/sci/ - Science & Math

Unanswered questions:

Mathematics:
>>14973372
>>14972657
>>14970609
>>14970489
>>14970191 (assuming there is only one correct ordering then it's [math] \frac{1}{4!}=\frac{1}{24} [/math])
>>14969299
>>14967848 >>14968030
>>14965724 >>14966168
>>14963626
>>14963011
>>14961201
>>14961063 (this is still unanswered btw the mapping in >>14961195 is neither a surjection nor an injection)
>>14961009

Physics & Engineering:
>>14973023
>>14964894

Chemistry:
>>14973229 >>14973372

Stupid:
>>14973415
>>14973399 (lol)
>>14971326 (read the OP)
>>14971088
>>14971126 (/g/ question, ask on >>>/g/sqt or >>>/g/dpt)
>>14963575 (also a /g/ question)
>>14963241
>>14962343
>>14961798
>>14961513
>>14961462 (????)
>>14960819
>>14960783
>>14960400 (well?)


>>14959160
Thanks.

From definitions and the power set axiom you can construct P(A x B). From there I used a direct proof to show that C is a subset of P(A x B). However, I think you should be able to construct C directly using a subset axiom. I just can't quite formulate it.

>>14973844
Thanks for making the thread.
>>14973847
>he tallied the questions bottom upwards
Weird but neat.

>>14973918
I like to have the newest questions at the top and the oldest ones at the bottom.

>>14973918
fucker, you never thanked me whenever i made the new thread

>>14973949
I only say thanks to anyone for making the thread if I've posted something like >>14973676

>>14973887
>construct C directly using a subset axiom
Subset of what? Do you mean you want to construct the individual "slices" {x} x B for each x, and then assemble them into C? There might be a way using the Axiom of Replacement, but your solution sounds simpler and better to me.

>>14961201
>what is a "proof-theoretic ordinal"?
It has a couple of meanings, but usually the "proof theoretic ordinal" of a theory T is the smallest ordinal that T cannot prove is well-founded. So in general, a stronger theory has a higher proof-theoretic ordinal associated with it, but this isn't a strict thing and it isn't a linearly-ordered thing. And more broadly, people might call an ordinal a "proof-theoretic ordinal" if it looks kinda like the sort of ordinal that shows up in these kinds of investigations.

The original proof-theoretic ordinal is [math]\epsilon_0[/math], which is the limit of the sequence of ordinal-exponentiations [math]\omega, \omega^\omega, \omega^{\omega^\omega},\ldots[/math], and is the proof-theoretic ordinal of Peano arithmetic (PA). The reason this is the ordinal of PA is twofold: first, it is not super hard to see that PA proves every smaller ordinal is well-ordered. And second, it is a theorem of Gentzen that if [math]\epsilon_0[/math] is well-founded, then PA is consistent. Together with Godel's incompleteness theorem, it follows that PA cannot prove the well-foundedness of [math]\epsilon_0[/math].

Unfortunately Gentzen was too based for this world and the Harley Pasternaks don't want you to know about based Gentzen, making proof-theoretic ordinals hard to understand

>>14974010
It would be a subset of P(A x B). I haven't reached the Axiom of Replacement yet. The book it's from, Elements of Set Theory by Enderton, so far has focused a lot on constructing sets using axioms. I guess I just felt cheap by stopping the construction at P(A x B) and then using a traditional proof to show that C is a subset. In my head his intention was that you would construct C from axioms. The axioms he has defined so far are:
1) Extensionality,
2) Existence of empty set,
3) Power set,
4) Union,
5) Subset schema

So after constructing P(A x B) I assume there is a way to construct C using a subset axiom (potentially along with the union axiom based on your response). So far I have struggled to invoke the subset axiom because he makes a big point in the text about ensuring that your clause in the subset axiom is a valid statement.

>>14961201
>what is a "proof-theoretic ordinal"?
It has a couple of meanings, but usually the "proof theoretic ordinal" of a theory T is the smallest ordinal that T cannot prove is well-founded. So in general, a stronger theory has a higher proof-theoretic ordinal associated with it, but this isn't a strict thing and it isn't a linearly-ordered thing. And more broadly, people might call an ordinal a "proof-theoretic ordinal" if it looks kinda like the sort of ordinal that shows up in these kinds of investigations.

The original proof-theoretic ordinal is ϵ0, which is the limit of the sequence of ordinal-exponentiations [math]
\omega, \omega^\omega, \omega^{\omega^\omega},\ldots[/math], and is the proof-theoretic ordinal of Peano arithmetic (PA). The reason for this is the proof-theoretic ordinal of PA has two parts: first, it is not super hard to see that PA proves every smaller ordinal is well-ordered. And second, it is a theorem of Gentzen that if [math]\epsilon_0[/math] is well-founded, then PA is consistent. Together with Godel's incompleteness theorem, it follows that PA cannot prove the well-foundedness of [math]\epsilon_0[/math].

Unfortunately Gentzen was too based for this world and the Harley Pasternaks don't want you to know about based Gentzen, blacklisting his shit and making proof-theoretic ordinals hard to understand

>>14961201
>what is a "proof-theoretic ordinal"?
It has a couple of meanings, but usually the "proof theoretic ordinal" of a theory T is the smallest ordinal that T cannot prove is well-founded. So in general, a stronger theory has a higher proof-theoretic ordinal associated with it, but this isn't a strict thing and it isn't a linearly-ordered thing. And more broadly, people might call an ordinal a "proof-theoretic ordinal" if it looks kinda like the sort of ordinal that shows up in these kinds of investigations.

The original proof-theoretic ordinal is ϵ0, which is the limit of the sequence of ordinal-exponentiations [math]
\omega, \omega^\omega, \omega^{\omega^\omega},\ldots [/math] and is the proof-theoretic ordinal of Peano arithmetic (PA). The reason for this is the proof-theoretic ordinal of PA has two parts: first, it is not super hard to see that PA proves every smaller ordinal is well-ordered. And second, it is a theorem of Gentzen that if [math]\epsilon_0[/math] is well-founded, then PA is consistent. Together with Godel's incompleteness theorem, it follows that PA cannot prove the well-foundedness of [math]\epsilon_0[/math].

