Anonymous No.12269197]

>>12268710
wow imagine being this salty

[Anonymous No.12269391]

>>12268814
You don't have to go to such lengths to show the weirdness of classical logic. In ZF, the statement [math]\exists x \in \{0,1\} (x = 0 \wedge P) \vee (x = 1 \wedge \neg P)[/math] is true for any P. But there are statements P such that ZF doesn't prove this statement for x = 0 or x = 1. Said otherwise, the existential doesn't commute with provability, or ZF fails the witness property.

[Anonymous No.12269425]

this discussion really makes me think
makes me think that one should stay away for logic and set theory as much as possible

[Anonymous No.12269439]

bifrucation diagrams of the trigonometric chaos functions I posted the other day.

[math]x_{n+1} = a\pi (1+sin(x_{n}))[/math]

[Anonymous No.12269443]

>>12269439
[math]x_{n+1} = a\pi (1+sin(x_{n}))[/math]

[Anonymous No.12269447]

>>12269439
[math]x_{n+1} = a\pi (1+cos(x_{n}))[/math]

[El Arcón No.12269448]

[El Arcón No.12269451]

[Anonymous No.12269719]

Stumbled upon an interesting math problem with my friendos:

How to choose from 3 options using one fair coin in finite number of actions? Probabilities should be equal.

Some of my friends argue it is not possible.
I think not only it's possible, but also you can:
1) solve it in 2 tosses
2) solve it for unfair coin
3) solve for unfair coin and evaluate coin error.

thots?

[Anonymous No.12269721]

>>12269447
>>12269439
neat. i like how there's clear lines where you might naively imagine the function might go but also clearly chaotic patterns. you could probably make some interesting statements about reducing chaos problems to density based problems, but i guess that's the whole of statistical physics.

[Anonymous No.12269745]

>>12269451
Tooker, as one high functioning schizophrenic to another, try to be more cautious with what you classify as truth. I say this from a place of empathy.

[El Arcón No.12269763]

>>12269745
I don't have any disease but I do have a genocidal mania against people who insist that I do. I say this mostly so I can remind you that i said it when I'm killing your family later but if you kill yourself first to avoid it then that is fine with me too.

[Anonymous No.12269839]

>>12266564
PLEASE HELP ME FAST.

Which of the equations in the image are homogenous? I really need the answer in less than an hour and a half. Thanks.

sen=sin btw.

[Anonymous No.12269859]

>>12267274
Lax

[Anonymous No.12269921]

>>12269839
I think just II

[Anonymous No.12269949]

>>12269763
Why is a physics fag like you on /mg/?
Shoo.

[Anonymous No.12269997]

>>12269949
Don't talk that way to Tooker newfag

[Anonymous No.12270399]

All of you are nerds lmao.

[Anonymous No.12270508]

>>12270399

[Anonymous No.12270580]

>>12269719
I'd like to hear your answer.
I can think of a way (replacement sampling) but finiteness is not necessarily guaranteed (although the probability of taking less than n flips approaches 1).

[Anonymous No.12270608]

>>12269719
You hide the coin behind one door and the 2 goats behind the other two. Rest is leftasanexerciseforthereader.

[Anonymous No.12270627]

>>12268753
That's not abstract algebra, or it is, but more specifically it is algebraic geometry.

[Anonymous No.12270642]

>>12269719
Please share, this is a very interesting problem. I don't think it's possible to always solve in finite steps but it might be interesting to prove that you can't simulate it in finite steps. It might also be fun to explore some generalizations of the problem, i.e. like you said, given a procedure with arbitrary probability (unfair coin) can you simulate any other probability in finite steps

[Anonymous No.12270648]

>>12269719
Same anon, it's not possible.
Say your proposed algorithm requires at most [math]n [/math] coinflips. We think of your algorithm as a partition of [math]\{0,1 \}^n[/math] into three equally sized sets (with an element corresponding to a sequence of flips). Clearly this is impossible as the set as 3 does not divide [math]|\{0,1 \}^n| = 2^n [/math].
We can make this argument even if your algorithm involves a conditionally varied number of flips. We do this simply by allowing all possibilities for the remaining unflipped coins.

[Anonymous No.12270665]

>>12269719
Heads, do two at random. (A, and B, lets say)

Tails, do one at random (C)

Then, cycle through these conditions every operation. (ABC, BCA, CAB)

So on average of all the rolls, each one has a 1/3rd chance. I did this in my head, am I right?

[Anonymous No.12270674]

>>12270665
What does "do two at random" mean

[Anonymous No.12270675]

>>12270665
>Then, cycle through these conditions every operation. (ABC, BCA, CAB)
What does this mean?

Your solution is definitely wrong btw because I have a disproof :^) >>12270648

[Anonymous No.12270677]

>>12270674
What an oversight. Well, then you could do this.

You configure them in the order I described in rotating order like I said. Then if heads, you pick the first one, tails, you pick the last one.

[Anonymous No.12270680]

>>12270677
I think you're misunderstanding the problem. You're not trying to get a fair average over multiple runs, you're trying to get a possibility of 1/3 for each outcome.

[Anonymous No.12270681]

>>12270680
I know, but from what I said you could easily restructure it into a solution to do your problem in 1 flip

[Anonymous No.12270686]

>>12270681
No you can't.
You've just reduced reduced the problem to choosing one of (ABC, BCA, CAB) at random, which is the same as the original problem.

Read >>12270648 and tell me what you don't understand.

[Anonymous No.12270689]

>>12270681
and if you want to be funny, you could not have something very easily predictable, something like an irrational number of some sort. For certain ranges you could have certain outcomes. For example, you could have a machine spitting out pie. Well, I have to ask, how predictable is pie?

[Anonymous No.12270691]

>>12270686
forget it man...

[Anonymous No.12270709]

A parabola does not approximate the cosh() function very well.

[Anonymous No.12270758]

>>12270709
[math]\sum _{n=0} ^{\infty} \frac{x^{2n}}{(2n)!}[/math]

[Anonymous No.12270792]

>>12270580
>>12270642
My friends are finitists, so they added requirment of finite steps.

[Anonymous No.12270815]

>>12270792
>not being a finitist
A proof that cannot be demonstrated in finite time is no proof at all.