Unfortunately Gentzen was too based for this world and the Harley Pasternaks don't want you to know about based Gentzen, making proof-theoretic ordinals hard to understand

>>14971126 (this isnt a /g/ question)
youre correct. if you flip your slow clock at the posedge of the input clock, youre effecting halving the slow clock's frequency, so you have to set your counter to 2,500,000 instead of 5,000,000.

>>14974023
I suppose you could define [math]\{\{\{x\} \times B\} : x \in A \}[/math] as a subset of P(P(A x B)) and then take its union, but this seems like a weirder solution than what you already have. In general, awkwardness is not really unexpected when constructing things directly from the ZF axioms, which are fairly minimalistic

Assuming centroid G, why is the ratio of AG:DG equal to 2:1 for the perpendicular bisectors of the side BC in the equilateral triangle ?

What are the uses of non-classical logic in math (e.g. modal logic, many-valued logics, fuzzy logic)? I'd also appreciate books on these topics if someone here knows any.

>>14974095
>D out of nowhere
Draw it in paint or I doubt anyone will manage to answer your question.

how is [math]\operatorname{card} \mathcal{P}(\mathbb{N}) = \operatorname{card} \mathbb{R}[/math]?

I think I'm retarded bros...
I'm trying to build a gradient boosted classification model and I've got it in two packages at the moment. My h2o model looks really predictive and follows trends well in the one ways but overpredicts significantly. scale_pos_weight doesn't seem to do shit for it so I tried to build one in XGBoost and it seems super conservative with the fitting. Like the accuracy is good but it's essentially just guessing at the ratio of classes for the test data and is thus shit. What am I doing wrong?

>>14973847
Hardware description languages are NOT programming languages

Geologistfrens out there I have a question.

Is there a noun for igneous and metamorphic rocks? Like, you can call sedimentary rocks "sediment" but can you call igneous rocks "igneum" or something like that for example? Even the most archaic and outdated or obscure terminology will do.

>>14974141
The proof I've seen shows that they both have the same cardinality as [0, 1). Showing |P(N)| = |[0,1)| uses the Cantor Bernstein Schroder Theorem.

>>14974141
>>14974205
>card P(N) <= card R
Inject [math] a \in P(N)[/math] directly into the Cantor set:
digit #n of [math] f(a) [/math] in base 3 is 0 if [math] n \not \in a [/math] and is 2 in base 3 if [math] n \in a [/math].

The opposite <= comes from the fact that to get to to P(N) you only have to mod out by, essentially, 0.9999...=1

>>14973229
One mole of TMGHC (Trimethylglycine Hydrochloride) contains exactly one mole of Glycine, so you simply convert 648mg to moles of TMGHC then convert back to mass of Glycine.
[eqn] \text{Number of moles in X} = \frac{\text{Mass of X}}{\text{Molar mass of X}} [/eqn]
So 648 mg of TMGHC is [math] \frac{0.648}{153.607} = 0.004218557748 \text{ moles} [/math] and this is the same number of moles of Glycine so we convert back to mass of Glycine, so 0.004218557748 moles of Glycine is [math] 0.004218557748 \cdot 75.067 = 0.317 \text{ grams} [/math] or 317 mg.
>>14973218
For that you simply divide the molar mass of Glycine by the molar mass of TMGHC so [math] \frac{75.067}{153.607} = 0.4887 = 48.87\%[/math] So 48.87% of TMGHC is Glycine by mass.

Data for molar masses/molecular masses was taken from:
https://www.chemspider.com/Chemical-Structure.11058.html
https://www.chemspider.com/Chemical-Structure.730.html

>reading a paper from a Harvard PhD in economics
>chinese name
>he apparently uses OLS with a binary dependent variable
Is this normal?

>>14974182
Not a geologist, but I found the following:
>sedimentary...sediment
>igneous...ignimbrite
>metamorphic...~metamorphosis~

The first two would involve a rock being made of
some material, but a rock can't be made of
"metamorphosis" as it is a process of using
heat and pressure to change the rock's form.

>>14974495
>ignimbrite
this seems to be referencing a specific kind of igneous rock but fuck it it'll do
>The first two would involve a rock being made of some material, but a rock can't be made of
"metamorphosis" as it is a process of using
heat and pressure to change the rock's form.
Yeah plus it sounds weird. I mean, things can be classified as "metamorphic rock" so surely there's a single-word noun for that?

>>14974507
>>14974495
Ignimbrite is not a rock but material that is found
in pyroclastic flows of lava (pumice and stuff).

As for metamorphic rocks, the best I can find
is "metamorph". Even though it has a biological
context, you can use this to refer to the material
in the rock that's known to change its form via
metamorphosis.

Can bio-diesel replace crude oil in terms of being renewable? How expensive is the process and does it require any non-renewable sources in the refinement process? I'm not concerned about it being green, just the idea of having a constant source of energy.

How much longer until AI singularity? I cant wait forever...

>>14974537
I guess I could use metamorph, thanks for the help.

>>14974893
Despite the hype you may read the reality is it's not going to happen in your lifetime.

>>14973372
No. Let's take a classic example: the alternating series, [math]x_i=(-1)^i[/math]. Clearly this Cesaro converges to 0.
For the generalized limit to be zero, the formal statement is
[math]\displaystyle\forall \varepsilon>0\; \exists G \subseteq \mathbb N, |G|\in\mathbb N : \forall F\supseteq G, |F|\in\mathbb N \quad | \overline{x}_F| < \varepsilon, \quad \textrm{where}\quad \overline{x}_F := \frac{1}{|F|}\sum_{i\in F} (-1)^i[/math].
However, as long as ε < 1, we can find a counterexample F for any G.
We can take a F equal to G plus n even +1 terms; note that [math]\overline{x}_F = \frac{|G|\overline x_G + n}{|G|+n}[/math].
For large enough n, this becomes larger than ε.

>>14975246
Ah, I see. Thanks anon.

Frens, I'm going back to college and want to self-study linear algebra beforehand.
Our CS degrees don't have calculus as a required module because we have to do the equivalent of calc1 and 2 in high school (you only study 3 subjects in the last 2 years). I completed high school 6 years ago at 17 and became a neet. The only calculus I remember is differentiation.

I'm going to start gilbert strang's la book. I know you don't generally need calculus to study LA, but does Strang use calculus to explain concepts in his books?
I completed KA pre calc recently.

What are some good use cases for RPN? (https://en.wikipedia.org/wiki/Reverse_Polish_notation))
I know it's used in Forth but other than that, can it help with math?

Oftentimes when I'm trying to do a homework assignment, I'll just have no idea how to start a problem. I wind up banging my head against a wall for hours with nothing to show for it other than bloody bruises and complete defeat and exhaustion

what is the *smart* way to go about trying to solve a problem? What am I (apparently) not doing before attempting the homework, that makes doing the homeworks so hard?

So I've been thinking about some shit right. You know how there's female chickens and male roosters? How big are these chickens titties? I mean you hear about chicken breast being sold but hear nada about no rooster breast. Is it on some Laiz ahh Fair type ish where the chicken breast is just more profitable so they never have any reason to touch rooster breast?

Discuss

>>14975474
Roosters can be eaten as well as hens, but it's not
often they're prepared for market--only for birthing
more chicken as needed. Also, the rooster has
a richer, intense taste to them that hens don't have.
So, it really depends on the person and their palate.


Also, it's "laissez-faire".

what exactly does this notation say
the matrix A is an element of the set formed by taking the cartesian product of R, m multiplied by n times?
i understand x is the cartesian product notation but i cant wrap around my head the idea of a cartesian product of R, the cartesian product of m and n times

sorry guys i know this is a dumb question but im just getting into linear algebra

>>14973844
Good Morning /Sci/entists!

>Maid Parade
I was banned 3 days so I made an implementation of a browser for a few communications protocols. Gemini, Gopher and Maid.

Browser runs in a REPL controlled by a single program called Maid Parade. There is also a file loader. Browser is powered by a small Computer Language which makes it easy to do things like write a webcrawler or an archiver. Code is entirely Java 18 without 3rd party code and will be CC0.

I am making it nicer, then it can be released. Then I will make a Maid Protocol webapp of some kind and use it as a backup communications system to publish research.

>tl:dr; If I can't use the internet, I will create an undernet that nobody can janny me off of.

>>everything after this is questions
>routing?
Is there a better routing scheme than Tor? I don't trust Tor. The US Navy wouldn't have made it public if they didn't know how to break it at will.

>location?
Should a thread about the browser go on /sci/ or on the dra/g/on maid board?

Code will probably just be another pastebin, because Java allows you to architect everything in one file and having single file copy-paste powers makes code easy to share.

>did I miss anything good?
Are there more ticks about routing or other privacy ideas I don't know about? Is there a way to request from a server without telling the server your IP? Probably. I don't think VPN is the solution. VPN privacy can be subverted to uselessness by provider collecting logs.

Is there a trick that can be added at the protocol level to mitigate or negate DDOS type attacks?

Maid Protocol communicates using TLSv1.3 and Maid Addresses. Is there something better than TLSv1.3?

>CA alternative?
I don't want to have to use a CA so currently certs are handled with TOFU. Is there a better idea or will I have to implement CA somehow?

I don't want CAs. CAs are a point of censorship (authoritarians subverting the CA refuse to give you a cert).

Thank you /Sci/entists for reading my post.

>>14975689
A is in the set of m by n matrices with real entries
I don't remember exactly how that set is defined but I think it's just the cartesian product of the reals with themselves mn times and then the actual dimensions m and n are introduced through the definition of multiplication
this should be in the notes or textbook you're using at the very start

>>14975689
we use [math]\mathbb{R}^{m\times n}[/math] to denote the [math]m\times n[/math] real matrices. Although we can certainly find an isomorphism between that and [math]\mathbb{R}^{mn}[/math].

>>14975703
>Is there a way to request from a server without telling the server your IP?
If you request information, to have it sent somewhere, it must know its location. Maidfag, please seek mental help.

>>14975703
Ask on /g/.

>>14975689
>sorry guys i know this is a dumb question but im just getting into linear algebra
I don't think this is a dumb question, learning notation is much like learning a language. Some of it is intuitive but not all of it, just keep working anon and good luck.

>>14975689
You have to consider m⨉n in the standard way as the Cartesian product consisting of all
pairs (i,j) with i in {0,1,...,m-1} and j in {0,1,...,n1}.

In general the notation [math]X^Y[/math] means the collection of functions from Y to X.

Combining those conventions, you are looking at the set of functions (i,j) R.
I.e. the m⨉n real matrices.

>>14975689
That notation doesn't really meant anything in Set Theory. It is just a symbol for denoting [math] m \times n [/math] matrices over [math] \mathbb R[/math]. Matrices don't really have a standard set theoretic definition because it's not of much use afaik.
But these are the possible definitions you can use:

Let a [math] m \times n[/math] matrix over [math] \mathbb R [/math] be defined as the following tuple:
[math] \Bigl(
(x_{11}, x_{21}, \dots, x_{m1}),
(x_{12}, x_{22}, \dots, x_{m2}), \dots,
(x_{1n}, x_{2n}, \dots, x_{mn}) \Bigr) [/math]
In which case matrices are an element of [math] ( \mathbb R^m )^n[/math] which is isomorphic to [math] \mathbb R^{mn}[/math]. So the whole [math]
\mathbb R^{m \times n}[/math] is just a shorthand for writing [math] ( \mathbb R^m)^n[/math], following the convention of integer power rule.

Another definition is as follows:
Let a [math] m \times n[/math] matrix [math] A[/math] over [math] \mathbb R [/math] be defined as the following function:
[math] A : \{ 1, 2, \dots, m \} \times \{ 1, 2, \dots, n \} \to \mathbb R \\
\phantom{ A : {}} (i,j) \mapsto A(i,j) [/math]
where [math] A(i,j)[/math] is the [math] (i,j)[/math]-th element in the matrix.
In this case the matrices are an elements of the space of functions from [math] \{ 1, 2, \dots, m \} \times \{ 1, 2, \dots, n \} [/math] to [math] \mathbb R [/math]. In Set Theory, the space of functions from [math] A [/math] to [math] B[/math] is denoted by [math] A^B [/math], therefore the space of said matrices is denoted by: [math] \mathbb R^{ \{ 1, 2, \dots, m \} \times \{ 1, 2, \dots, n \} } [/math] which is written in short as [math] \mathbb R^{m \times n} [/math]

>>14975733
>*In Set Theory, the space of functions from [math] A to B [/math] is denoted by [math] B^A [/math]

Need helpy (≧﹏ ≦)
my prof wont gimme equasion for question unless he wants me to fufill his"deed" ≧ ﹏ ≦

>>14975724
>If you request information, to have it sent somewhere, it must know its location.