[Anonymous No.12270827]

>>12270648
True, no way to solve with coin flips only, but maybe there is a way with some additional constructions.

[Anonymous No.12270839]

>>12270815
He's not wrong.

[Anonymous No.12270877]

>>12269719
toss twice
00 - first option
01 - second option
10 - third option
11 - try again

[Anonymous No.12270924]

>>12270877
1) non equal probabilities
2) no guarantee its finite.

[Anonymous No.12270960]

>>12270924
1) the probabilities are equal
2) process terminates with probability 1

[Anonymous No.12270971]

>>12270877
>two tosses

[El Arcón No.12270978]

>>12270627
I understand that algebraic geometry is an area within abstract algebra.

[Anonymous No.12270979]

>>12270960
>the probabilities are equal

[Anonymous No.12270981]

>>12270971
yes two tosses and then maybe another two and then maybe another two and so on

[Anonymous No.12271004]

>>12270979
you toss a fair coin twice
heads-heads: outcome A
heads-tails: outcome B
tails-heads: outcome C
tails-tails: start again

yes the probabilities of getting A, B, C are all equal

[Anonymous No.12271012]

>>12268753
>I understand calculus and analysis very well
:^)

[Anonymous No.12271028]

how do you prove: "if every complex root of a monic polynomial P(x) has absolute value at most 1, then P(x) is cyclotomic"

[Anonymous No.12271047]

>>12269719
use the coin to buy a 3 sided dice idiot

[Anonymous No.12271054]

>>12270648
>>12271004

Whom do i believe? >.<

[Anonymous No.12271055]

>>12269719
You can do it in a number of actions that is almost surely finite and has finite expectation, but not one that is bounded in advance.

[Anonymous No.12271061]

>>12271047
Oh nice, a "funny" answer.

[Anonymous No.12271066]

>>12271054
neither
the first assumes fairness requires all outcomes to appear in an equal number of trials
the second leaves the possibility of infinite trials

[Anonymous No.12271093]

>>12271066
Thank you

[Anonymous No.12271101]

>>12269719
I know how to solve it in 2 flips exact.
But i'll hold on the anwer, so you guys can have fun solving it.

(2) and (3) i'm not sure about.

[Anonymous No.12271112]

>>12271101
Did you get the 1 flip method? Depending on the range of the most recently calculated digit of pie, you arrange the outcome in 1 of 3 ways. When you get the outcome, heads means first, tails means last. If you can predict pie it would be breakable.

Fun little thought experiment. It would be fun for a game of seeing how long someone can predict pie.

[Anonymous No.12271121]

>>12271112
I predict pie...in my tummy! haha

[Anonymous No.12271124]

>>12271112
>most recently calculated digit of pi
why bother with the coin if you already have a random number generator

[Anonymous No.12271129]

>>12271124
Hey the coin was your idea

[Anonymous No.12271130]

>>12271066
>the first assumes fairness requires all outcomes to appear in an equal number of trials
Because all outcomes have equal probability by definition of a coin flip.
Please /mg/ this proof is not complicated

[Anonymous No.12271136]

>>12271130
>>12271066
In case I really need to spell this out: the probability of a specific sequence of n-flips is [math]2^{-n} [/math]

[Anonymous No.12271150]

>>12271028
How about the polynomial P(x) = x ?

[Anonymous No.12271193]

Here's how the coin would work MG

ABC

Do all the math stuff, have a coin with an accelerometer and cheap display. When it flips in the air it displays two possible outcomes, with certain colors, then falls.

When you pick it up you can see what two outcomes were selected, and which one it landed on.

[Anonymous No.12271201]

>>12271193
One thing that would make it gameable is adding in some way to monitor which number of pi it's on.

[Anonymous No.12271203]

>>12271150
you're right
there should be an additional assumption that P(x) != x and P is irreducible
i managed to find the proof in case anyone cares
https://arxiv.org/pdf/1507.02419.pdf

[Anonymous No.12271204]

>>12271203
>>12271201
but the clever thing about the game would be, it would seem to the casual observer as thought the coin truly is random, due to the nature of the falling mechanism. You'd even be wrong sometimes. But if you know the way the pie is going you know the order, and your chances go from 1/3 to 1/2.

weird little concept... That's why I think it'd make a fun game. Especially to play for money with pi. You add in the element of time, the coin flipping, and being able to calculate it all, it'd be really interesting in competition. If it's even possible. Or worth anyone's time... but a fun novelty

[Anonymous No.12271232]

>>12271204
There's a simple way to fix the issue of .333 and dividing and shit.

If the digit of pie is 0, for example, discard that result and assume the next one. So, 1-3 = A, 4-6 = B, and 7-9 = C.

So yes, you can get 3 results after one coin toss, it'd just take a lot of math and logic. That's my answer.

[Anonymous No.12271271]

>>12271193
Retarded solution.
If you already have a display that randomly chooses two colours out of three, you might as well shove the coin up your ass and just always pick the one in the left, and then each of the three possibilities is equally likely to be picked.

[Anonymous No.12271277]

>>12271271
But it’s a coin, there are are two possibilities in each toss.

The coin decides two possibilities in the air, gravity decides the final result.

[Anonymous No.12271497]

>>12270758
It indeed seem like a better approximation (if I got it right). How did you come up with this formula?

[Anonymous No.12271503]

>>12271497
It is the Taylor series expansion of [math]\cosh x[/math].

[Anonymous No.12271519]

>>12271028
This makes no sense. You can write down a polynomial with any roots you want.

[Anonymous No.12271525]

>>12271203
>P is irreducible
every complex polynomial is reducible or degree 1

[Anonymous No.12271530]

>>12271525
>>12271519
fuck obviously it's supposed to be polynomials with integer coefficients, and we're talking about reducibility in Z[x]

[Anonymous No.12271532]

>>12271497
I dont think you did. Should be 1 + x^2/2! + x^4/4! + ... = 1 + x^2/2 + x^4/24 + ...

[Anonymous No.12271537]

>>12271530
Who the fuck talks about complex roots of polynomials with coefficients in Z? Why would I ever assume you mean that instead of assuming you're just dumb? I fucking despise algebraists and number theorists.

[Anonymous No.12271649]

>>12271537
It's basic cyclotomy theory, lad. Chill.