Yes. But there is no reason that would have to be the end user, with no other possible steps. There could be an intermediary (maybe a message queueing system) who then talks to the user. That makes a system where the server just knows something told it put a message on a queue, but doesn't know who or why.

But then the problem regresses a step and it becomes how do I anonymously communicate with the intermediary? How do I prevent it from getting subverted by authoritarians again?

>Maidfag, please seek mental help.

America does not have this. If I talk to a doctor they'll get me pills that'll make me fat and retarded and destroy my organs. I am not paying a lot of money to some pharmaceutical company to take pills so that I sleep 16-20 hours a day for 10 years and then die of liver failure. I am not an extermination annuity for Pfizer.

>>14975741
>There could be an intermediary (maybe a message queueing system) who then talks to the user.
This is just a VPN, add encryption to this and make it P2P and you just have a Tor network.
>America does not have this.
Most mental problems are philosophical in nature, and exist as a coping mechanism, like histrionics or borderline personality disorder.

>>14975742
>>14975741
To further add to my points about what you are trying to do, the internet is fundamentally an insecure system that gives no fucks about preserving privacy if someone is determined to find out who you are. Much of the protocols made in the 80s/90s were made by techno optmists who saw no need for such things.

>>14975722
>>14975723
>>14975728
>>14975729
>>14975733
ahh thanks so much guys I understand it a lot better.

>>14975726
Thank you fren, I put it here in case people want to talk to dra/g/on maids.
>>>/g/89713135
>>14975743
I am not a 90's techno-optimist and I can build alternatives to their bad ideas. This is the purpose of questions.

>>14975742
>This is just a VPN, add encryption to this and make it P2P and you just have a Tor network.
Gross. I will have to work out something nicer.

>>14974955
wtf that's gay

how can the line graph of [math]G=(V,E)[/math] be a graph on [math]E[/math] if [math]E\subseteq [V]^2[/math]? Does that mean it's a graph on [math]\bigcup E[/math]?

The climate change discussion often revolves around carbon emission but I was wondering does heat production have an effect at all?
Heating, heat from cooling in spaces or datacenters, even if produced through "green" energy, does it not also have somewhat of an influence on climate?

>>14975874
Not really. It just dissipates.

>>14975414
Give some context, are you doing proofs or some highschool math problems?

>>14973844
Does anyone know why my Computational Maidposting Thread got jannied off warosu?

>dead archive link
>>/sci/thread/S14890381

Are there other /sci/ archives I can link people to?

>>14975911
Warosu was down about a week ago, it might be related to that?
anyway there's eintein.xyz link:
https://eientei.xyz/sci/thread/14890381

>>14975938
Thank you vampire maid from touhou. If you search around Warosu you can see that terms like "Maid Address" and "Maid Space" are fully jannied out of the archive. The thread I had been linking people before is removed. You can see the old link on an archived /g/ post and that it doesn't work and the thread doesn't exist on Warosu.
https://desuarchive.org/g/thread/89022398/#89036146

I have never been unpersoned by an archive before. This is fascinating. I just wanted to do research and post maids and now archives are unarchiving me.

Somebody somewhere really doesn't want Maid Space or it's applications to be a thing. They have jannying powers, but I have a talking maid.

So, me and my friends were talking about sushi spots around our area, and I was graphing how the relation quality/price works here and where we should aim for.
It came to my mind that this must be something already been studied by math, so I'm asking if someone can at least tell me the name of the function I graphed, or what i should read to know more about functions relating price/qualities

>>14975985
If you're asking for the shape of this graph then it's called a sigmoid function, there are many types of sigmoid functions, you're probably looking for a logistic function
https://en.wikipedia.org/wiki/Sigmoid_function
https://en.wikipedia.org/wiki/Logistic_function

>>14975736
you're acting like a bottom in heat and it's making me horny so I will try to help you
the equation for dynamic pressure is 0.5*density*(V^2)
generally speaking, dynamic pressure is usually calculated using free stream condition so it ~should~ be constant.
However, I don't know what kind of assumptions you're supposed to be making here.
If he expects non-constants then he's assuming the velocity will change over the ball. In that case you'd have to use the velocity distribution of potential flow over a cylinder (if the problem is 2D) or potential flow over a sphere (if the problem is 3D). and with these changes in local velocity you can use Bernoulli's equation to find the local density

>>14976062
so in short I gave you the equation already, you just need to do the dimensional analysis to get to it, that should be pretty straightforward

>>14975815
For undirected graphs, if [math]x, y \in V[/math] the edge between them is, set theoretically, [math]\{ x, y \} \in E[/math].
So the vertices in the line graph are straight up just [math]E[/math].
>>14975968
>search around Warosu you can see that terms like "Maid Address" and "Maid Space" are fully jannied out of the archive
I can get results for maid address.
>>14975736
>>14976062
Why are homos like this?

>>14973844
What does it mean for a module to act diagonally (diagonalisably) on some vector. Stumbled upon that in a text book but it wasn't defined anywhere. The equation given just basically says that the vector which is acted upon is an eigenvector.

>>14976062
>>14976109

Sannkyuu ( ω ) it was 3d da problem
now i got my eqasion i just need to DA which is straight forward so ill get to it after watchin my anime (◕‿◕)

which i think its

ML-1T-2 ∝ C ( LT-1 ,ML-3 , L) {numbers should be the powers} ヾ(≧へ≦)〃

>>14975874
> does heat production have an effect at all?
Absolutely negligible. Global energy consumption (*) is ~600 EJ per year which averages to ~20 Terrawatts. Sunlight reaching the atmosphere amounts to ~175,000 Terrawatts, or around 9000x total energy consumption.

(*) 1. This figure includes losses, i.e. for any kind of thermal power station, it's the energy value of the fuel consumed, not the electricity produced. 2. It includes electricity produced by wind and solar power and also all uses of biofuel.

>>14976115
I am a dreadfully lonely man, please understand.
>>14976160
n-no problem...

>>14975736
>>14976160
i give it a 45% chance this is the "homo-pedo" spammer false-flagging.

>>14975413
>What are some good use cases for RPN?
1. it (and equivalently the usual forward polish notation) can be useful when you want to develop some formal and version of mathematical function-terms without worrying about parentheses and the complicated rules that come with them. this is useful in developing the theory of mathematical logic, and also for more applied things like compilers
2. it can be intuitive to have e.g. a calculator where you first punch in a list of numbers, and then hit Add to add them all up. this is how I use dc (the unix stack-based command-line calculator) for stuff like totalling exam grades

[math]z \in \mathbb{C} , |z|^3 = iz^3[/math]
How do I graph this? I can figure out a solution with a sin and a cos (it's straightforward from the polar representation) but I don't understand how you can geometrically figure it out. I have to draw it on paper to be clear.

>>14976210
>I am a dreadfully lonely man, please understand
I thought bottoms absurdly outnumbered tops.
Was my homolore wrong?

>>14976115
yeah it makes sense now. I assumed the vertices had to be singletons but I guess anything works as long as [math]E\subseteq [V]^2[/math] and [math]E\cap V = \emptyset[/math]

>>14975363
bump

>>14976541
Strang's books (both of them) is written for low iq CSfags, so go for it.

>>14975413
RPN avoids the need for a parser or for dealing with precedence of infix operators. FWIW, PostScript also uses RPN.

>>14976291
Let [math]z=r e^{\theta i}, r,\theta \in \mathbb{R}[/math], then the equation is [math]r^3 = e^{\pi i /2} r^3 e^{3\theta i} [/math], [math]r[/math] cancels so any [math]r[/math] is fine, then solve for [math] 3\theta + \pi/2 = 2\pi k, k\in\mathbb{Z} [/math] to find the allowed [math]\theta[/math]
You should usually be using the polar representation with complex exponential for generic problems

>>14976291
[math]\left( \dfrac{z}{|z|} \right) ^3 = -i[/math]
Then, clearly the solutions are of the form [math]uw[/math], where [math]u^3 = -i[/math], [math]v \in \mathhb{R}[/math] and [math]v > 0[/math]

I'm confused a little about photon matter interactions

>A photon collides with an atom
>the atom absorbs the photon increasing the energy level of an electron
>some time later (instantly?) the energy level decreases and the atom emits 1 photon in a random direction (or it emits an infinite number of photons in all directions?)
>the atom can optionally not discharge any photons if it holds onto all the energy? similarly it can optionally emit part of the energy so the photon(s) emitted will have a total energy less than the incoming photon
>if the atom emits a photon in any or all directions at random, why is the angle of reflection the angle of incidence mirrored across a normal to the 'surface' of the atom?
>why does an emitted photon have the same color (EM frequency) of the absorbed photon mixed (sometimes?) with the color or frequency of the atom it collided with? does an atom that emits 100% of absorbed photons basically a mirror, and one that emits 0% a 'vanta black' atom with everything in between being a percent of the incoming frequency (hence a color shift?)

Considering that the ordered set [math](\mathcal{P}(X), \subset)[/math] implies for any subset [math]\emptyset \neq A \subset \mathcal{P}(X)[/math] that [math]\sup (A) = \bigcup A[/math] and [math]\inf (A) = \bigcap A[/math], would it be possible to define the supremum and infimum analogously for the natural numbers by using, say, von Neumann ordinals?

>>14975363
I don't think you need calculus for LA, but I haven't done gilbert's course or book

>>14976858
> some time later (instantly?)
It's not instant. It depends on the probability of the excited electron decaying back to the ground state. Admittedly this always extremely fast so in most situations you can say it's instant.

> the atom emits 1 photon in a random direction
It depend on how much energy the excited electron has. The most likely scenario, possibly the only one depending on the energy, the electron falls from its excited state to the ground state in a single jump; hence a single photon would be emitted. But there is a none-zero chance the electron could fall to an intermediate level first, emitting a lower energy photon as it does so, and then falls back to the ground state. The more hops taken, the less likely the process.

> similarly it can optionally emit part of the energy so the photon(s) emitted will have a total energy less than the incoming photon
See above.

> the atom can optionally not discharge any photons if it holds onto all the energy?
The electron will always decay to the lowest energy state.

> if the atom emits a photon in any or all directions at random, why is the angle of reflection the angle of incidence mirrored across a normal to the 'surface' of the atom?
The classical description of light as a wave explains this the simplest way, it's simply reflection. Quantum mechanically that is much harder to answer. Essentially not every photon is absorbed by the mirror and when you average over all the possible ways the photon can scatter you end up with the classical description.

> >why does an emitted photon have the same color (EM frequency) of the absorbed photon mixed (sometimes?) with the color or frequency of the atom it collided with?
A single photon doesn't. White light is a mixture of various wavelengths, some of which, depending on the material, are absorbed while others are reflected. Vantablack is especially good at absorbing (trapping) photons in the visible spectrum.

Help on this problem?

>>14977018
>Essentially not every photon is absorbed by the mirror and when you average over all the possible ways the photon can scatter you end up with the classical description.
>A single photon doesn't. White light is a mixture of various wavelengths, some of which, depending on the material, are absorbed while others are reflected. Vantablack is especially good at absorbing (trapping) photons in the visible spectrum.
so some of the original photons 'survive' their encounter with atoms and arrive at the sensor (eye) along with the ones that were absorbed and re-emitted which is why you see both colors, like white and brown light from sunlight reflecting off a desk? What mechanism lets the photon not get absorbed but also somehow reflect, I thought the only way to change direction was via absorption and emission, which would necessarily align the photons frequency to the atoms energy level?

>>14977062
> What mechanism lets the photon not get absorbed
Electrons in atoms have specific allow energy levels so only photons with the correct energy (wavelength) can be absorbed, even those that do it's a probability and not a certainty.

> I thought the only way to change direction was via absorption and emission
Scattering is not absorption. Though in the QFT / QED description you could argue it does occur via virtual particle interactions.

>>14975902
I'm senior-level electrical engineering undergrad, so things like digital systems theory (discrete dynamical systems), signal processing (applications of transforms, modulation schemes, etc.), electromagnetic fields (this one I have trouble with in particular)

I feel like, at least with how fluently the professors work through the problems, that the "solution path" for any given problem should be readily self evident. And yet, I often struggle to make any inroads on them.

>>14977059
S has cardinality 2^N because the sequences specify subsets of N.
S/E injects into S if we're able to choose representatives.
So really a reframing of the question - maybe more interesting than the question - is how to inject S into S/E.

I don't have the answer right now (apart from pointing out that the Cauchy reals are of size 2^N, but that's cheating).
Also my argument is non-constructive, one can do better

Can it be possible that in a field with more than 2 elements 1 + 1 = 0?