[Anonymous No.12271673]

>>12271649

[Anonymous No.12271693]

I'm actually starting to like maths much more than I used to. Not sure what changed.

[Anonymous No.12271890]

>>12267471
Based all savants like Newton,gauss,Ramanujan etc. were lead by divine intervention

[Anonymous No.12271933]

>>12271537
>Got filtered by fucking complex numbers
Seethe

[Anonymous No.12272177]

I've never felt such disdain for life as I had when reading the coin toss posts. Do the people that claim to have solutions not speak English well or do they not speak math

[El Arcón No.12272331]

I know there's a mathematical theory of probability that is useful for applications but in physics best practice dictates that probability distributions should only be trusted if they result from taking a large sample of statistics.

[Anonymous No.12272363]

What's a good way to see that the imaginary part of [math]log z[/math] is [math]arg z[/math]?

Seems like my professor just pulled it out of his ass. Should I try comparing the Laurent series?

Not a hw question btw (not a proof based course anyway) I'm just trying to get a sense for intuition here

[Anonymous No.12272367]

>>12269763
I'm not saying you have a disease. Schizophrenia isn't inherently negative, it's just a way of thinking. But it has its drawbacks as all do, and the main one is hastiness with drawing conclusions, especially when inspired by overwhelming emotion

[Anonymous No.12272371]

>>12272363
for real x,y
e^(x+iy)=e^x ( siny + icosy)

[Anonymous No.12272379]

>>12272371
>for real x, y

[Anonymous No.12272382]

>>12272363
[math]log(r*e^{i\theta}) = log(r) + log(e^{i\theta}) = log(r) + i\theta[/math]
therefore,
[math]log(a+ib) = log(|a+ib|) + arg(a+ib)[/math]

[Anonymous No.12272402]

>>12269719
What about this:
>with 2 flips, you have 4 possibilities:
>HT, TH, TT, HH
>assign all possibilities but HH to one option
>each of HT, TH, and TT are equally likely, 1/4 likelihood each
>if you get HH, do nothing and restart
Technically it could be infinite and you could do HH infinite times but realistically you will eventually get one of the assigned combos

[Anonymous No.12272447]

>>12269391
Can x be free in P? If so let P mean x=1
If x can't be free in P then I don't see anything particularly wacky about this fact. Could you give an example of P where this is true but you can't prove it?

[Anonymous No.12272522]

>Begin studying mathematics with basic arithmetic.
>Pretty quickly catch up and develop a fairly good comprehension of it overall.
>Start dreaming in mathematical symbols and logic.

I don't like this.

[Anonymous No.12272529]

>>12272447
Oh never mind I see what you're saying, this is basically a way of saying "woah look we have LEM but we also have undecideable statements". Yeah I can see how that makes classical logic wacky

[Anonymous No.12272535]

>>12272522
What is the subject of the dream? That sounds pretty epic and I wish I could have that

[Anonymous No.12272552]

>>12272535
The abstract conceptualization of the equation, or perhaps "equanimity" has been suffused throughout the logic of my dreams.

It's almost like my brain is attempting to leverage the new language to compress information.

[Anonymous No.12272574]

>>12272552
You are becoming a formalist. Many such cases!

[Anonymous No.12272705]

>>12272522
Don't you though?

[Anonymous No.12272711]

>>12271693
Same, but it's happened so late in uni that I'm stuck in a life of wage slavery. at least I'll be making 10-15x the salary of a grad student so that lessens the pain.

[Anonymous No.12272722]

>>12272535
this doesn't happen with you? my dreams are almost always about math. it's usually stressful though because I formulate the problems I'm facing correctly but without pen or paper I seldom make progress. once in a while though I'll figure out a step to a proof in a dream and that's pretty nice :)

[Anonymous No.12272748]

>>12272535
I never dream anything too abstract but I sometimes dream I'm explaining concepts to someone or something along those lines. Last time I was lecturing my brother on linear algebra, iirc

[Anonymous No.12272789]

Two things:

What's the best way for an undergrad to relearn long division?

Are there any useful applications of the non-negative rationals or non-negative reals that don't also show up in the full rationals and reals?

[Anonymous No.12272796]

>try to discern the probability that an event occurs on the first trial but not the second trial
>2 possible outcomes per trial, let's say
>you can either say there are 4 possible cases, and event occuring first time but not second time is 1/4 of the cases
>or you can say, if the event doesnt occur at all on the first trial, forego the second trial
>this leaves 3 possible cases, making the probability 1/3
But why should it be different?

[Anonymous No.12272803]

>>12272789
>What's the best way for an undergrad to relearn long division?
Purple math dot com

[Anonymous No.12272813]

>>12272705
My area of expertise is in abstract linguistics, so, it's a little weird.

[Anonymous No.12272814]

>>12272796
The cases only have equal probability if you divide them up the first way.

[Anonymous No.12272817]

>>12272813
Where would one start learning the nature of grammar to help learn a language practically?

[Anonymous No.12272827]

>>12272814
How come?

[Anonymous No.12272835]

>>12272817
Always start with your native language, and then English, and then Latin.

You're going to want to determine if you're a descriptive or prescriptive grammarian; sometimes you'll naturally align with one school of thought, and this will direct your subsequent studies organically.

If you're white this shouldn't be an issue.

[Anonymous No.12272861]

>>12272552
very nice
embrace this compression and abstraction and ascend
don't devolve back into the prose sentence inner consciousness bugmen

[Anonymous No.12272895]

>>12272861
I'll be honest, I didn't realize just how arbitrary many of the conventions in mathematics actually are. For example, -5 - (-14) equaling positive 9.

Try as I might, I just don't fully comprehend the logic behind it. I understand that it needs to be this way for the distributive property to function, but still. It's little different than the conventions of language.

[Anonymous No.12272897]

I know that (a*b) mod m = (a mod m) * (b mod m)

does such an identity exist for division?


this is one approach I'm trying to take to calculate a the modulus of a binomial coefficient, where the numerator and denominator would be too expensive to calculate normally (but it's fine to calculate their modulus because of that multiplicative property)

[Anonymous No.12272908]

>>12272835
>If you're white this shouldn't be an issue.
Wait what would be the problem for non whites

[Anonymous No.12272916]

>>12272897
Yes. You need the denominator to have an inverse mod m for division to make sense. This occurs when it is coprime to m.