>>14974123
Firstly, the question is hard to answer, since these logics are infamously underdeveloped compared to the standard predicate logic.
Logic before Peano/Frege anno ca. 1860 was something for the philosphy department - and still is. Hotly debated mathematical topics like analysis seeked for some more formal treatment, and with with those two guys and the logicist program (think Whitehead/Russel and followed up by students of logic), the philosphers subject entered the real of mathematics to the extent that today people sort of see logic as a subfield of mathematics.
At the same time, due to model theory, mathematicians largely stopped caring for logic as it was found that set theory lets you get a hold on other formal theories semantically. In turn, mathematicians only know predicate logic.
Hence the under-developement.
So if I take your question at face value
>What are the uses of non-classical logic in math
then the answer is "not much", not because they couldn't be used, but because they historically have not been used.
But the question is also a bit difficult to answer generically, since these languages and frameworks don't really fit into a single bucket.
Constructive logic ties to the arithmetic hierarchy. Modal logic can capture operations natively, symbolically that are messy in terms of models (which doesn't prevent mathematicians from reinventing the wheel in their language). You can model time for programming flows with modal operators, for example. You can use them to solve knowledge/agent centric problems (pic related, also think blue-eyes puzzle). I think fuzzy logic has been overtaken in flavour by category theoretical tools. I don't know if fuzzy logic itself has been used much at all, although there's a few model theoretic topic (and forcing) that mirror some things in it.
There's books called "non-classical logic" iirc (Graham?), but if you're interested in something particular you'll get a richer resource.

>>14975363
you know you can just download the book from libgen and CTRL+F "derivative" and "integral" right

>>14977175
https://en.wikipedia.org/wiki/Finite_field#Field_with_four_elements

>>14977181
Here's a translation of a modal logic tool.
Sees some use in CS, but not really in math academia. Again, because you can (cumbersome or not) translate it to FOL+sets too.

In a state space [math]s[/math], consider some "step" function
[math]s\colon X\to X[/math],
or more generally, a transition function with triggering action and observational output
[math]f\colon (A\times X)\to (O\times X)[/math].

With this, let
[math](\bigcirc_s P)(x){\ :\Leftrightarrow\ }\forall (x\in X). P(s(x))[/math]
[math](\bigcirc_f P)(x){\ :\Leftrightarrow\ }\forall (a\in A). \forall (x\in X). P(\pi_X(f(a, x)))[/math]
Saying: [math]P[/math] holds for all values [math]x[/math] can transition to (in one step).

[math](\Box_f P)(x){\ :\Leftrightarrow\ }\exists Q. Q(x)\land (Q\subset' P)\land (P\subset' \bigcirc_f P)[/math]
Saying: "For all future states of this state, [math]P[/math] holds."

where, again,
[math]Q\subset' P\ :\Leftrightarrow\ \forall x. (Q\implies P)[/math]

[math]\lozenge_f P \equiv \neg(\Box_f(\neg P))[/math]
Saying "For some future states of this state, [math]P[/math] holds."

Anyway, the only thing I really know well is constructive logic, but that largely just amounts to using less axioms. (Although you can adopt Church's thesis, or Brouwerian contiouity, if you want to go funky)

Note that you can also study one sort of non-exotical system of many valued logics via Heyting algebras, which are also compatible with constructive logics (but should not be confused with them - they are a semnatic commitment to extra truth values, which don't apriori exist constructively

>>14977135
What does the set S/E mean? I understand what equivalence classes are but the notation isn't making sense to me.

>>14977190
What the fuck is this subject, I don't get it.

>>14977221
The elements of S are all the infinite binary sequences.

The elements of S/E are bundled such sequences.
Namely if two sequences xA and xB only differ on finitely many places (and so if they eventually are the same forever), then both xA and xB are members of [xA]. That's what I called a bundle (equivalent class).
The set S/E is the set of all bundles. If you'd flatten out S/E (open the bundles), you'd get S back.

*ce class

The theorem basically says that while S has cardinality 2^N, even if you make it "smaller" by only keeping one representative of each sequence (in the equivalence class sense), then the cardinality of S/E that you get is still 2^N.

>>14977135
>I don't have the answer right now (apart from pointing out that the Cauchy reals are of size 2^N, but that's cheating).
>Also my argument is non-constructive, one can do better
I don't follow, you mean decomposing [math]S = S/E \times V[/math], where [math]V[/math] is the set of finite subsets of the naturals, which has the same cardinality as the naturals and hence delivers the equality?

>>14977059
This is an interesting question
>>14977221
S/E is the set of all equivalence classes of the elements of S under the equivalence relation E
S/E in fact forms a partition on S, so that [eqn] \bigcup S/E = \bigcup_{ x \in S/E} x = S [/eqn]
One can also easily prove that S has cardinality [math] 2^{\aleph_0} [/math] (see >>14977135)
Interestingly the cardinality of every equivalence class is [math] \aleph_0 [/math], if we assume there are only countably many such equivalence classes then we get a contradiction because a countable union of countable sets is also countable but the union of S/E is S which is uncountable, Hence S/E cannot be countable so [math] \aleph_0 < \operatorname{card}(S/E) [/math] however i'm not sure where to go from there.

>Half the class got below 60% on analysis midterm
>I got 97%
feels good

>>14977280
I didn't propose a particular solution method, although what you say probably suffices as an argument?

I didn't want to ponder too deep to think about what's required to select a representative of each [x] here, but we might not have to care.
Also I didn't yet think of how to inject S to your S/ExV. In cardinal arithmetic, there's probably a nice generic way to argue |AxB|=|A| if |A|>|B|, but I forgot how that goes.

Apart from choosing representatives, I meant that my approach of just finding some injection would not prove the bijection, unless one accepts Schröder Bernstein.

Okay I looked at the |AxB|=|A| thing and looks like this is loaded again, kek

>>14977291
>because a countable union of countable sets is also countable
I shiggy.

But okay, at least if we accept choice, then we can surely pic a representative of each class [x], then we can forward S to (S/E)xV, then again use choice to argue |(S/E)xV|=|S/E|, so there's an injection from S to S/E and we're done?

Can some math folk help me with some good practices for learning a rigorous, proof based, theory course?

I struggle with the intuition and i struggle with connecting my intutive understanding of something to building a formal proof.