[Anonymous No.12272930]

>>12272908
Lower brain volume and less sophisticated cortical processing faculties.

Most non whites don't even think with delineation, they think more like animals without articulating verbally their thoughts, feelings, or abstractions.

[El Arcón No.12272936]

>>12272367
>it's just a way of thinking.
The dictionary and I both disagree with you. Schizophrenia is the most debilitating psychiatric disease that exists. All of the other psychiatric diseases are less serious.

>especially when inspired by overwhelming emotion
Pic doesn't say, "Wait til you cool off, Lord, and then act with some careful measure of vengeance."

[Anonymous No.12272944]

>>12272916
holy shit anon that's exactly what I want
I found a khan academy article about it which seems to also mention a faster algorithm! thanks so much

[Anonymous No.12272962]

>>12272522
Anon you've learned long division, you're not fucking Hamilton

[Anonymous No.12272971]

>>12272962
I'll have you know I also mastered fractions. Lookout Einstein.

[Anonymous No.12272988]

>>12272936
>when inspired by emotion
That's not what I meant. I don't mean the emotion that causes the action, I mean an uncertain emotion that forces one to believe a judgement. For me, delusions have just been anxieties that are so overwhelming I've been forced to believe them as true. The reason this isn't an illness is because the same thing that causes the anxiety and their intensity is a powerful pattern recognition machine.

[Anonymous No.12272992]

>>12272962
>anon makes post about his dreams
>YOURE RETARDED YOURE NOT ALLOWED TO HAVE DREAMS

[Anonymous No.12272995]

>think of myself as logic
>still get paranoid after watching a horror movie and can't sleep


god I have being a h*man being we are such emotional bags that will NEVER make it

[Anonymous No.12272998]

>>12272992
I am actually a psychoanalyst so please feel free to post your dreams and I'll interpret them.

[El Arcón No.12273008]

>>12272988
A delusion is a belief which is easily disproven. I don't have any of those.

[Anonymous No.12273026]

>>12273008
Many things are difficult to prove or disprove. Many things are thought to be illusory and turn out true, and the converse.

[Anonymous No.12273028]

>>12272998

my dreams are the depressive episodes of twilight zone

[Anonymous No.12273035]

>>12273028
Tell me about one.

[Anonymous No.12273042]

https://www.mathscareers.org.uk/article/calculating-pi/

We have the technology

[El Arcón No.12273046]

>>12273026
For instance, you don't believe that all curses I've written will come to be. You don't think I'm going to make your people regret your having written the things you wrote. That's a wrong belief but it's not a delusion because their is no proof of your wrongness. When I do prove it, however, then everyone will know.

[El Arcón No.12273049]

>>12273026
For instance, you don't believe that all the curses I've written will come to be. You don't think I'm going to make your people regret your having written the things you wrote. That's a wrong belief but it's not a delusion because there is no proof of your wrongness. When I do prove it, however, then everyone will know.

[Anonymous No.12273051]

>>12273042
If the universe is a holon then all we're doing is zooming in on a fractal. The deeper we calculate pi, the longer it gets.

[Anonymous No.12273056]

>>12273046
>>12273049
/mg/ is on your side, 2ker
You will always be welcome here

[Anonymous No.12273058]

>>12273051
Who cares man I have a coin game

[El Arcón No.12273085]

>>12273056
Then why did this other bullshit math problem
>An anonymous 4chan post could help solve a 25-year-old math mystery
>https://www.theverge.com/2018/10/24/18019464/4chan-anon-anime-haruhi-math-mystery
end up in the news the same time I posted my RH solution, pic related, and you all still refuse to praise my name for the good things I've done? Seems to me like you're on the side of the parties who insist that you never praise my name, ever, regardless how many good things I've done or how much good news there is to spread about me.

You might tell yourselves that it is possible to serve two masters. I, however, do not subscribe to that notion.

[El Arcón No.12273090]

[Anonymous No.12273104]

>>12273049
Or perhaps I am trying to explain to you how I do not insult you out of my belief in your potential to cause worldwide suffering :P. But I have goals too, and you'll have to outpower my Galactic Body if you're too slow.

[Anonymous No.12273110]

>>12273085
None of us work in the media though so we have no influence over this

[Anonymous No.12273117]

>>12273035

There's one for example that my helicopter mom just awakes up and kicks me out of her house in the middle of the night for not reason. The dream then is me feeling very hungry, thirsty or wanting to piss/shit really bad while trying to hide from nightlife menaces like crackheads, mobs of criminals and even some supernatural ones or screaming myself to soreness begging her to let me in. The dream seems to be stuck forever at night too, the sunrise never comes.

[Anonymous No.12273121]

>>12273117
Do you live with your parents?

[Anonymous No.12273129]

>>12273121

only with my mom

[Anonymous No.12273133]

>>12273129
And you're a virgin?

[Anonymous No.12273143]

>>12273133

that's a given

[El Arcón No.12273154]

>>12273110
I see what you're saying there. Do you see what I'm saying about me wanting you all to praise my name in public and spread the good news about me, and my adversary wants you not to do it, and you do exactly what he wants 100% of the time?

>>12273104
When you call me that word, I am insulted. You know I don't like it and you insist on doing it probably for that exact reason.

[Anonymous No.12273172]

>tfw can't stop using wolframalpha to compute streamlines for ideal flows

how do i break my addiction? someone give me some good, articulated reasons for why I need to struggle through these derivations

[Anonymous No.12273178]

>>12273143
Being kicked out of your home by your mother, in the middle of the night, for "no reason" is a lovely analogy for rejection by the archetype of nature as personified by the mother. You feel hungry, thirsty, and wanting to relieve yourself; this is a metaphor for the desire to satiate the instincts of the body, and of the unconscious. Repression is your issue.

You're failing to properly transition into the next stage of life, and the outside world looms large and menacing. In traditional tribes you would be ripped away from your mother by the men of the tribe and initiated, through pain and ritual, into manhood.

The perpetual night is an imagistic representation of the fact that you are remaining unconscious of your destiny and potential as an individual to differentiate yourself from your parents and from your persona; the personality you've had constructed on behalf of society to allow you to control and suppress the basal instincts.

These instincts need release.

Otherwise you'll be rejected by the feminine and condemned to an endless unconsciousness; a dark night, teeming with monsters and supernatural entities seeking you hard and projected out from within.

[Anonymous No.12273183]

>>12273154
How else can I speak with you but publicly?

[Anonymous No.12273188]

>>12273117
>she kicks you out
Its a natural and even reasonable fear, incapability against a future that haunts. Start learning lifeskills now.

>>12273172
It's good practice.

[Anonymous No.12273205]

>>12273178

Should I have sex with an escort so my unconcious gets over it? Pretty rude of my body to torture me with dreams like these because of pussy ... besides of shitposting on 4chan I use all of my time working out and studying which I know is going to do more good to me than women.

[Anonymous No.12273208]

>>12272796
>>12272814
I just programmed it on my computer and both methods give 1/4 probability, experimentally. Can someone elucidate? I was even starting to think the 1/3 rationale makes sense, since there's 3 possible outcomes.

[Anonymous No.12273213]

>>12273205
No, move out and stop living with your mom if you can, or if you can't, start doing your own chores, laundry, cookinge etc. Become independent as much as you can so that you don't fear it. And distance yourself from Mutter, helicoptering is psychotoxic.

[Anonymous No.12273215]

>>12273205
No, that's unwise.

>besides of shitposting on 4chan I use all of my time working out and studying which I know is going to do more good to me than women.
If you aren't trying to become attractive to women then what precisely are you doing?

[Anonymous No.12273230]

>>12266607
Learning material quickly is over-rated. You want to push the boundaries of your understanding so it's slow and thorough. The earlier you hit this point, the deeper your fundamentals will be.

Be patient and don't rush it. If you hit this point early, it means your fundamentals have the potential to be that much deeper. Just dig deep.

[Anonymous No.12273256]

>>12273213

I can do that but the moving out part -- she's elderly already and will need my care soon plus the house is big enough for me to have my personal space if I want to.

>>12273215

Because it feels good to lift the big weight and learn the big math

[Anonymous No.12273270]

>>12273208
Just counting possible outcomes only works if the outcomes all have the exact same probability. This only happens in very simple problems and it's a very easy condition to break. Try working it out for the case of a biased coin that gets heads with probability p and then plug in p =1/2

[El Arcón No.12273282]

>>12273154
I don't know who you are so I cannot say. In any case, I don't see you praising my name and proclaiming my good works, in public or elsewhere.

[Anonymous No.12273322]

>>12272992
I've just met so many larpers man.

[Anonymous No.12273327]

>>12272992
>YOURE RETARDED YOURE NOT ALLOWED TO HAVE DREAMS
This but unironically.

[Anonymous No.12273522]

>>12273270
But how can you tell that the likelihood of HT is less than the probability of T- other than by counting the outcomes?

[Anonymous No.12273537]

>>12273270
>>12273522
Oh, I think I figured it out. Even if you don't flip again if you get T, T still occurs just as often as any pair starting with H. So there are as two Ts in the final outcome, HT, HH, T, T

[Anonymous No.12273552]

>>12273522
Multiply out the probabilities. HH = p^2, HT =TH =p(1-p),TT =(1-p) ^2

[Anonymous No.12273602]

>the problem has a hint
>ignore the hint

[Anonymous No.12273639]

Okay let me explain this because I clearly didn't write enough for /mg/ to get it >>12270648

Suppose your method requires at most [math]n[/math] flips. You might use less than [math]n[/math] flips depending on earlier flips. Consider all allowed sequences of flips under your algorithm. What your algorithm is doing is assigning each allowed sequence to one of the three options. You might argue that you could ignore the order of flips (all or some of them), but then all that's happening is you're just assigning sequences which are permutations of each other to the same option.
Now suppose we modify the algorithm slightly. If there is a sequence of less than [math]n[/math] flips which we use to make a decision then modify the algorithm to keep flipping (until [math]n[/math] total flips) after the decision has been made but just ignore the later flips.
For example, maybe [math]n=3[/math] and your algorithm assigns HT to the first option. Then the modified algorithm assigns HTH and HTT to the first option. We note that the assignments from the modified algorithm have the same probabilities as the original one (this is the sum rule of probability).
The modified algorithm is an assignment of each element of [math]\{0,1\}^n[/math] to one of the three options. Since each element of [math]\{0,1\}^n[/math] has equal probability ([math]2^{-n}[/math] the algorithm must partition [math]\{0,1\}^n[/math] into three equal sets if we want there to be an equal probability. This is impossible as 3 does not divide [math]|\{0,1\}^n|=2^n[/math].

Please /mg/, this is not a difficult proof to understand. I'm happy to answer any questions you have about it. If I see one more fucking person claiming it is actually possible...

[Anonymous No.12273711]

>>12273602
>get stuck
>bash head against problem for days
>quit, promise you'll come back to it later
>still haven't seen the hint

[Anonymous No.12273717]

>>12273639
Your proof is mathematically sound but has no relation to the real world thus irrelevant to the problem.
>>12271004
Correct.
>>12271066
>the second leaves the possibility of infinite trials
No it doesn't. The logical possibility of an infinite sequence of heads does not mean it's actually possible.
In reality, eventually you will get a different result and anon's argument always terminates in a finite number of steps (to be more specific, you never need to throw more than 30 times).

[Anonymous No.12273740]

>>12273717
>The logical possibility of an infinite sequence of heads does not mean it's actually possible.
???
>to be more specific, you never need to throw more than 30 times
????
What about the sequence TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT?

[Anonymous No.12273748]

>>12273740
>What about the sequence TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT?
It's an impossible sequence. It will never happen in real life.

[Anonymous No.12273753]

>>12273748
>>12273740
You can prove me wrong by showing me one(1) video of some person rolling 30 tails in a row. But it doesn't exist because it's actually impossible.

[Anonymous No.12273759]

>>12273753
I wrote a python simulation and it only took 7 seconds for it to happen.
>ultrafinitists on suicide watch

[Anonymous No.12273763]

>>12273759
>python simulation = doing it in real life
Why don't you go write a python simulation for having sex?