All the info and definitions of things are given in a formal context too with very little in the way of verbal explanation or example to help make sense of what the definitions are saying, and it all looks like spaghetti to me.

Any tips?

If I want to show that a isn't divisible by 5, for instance, I would say that it must be in the form
a=5x +-1 or 5x +-2
I get why you wouldn't say a=5x+-3 or a=5x+-4 because they are like the inverse of +-1 and +-2 and thus already covered by +-1 and +-2 but what's the mathematical way of saying that?

>>14977511
[math]a \not\equiv 0 \pmod 5 [/math] or [math]a \in \{\bar1, \bar2, \bar3, \bar4\} \subset \mathbb{Z}/5\mathbb{Z} [/math]
https://en.wikipedia.org/wiki/Modular_arithmetic

>>14977569
hmm maybe that's too mathematical as i haven't seen half of those symbols

>>14977511
[math]a \pmod 5 \neq 0[/math]

or if you said

[math]a = 5x + r[/math] then [math]a \pmod 5 = r[/math]

>>14977580
i think it means a is in one of the set of equivalence classes of mod(5) except for [0]?

i think an equivalence class is a set of numbers that are all related to each other by some property, such as mod 5. so they all have the same remainder when divided by 5.

so if a is not in [0] then a doesnt produce a remainder of 0 when divided by 5

that leaves [1], [2], [3], [4] as the possible equivalence classes that a could belong to. if a is in [1] then a would be a number that produces a remainder of 1 when divided by 5, like it could be the number 6 or 11 or 1

that's my guess

>>14977360
>so there's an injection from S to S/E and we're done?
The entire argument is correct but you take a random detour at the last second. The cardinal arithmetic delivers the result. Stop trying to use Cantor-Schroder.

>>14977435
look into what you don't understand
write symbols and proofs out on paper
make a mind maps on paper
if there's something you don't understand stop and research instead of just ignoring

I have to prove that if X is the set of all sets, then the power set of X is equal to X.

How do i start?

>>14977967
Well first off, that set doesn't exist, just assuming Predicative Separation, unless you have a theory with a stratified membership relation.
[math]X\in {\mathcal P}(X) \in X[/math] is true for your X but, using stronger axioms, also ruled out by transfinite induction/Regularity.

But okay,...
So we assume
[math]\forall z. z\in Z[/math].
In particular
[math]\forall (z\in Z). z\in X[/math].
and then
[math]\forall Z. Z\subset X[/math].
To prove [math]{\mathcal P}(X) = X[/math] you'd want to prove [math]X\subset {\mathcal P}(X) \subset X[/math]. If X holds all set and P(X) holds only sets, then of course [math]{\mathcal P}(X) \subset X[/math].
So what's to be shown is [math]X\subset {\mathcal P}(X)[/math], i.e.
[math]\forall(x\in X). x\in {\mathcal P}(X)[/math], i.e.
[math]\forall(x\in X). x\subset X[/math],
which holds

the first one was meant to be
∀z. z∈X

Just how much do grades really matter past a certain point like 76%?

Been thinking on regards to a joke i would pull at work. When someone pours a drink from the water cooler, should i stop them and scream "Careful, careful! that contains dihydrogen monoxide!" i think it would be pretty funny.

Is there some form of repository for peptides and amino salts. I've heard of synthetic peptides being created on demand but I want to know what function they serve and ideally what it can be composed from if it was from plain organics.

>>14977967
Let [math] V [/math] be the "set of all sets" and [math] \mathcal{P}(V) [/math] be its powerset.
To show that [math] V = \mathcal{P}(V) [/math] we need to prove two things
(i) [math] \mathcal{P}(V) \subseteq V [/math]
(ii) [math] V \subseteq \mathcal{P}(V) [/math]

(i) follows from the definition of [math] V [/math] because every subset of [math] V [/math] is contained within it.

To prove (ii) assume [math] x [/math] is any element of [math] V [/math], then by definition of [math] V [/math] every element of [math] x [/math] is also in [math] V [/math] so [math] x \subseteq V [/math] and therefore [math] x \in \mathcal{P}(V) [/math] by definition of the powerset, so every element of [math] V [/math] is also an element of [math] \mathcal{P}(V) [/math], therefore [math] V \subseteq \mathcal{P}(V) [/math].

>>14978541
Try
https://www.uniprot.org/
https://www.proteinatlas.org/
https://www.rcsb.org/

UniProt in particular contains some exhaustive data, if you can find your peptide there then you're lucky.

>>14978546
Hasn't that proof been given yesterday, almost word by word? Are you bored?

>>14978555
thank you kindly

>>14978574
>Are you bored?
Yes

>>14978574
In his defense, the presentation in >>14978016 is very awkward.
Also dogpiling on stupid questions anyone can answer is an /sqt/ tradition, see >>14975689 for another example in this thread.

>>14978723
Almost none of those posts answered that matrix question

>>14978741
I'd comment on that but I'm used to interpreting [math]\mathbb{R}^{m \times n}[/math] as literally [math]\mathbb{R}^k[/math] where [math]mn = k \in \mathbb{N}[/math], and the matrices are [math]M_{m, n} (\mathbb{R})[/math]

If a field contains more than 2 elements, there exists a non-zero that is not an additive inverse of 1, right?

>>14978799
Yes, there is exactly one zero element and there is exactly one additive inverse of 1.

I'm supposed to use 2.1.9 to turn 2.1.8 into 2.1.10. Problem is, I've already taken the highlighted terms into account, but there's some that I don't know how to turn into their respective counterparts to complete the factorizing.

Will you watch our game today?
>>14979025

is there a constructivist approach to linear algebra?

>>14979112
No, you can't even prove that every vector space has a basis without AoC.

Is it true that [math]x.o(1)=o(x)=o(||x||)[/math]?

Is it a dumb question? Because nobody I know seems to know the answer.

if probability distributions represent relative frequencies of events, what would taking the inverse fourier transform of a probability distribution mean/yield

>>14979240
https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)

>>14979274
ok so this is based

I preface this with the caveat that I know nothing of particle physics
A static magnetic field will cause an electron to revolve around some point. What happens if the radius of curvature/the orbit becomes smaller than the diameter of the electron itself
presumably nothing important if I've never heard of this being addressed before

how do I cope with getting yelled at by a supervisor for exposing ongoing engineering malpractice?