[Anonymous No.12273767]

>>12273763
I'm already drowning in pussy as an applied math CHAD. Keep flipping those coins though anon!

[Anonymous No.12273772]

>>12273767
My point is that python simulation and real life is not the same thing.
For a python simulation, the limit number is more like 200.
Still in real life it's impossible to get a sequence of 30 tails.
Anon's algorithm will always terminate in less than 30 tosses, and that's a scientific fact.

[Anonymous No.12273782]

>>12273767
Also as an appliedfag you should be first to realize that anon's algorithm is the correct solution and that it always terminates in less than 30 tosses.
Do you also consider
1,1,1,1,1,1,1,..... (all 1s)
to be a uniformly random sequence of 0s and 1s?

[Anonymous No.12273783]

>>12273772
>scientific fact
You appear to be in the wrong thread anon. Scientists aren't exactly welcome here.

[Anonymous No.12273793]

>>12273783
It's also a mathematical fact (in the sense of Arnol'd).

[Anonymous No.12273797]

>>12273782
>to be a uniformly random sequence
Define uniformly random sequence. I have no such notion.

[Anonymous No.12273803]

>>12273797
A sequence of independent random variables with Bernoulli p=1/2 distributions.
I know that technically random variables are just measurable functions from the outcome space but you could view them in this case as just a particular certain outcome (identified with the value of that outcome of each random variable).

[Anonymous No.12273814]

>>12273803
The sequence (1,1,1,...) is in the outcome space.
It of course has probability zero in the measure theoretic sense.

[Anonymous No.12273824]

>>12273814
>It of course has probability zero in the measure theoretic sense.
As does every sequence.
My point is the sequences are not distinguished mathematically and are all equally random. However, in reality nobody considers the sequence
1,1,1,1,1(all 1s) to be a random sequence. However, they do consider the sequences that a pseudorandom algorithm generates to be random or at least more random.

[Anonymous No.12273831]

>>12273824
>>12273824
>nobody considers the sequence
>1,1,1,1,1(all 1s) to be a random sequence
You keep using this term "random sequence" but I don't think you have any definition or understanding of what it means.

[Anonymous No.12273834]

Two hundred fifth for the Cartan-Hadamard theorem.

[Anonymous No.12273846]

>>12273834
>250th = Two hundred fifth

[Anonymous No.12273851]

>>12273846
Stop posting.

[Anonymous No.12273859]

>>12273846
I want to pretend it was bait, but it wasn't, airhead moment.

[Anonymous No.12273864]

>>12273851
Never. If I don't bulli the anime poster, who will?

[Anonymous No.12273866]

>>12273782
>Do you also consider 1,1,1,1,1,1,1,..... (all 1s) to be a uniformly random sequence of 0s and 1s?
There is no such thing as a random sequence. There are randomly generated sequences, but that is a property of the process that generated them, NOT a property of the sequence. So the question of whether [1,1,1,...] is a random one is meaningless.

[Anonymous No.12273872]

>>12273864
That's not just any anime poster...

[Anonymous No.12273875]

>>12273872
Go on.

[Anonymous No.12273881]

>>12273866
This is what bourbaki does to your brain. Embarrassing.

[Anonymous No.12273884]

>>12273875

[Anonymous No.12273887]

>>12273881
Go on anon, give a definition of a random sequence. We're all waiting.

[Anonymous No.12273888]

>>12273884
Oh man it's been a while

[Anonymous No.12273892]

>>12273887
Just stop posting bro. You're embarrassing yourself.

[Anonymous No.12273901]

>>12273892
The thing I'm most embarrassed about is the fact that I'm posting in the same thread as glue eaters like you. Every time someone mathematically BTFOs you you just respond with memes because you have no idea what you're talking about.

[Anonymous No.12273914]

>>12273884
what is this

[Anonymous No.12273919]

>>12273884
Based.

[Anonymous No.12273931]

>>12273914
https://nucular.github.io/stuff/magicpng/

[Anonymous No.12273934]

>>12273887
No finite sequence can be random, because there is always a function describe it. As far as infinite sequences? I think they can be un-embeddable in reality, maybe letting them be random

[Anonymous No.12273938]

>TRAI HOX

[Anonymous No.12273942]

>>12273938

[Anonymous No.12273969]

>>12273931
ah that's interesting, I'm on Safari so I saw a flash of a man saying ""JE REVIENS BIENTOT"" but then the image was otherwise the same. Back to PDE I guess :)

[Anonymous No.12273971]

>>12273934
The term you are looking for is "noncomputable sequence". Exercise: show an infinite Bernoulli sequence is noncomputable with probability 1.

[Anonymous No.12273978]

>>12273971
>noncomputable
Not the same thing as random

[Anonymous No.12273986]

>>12273978
I agree. What you described (not describable by a function) is noncomputable though.

[Anonymous No.12273994]

Which one of you took my whiteboard sharpies

[Anonymous No.12273996]

>>12273986
Fair enough.
I am imagining that anon who said random sequence is a meaningless term going back in time of Euler and telling him everything hes doing is pure nonsense because he doesnt have a rigorous definition of a real number or screetching at anyone whos done probability theory before Kolmogorov.

[Anonymous No.12274002]

>>12273994
Me.

[Anonymous No.12274003]

>get a math problem
>throw a bunch of random thoughts and sentences together, not thinking at all
>put "QED" at the end, call it a "proof" and hand it in
>professor lauds me for my brilliance
Lol this is just too easy. Shouldve gone to the humanities instead.

[El Arcón No.12274008]

>>12273759
how many coin flips in 7 seconds?

[Anonymous No.12274030]

I just realized that the division axiom symbol with the long line ( [math]n\overline{)12345}[/math] ) is actually so uncommon in higher academia that you cant do it in Latex without some trickery

https://tex.stackexchange.com/questions/131125/better-way-to-display-long-division

How weird is that

>>12274002
Give it back you monster

[Anonymous No.12274047]

>>12273971
"With probability 1" do you mean that no infinite B sequences can be computed? What if its an infinite sequence such as 0000.... or 111...?

>>12273978
>>12273996
I'm proposing that it might actually be the same. Randomness in my opinion is actually a difficult philosophical concept, because random means "no pattern." What could a thing with no pattern be other than nonexistent? I would say noncomputable numbers are nonexistent at least within the domain of math; they can't be effected by or effect any other systems in math because their value is meaningless, or at least the part that's noncomputable is (but maybe they have a lower or upper bound that can be worked with)

[Anonymous No.12274049]

>>12274030
I only use fractions and never perform long division, I don't even understand how it works and never have. You can divide any fraction by simplying expanding it into tenths.

[El Arcón No.12274060]

>>12274030
[math]\big|\overline{\,12345}[/math]

\big|\overline{\,12345}

[El Arcón No.12274066]

$\big|\overline{\vphantom{\hat 1}\,12345}$

[Anonymous No.12274118]

>>12274047
>I would say noncomputable numbers are nonexistent at least within the domain of math
Computability is a property of functions, not numbers.
The most charitable interpretation I know of (in the sense that it makes what you're saying mathematically meaningful) would be to identify this
>but maybe they have a lower or upper bound that can be worked with
with the Church-Kleene ordinal, but that's still countable and hence far from the measurable cardinals required for traditional probability theory (maybe you can get around it with Solovay's R, but that's not my bailiwick).
To get a loose idea of the size of the infinities required, consider that the infinite sequence of coin flips is probabilistically equivalent to drawing from an urn containing balls of 2 colors, where the number of balls is "so infinite" that the relative proportion of the colors remains 0.500000... even as you're removing balls in sequence (and that's just for finite sequences; admitting infinite sequences as measurable just introduces even more complications).

tl;dr Identifying randomness with noncomputability may be philosophically appealing, but there is little mathematical motivation to do so as it renders standard probabilistic calculations incoherent.

[Anonymous No.12274153]

Why are some people so bad at communicating math? I'm working with someone who fills his LaTeX homework with just loads of mathematical fluff. I've ripped on him every time I read it because he just absolutely refuses to be concise and clear. Furthermore, the math jargon he uses is just absolute cringe. Any ideas on how I can convince him to not LaTeX like a mong?

[Anonymous No.12274157]

If I have two independent and identically distributed random vectors [math] X,Y[/math] with distribution [math] n(0, \Sigma)[/math] how can I show that they're independent at each component? I know that in general this isn't true so I guess that the fact that they have normal distribution is important, I've been fiddling with their joint PDF but I get stuck quickly

[Anonymous No.12274179]

>>12274153
>Furthermore, the math jargon he uses is just absolute cring
example?

[Anonymous No.12274184]

>>12274157
You can find the distribution at each component by integrating over the other components. You then want to use your independence assumption to write this integral as the product of two integrals, corresponding to a component in X and Y respectively. You shouldn't need to actually evaluate any of the integrals.

[Anonymous No.12274188]

>>12268871
>tension in my neck and shoulders
try using a lighter tin hat

[Anonymous No.12274205]

>>12274153
Are they an undergrad? If so it's fine they just need experience. If you have the time maybe give them examples of how to write it more succinctly

[Anonymous No.12274210]

>>12273090

[Anonymous No.12274284]

>>12274153
takes a while to learn how to do it comfortably. when i grade all the students put the three dots in triangles, right side up and upside down. i have no idea what they mean. if i ignore them, the argument is still perfectly coherent. i think one of them means "therefore". they write one or the other on every line and never just english words.
i want to mark them off for being disgusting morons, but i don't, they'll learn later.

[Anonymous No.12274294]

>>12274030
long division feels like less of a symbol to be used in an expression, and more of a tool to compute a division symbol or fraction to decimal notation.

[Anonymous No.12274297]

>>12274157
If the joint distribution of (X,Y) is normal, then they're independent iff uncorrelated, i.e. the covariance matrix [math]\Sigma = \begin{pmatrix} \textrm{Cov}(X,X) & \textrm{Cov}(X,Y) \\ \textrm{Cov}(Y,X) & \textrm{Cov}(Y,Y)\end{pmatrix}[/math] is block-diagonal, i.e. [math]\textrm{Cov}(X,Y)=0[/math].
In particular, the individual components [math]\textrm{Cov}(X_i,Y_j)=0[/math] are uncorrelated, and since they're also (univariate) normally distributed, they'll be independent.
This is easier to see when you're working with the joint MGF (or characteristic function) rather than the joint PDF, in particular the generalization to multivariate X,Y is straightforward and avoids the need to fiddle with iterated integrals.

[Anonymous No.12274313]

>>12274157
If the joint distribution of (X,Y) is normal, then they're independent iff uncorrelated, i.e. the covariance matrix [math]\Sigma= \begin{pmatrix} \textrm{Cov}(X,X) & \textrm{Cov}(X,Y) \\ \textrm{Cov}(Y,X) & \textrm{Cov}(Y,Y) \end{pmatrix}[/math] is block−diagonal, i.e.[math]\textrm{Cov}(X,Y)=0[/math].
In particular, the individual components [math]\textrm{Cov}(X_i,Y_j)=0[/math] are uncorrelated, and since they're jointly (bivariately) normal distributed, they'll be independent.
This is easier to see when you're working with the joint MGF (or characteristic function) rather than the joint PDF, in particular the generalization to multivariate X,Y is straightforward and avoids the need to fiddle with iterated integrals.

>>12274284
>when i grade all the students put the three dots in triangles, right side up and upside down.
If you're referring to the symbol [math]\because[/math]
it's the TeX-approved abbreviation for "because".
Try this: [math]\because[/ math]

[Anonymous No.12274343]

>>12274313
>it's the TeX-approved abbreviation for "because".
unreal

[Anonymous No.12274348]

>>12274313
The because-symbol, like logical connectives and quantifiers, should be avoided in good mathematical text. Leave it for the logicians and the meta-mathematicians.

[Anonymous No.12274406]

>>12274343
Oh yes, and [math]\therefore[/math] is indeed "therefore".

>>12274348
>Leave it for the logicians and the meta-mathematicians.
I don't consider myself an example of either, but I do lots of both, and not once have I ever needed to use \because or \therefore, or even felt the urge to.
Unlike quantifiers and connectives, which have metamathematically meaningful interpretations qua Lindenbaum-Tarski, [math]\because[/math] and [math]\therefore[/math] are nothing but shorthand for people too lazy to spell out English words in full.
That said, those symbols aren't overloaded (unlike [math]\to[/math] or [math]\wedge[/math], say), so there's no chance of ambiguity, making them fairly benign as far as abbreviations go.

Incidentally, my response to >>12274157 illustrates what I consider a justified use of the ugly abbreviation "iff": being "independent iff uncorrelated" (or equivalently, "independent xor correlated") is a single property of jointly distributed random variables, and writing it as
>If the joint distribution of (X,Y) is normal, then they are independent if and only if they are uncorrelated
only seems to obscure the equivalence between the (in)dependence and (lack of) correlation.

[Anonymous No.12274414]

>>12272522
>>>Start dreaming in mathematical symbols and logic.
i do this too when i spend too much time on maths. it's all gibberish i think

watch porn and you will dream about porn

[Anonymous No.12274519]

How do you mathiggers understand this shit. I can barely do 12x13.

[Anonymous No.12274527]

>>12274519
https://www.youtube.com/watch?v=SlCRfTmBSGs

[Anonymous No.12274555]

>>12274527
but it's boooooooooooooooooooooring.

[Anonymous No.12274676]

>>12274555

[Anonymous No.12274799]

>>12274348
>The because-symbol, like logical connectives and quantifiers, should be avoided in good mathematical text.
I read this recommendation in other places too, but I consider it a bad one. Nothing wrong with using [math]\land[/math] and [math]\to[/math] to express theorems. Just don't mix it with common language within a sentence.

[Anonymous No.12274840]

[math]\bullet[/math] What textbooks, papers or text did you read today?
[math]\bullet[/math] What non-textbooks did you read today?
[math]\bullet[/math] Did you write something today?
[math]\bullet[/math] Did you do some programming today?
[math]\bullet[/math] Did you build something today?
[math]\bullet[/math] Did you clean up something today?
[math]\bullet[/math] Did you plan something today?
[math]\bullet[/math] Did you manage to work off some bureaucracy/paper work today?
[math]\bullet[/math] Did you practiced any skills today? If so, which?
[math]\bullet[/math] Did you do sports/cardio/weightlifting today?
[math]\bullet[/math] What were you eating today?
[math]\bullet[/math] How much sleep did you get yesterday?

[Anonymous No.12274855]

Apparently I got a simpler and shorter solution to this problem and with less assumptions, compared to the one the book provides. I'd like to see if there's any mistake.

Since [math]M[/math] is finitely generated, there's a minimal integer [math]n \ge 0[/math]. We can assume [math]n>0[/math] wlog. Let [math]\mathfrak{m}, \mathfrak{n}[/math] be the maximal ideals of [math]A, B[/math] and [math]k_A, k_B[/math] be the corresponding local fields, respectively.
By a previous result, the first phrase of the previous paragraph means that [math]V := M/\mathfrak{m}M[/math] is a [math]n[/math]-dimensional [math]k_A[/math]-vector space. Likewise, [math]N/\mathfrak{n}N[/math] is a 1-dimensional [math]k_B[/math]-vector space. However, we have
[eqn]k_B \cong N/\mathfrak{n}N \cong N\otimes_B k_B \cong (M\otimes_A B)\otimes_B k_B \cong M\otimes_A(B\otimes_B k_B) \cong M\otimes_A k_B\cong M\otimes_A (k_A\otimes_A k_B) \cong (M\otimes_A k_A)\otimes_A k_B \cong V\otimes_A k_B \cong k_A^n\otimes_A k_B\cong (k_A\otimes_A k_B)^n\cong k_B^n, [/eqn]
where I used a bunch of the basic properties of the tensor product functor by a fixed module. The one involving the two fields also uses the fact that it's a local homomorphism (but not that it's flat!), which implies [math]\mathfrak{mB}\subseteq \mathfrak{n}[/math].
So we got that [math]k_B \cong k_B^n[/math] as [math]B[/math], and hence as [math]k_B[/math]-vector spaces. Thus [math]n=1[/math] and we're done.

[Anonymous No.12274863]

>>12274855
Fixes:
>"there's a minimal integer [math]n\ge 0[/math]" with [math]M[/math] having [math]n[/math] generators over [math]A[/math]
>[math]\mathfrak{nB}\subseteq \mathfrak{n}[/math]
[math]\mathfrak{n}B\subseteq \mathfrak{n}[/math].
>"So we got [math]k_B\cong k_B^n[/math] as [math]B[/math],"
as [math]B[/math]-modules.

[Anonymous No.12274881]

>>12274840
>What textbooks, papers or text did you read today?
The Rising Sea and Elementary Applied Topology
>What non-textbooks did you read today?
None
>Did you write something today?
No
>Did you do some programming today?
No
>Did you build something today?
No
>Did you plan something today?
I got on a waiting list for a gastroscope
>Did you manage to work off some bureaucracy/paper work today?
I went to the doctor
>Did you practiced any skills today? If so, which?
Not really, a few hours of maths
>Did you do sports/cardio/weightlifting today?
No
>What were you eating today?
Breakfast: oats, sultanas, milk
Lunch: refried beans + rice
Snack: some tuna
Dinner: scrambled tofu
>How much sleep did you get yesterday?
Nine hours

My life is a gigantic mess and I am depressed as shit.

[Anonymous No.12274886]

>>12274881
>My life is a gigantic mess and I am depressed as shit.
Although your day sounds quite based.

[Anonymous No.12275006]

>>12266564
What do I do if I need an advisor for a paper but I'm not in school? How do I go about that?

[Anonymous No.12275033]

>>12274840
i'm reading "classical descriptive set theory" by kechris
i went to a doctor today
gonna study japanese later in the day
"no" to all other questions, sadly

>>12274881
>My life is a gigantic mess and I am depressed as shit
bro... i share this sentiment... good luck...

>>12275006
do you have any kind of math degree?
what do you mean by "advisor for a paper" - someone who's going to help you with writing a paper?
you should write up whatever you came up with, as clearly as possible
then find a person relevant to your topic and politely ask him for an opinion

[Anonymous No.12275046]

>>12275033
Sounds good.
I always quickly got tired about "tree stuff", which is why I never got into descriptive set theory

[Anonymous No.12275238]

New >>12275236