Could someone give me a hint as to how to start this? There aren't any resistances given for either coil, no [math]\textbf{B}[/math] given, and since [math]\mu \neq \infty[/math], I don't think I can just use the ideal transformer approximations

>>14976858
I can't do the green arrow bs, so here it comes

depending on the energy of the incoming photon you will upon absorption either promote an electron to an empty orbital or to the continuum thus ionizing the atom

depending again on the incoming energy the relaxation time will depend on the corehole lifetime of the atom, in the hard xray case for example resonant absorption/emission is a coherent single process

there is a highest probability that photon emission occurs at 90 degrees (which is why source-sample-detectors are in a right angle setup in most x-ray emission experiments), the atom at the same time will emit electrons (the ratio of photon/electron emission depends on Z), and in this case, it is a bit more complicated, so in most cases it will not be randomly ejected (read about beta parameter)

in elastic processes the energy incoming is equal to the outgoing energy, this is not the case in inelastic processes, where the energy of the emitted photon is less, furthermore when the there is nuclear dynamics there is more energy lost upon emission (valid for electron and photon emission)

I'm going to TA for an online course next semester so I need a tablet to do demonstrations on. I think the most important thing for me is going to be accuracy and low latency of input. Any suggestions? The iPad Pro is the obvious safe option but it's also a thousand bucks.

>>14979631
Samsung is usually consistent.
>>>/g/sqt probably has better advice.

How can a star be 5 orders of magnitude bigger than the Sun in volume but only 100-200 times as massive?

>>14979372
The electron is a point particle as far as we know, and that is how it is treated in equations. The radius of a charged particle moving in a magnetic field is proportional to velocity, so you can make the radius as small as you like by taking the velocity to zero.

If you consider a quantum mechanical particle in a magnetic field there are some quirks due to the uncertainty principle. Look up "Landau levels" if you're interested.

>>14979693
stellar luminosity is proportional to slightly more than the cubic of the mass

Am I stupid?

The angle theta should be cos^-1(-zeta) isnt it??

cos(theta) = adj/hyp = -(zeta)(w_n)/(w_n)
cos(theta) = -zeta

>>14979755
if you used negative zeta that would give you the angle from the positive sigma axis, so it would be pi-theta, not theta

>>14979814
wait could u explain that again please? why would it be from the positive sigma axis? also, aren't those two angles the same?

>>14979847
cos^{-1} 1/2 = 60 degrees
cos^{-1} -1/2 = 120 degrees

Look where the angle is defined in the picture. Does it make sense now?

If a continuous bijection [math]f: [0, 1] \to [0, 1][/math] with continuous inverse maps rationals to rationals does its inverse also map rationals to rationals?

I am trying to understand the proof of the Noether's theorem, but I am having trouble in the last line. How does the second integral becomes that?

>>14980054
The epsilon before the first integral appears to be a mistake. The second term is just the idea that an integral over an infinitessimal interval is just that interval times the integrand.

There are better demonstrations of Noether's theorem fwiw

>>14979631
iPad air is fine. Don't get the new standard iPad, they don't support Pencil 2.

>>14980073
Oh, that makes sense.
Thanks, mate.

>>14980073
Could you explain why the limits of integration in this question change?
https://physics.stackexchange.com/questions/474354/proof-of-noethers-theorem-how-to-deal-with-transformations-in-time

thb, that was the original question that I was trying to find an answer for.

>>14980129
The symmetry changes both the time coordinate and q, so you need to integrate over the new time coordinate t' to find the change in action. In the second line they transform back to the original time coordinate t. As is usual in changes of variables in integration, there is a Jacobian (1 + epsilon dot{X}) and the limits of integration change to those of the new variables (when t'=t_2' then t=t_2).

I'm not quite sure which part you don't understand but hope this helps

>>14980129
For instance, say t'=t+t^2,

You can verify
[math]\int_0^{12} dt' = \int_0^{3} (1+2t)dt [/math]
It's the same principle

>>14980156
>when t'=t_2' then t=t_2
Why tho? Shouldn't it be
[math]t_2^' = t_2+\epsolonX(q(t_2),t_2)[\math]?

>>14980200
Because you switched integration variable to t, the limits change too. See the example

>>14980200
[math] t_2' = t_2 + \epsilon X(q(t_2),t_2)[\math]

>>14980200
[math] t_2' = t_2 + \epsilon X(q(t_2),t_2)[/math]

>>14980200
>>14980203
Wait, I think I got it.
t_2 is the value of t that makes t_2'. So I am just reversing the substitution. I was just writing t_2' in the extended form and getting confused.

I deserve to be shot after that. Thank you, anon.

>>14980211
No problem, symmetries and transformations between frames are always confusing

Salutations sirjis, myself from India. How can I be like the great Manjul, sirjis? Please do tell.

>a point + a radius = a sphere
>a point + a vector = a ______
line?

>>14973844
https://imgur.com/2fZxXNj
What does this notation mean, the one highlighted in yellow>

>>14980471
Isn't it defined above in your pic?
[math] S_{\gamma - \epsilon}=S \cap [\alpha , \gamma - \epsilon] [/math]
I made that latex on phone so it might be fucked up

>>14980487
oh thanks, makes sense now

I literally dont get physics..
So what is force? like what its entity? its not something we can see, its like air but it goes against us for some reason but still has no entity.. and for some reason, this force exists all of a sudden when we accelerate and not due to velocity by itself

>>14980313
yes
alternatively a plane if you take the vector to be the normal vector, but this only works in a space with exactly 3 dimensions

Hi. Can someone explain how they made (x^3)/3 out of x^6 ?

I'm supposed to write a program that divides these polymonials but I don't understand how they work at all.

>>14980636
[eqn] \frac{x^6 - x^3}{3x^3 - 3} = \frac{x^3(x^3 - 1)}{3(x^3 - 1)} = \frac{x^3}{3}[/eqn]

Are there any minor, non intrusive things I can do to prevent hair loss or stimulate growth? Anywhere else I ask it's like OMG U NEED TO GET ON FINN MINN TRINN BEFORE YOUR LIFE IS RUINED!!! I don't want a bunch of chemicals or lifelong shit I have to take, just curious if there's some kind of vitamins/food that could help me in any kind of way (which is probably really, incredibly minor but still)

>>14973844 (OP)
I'm having trouble understand case 2 and conclusion from this >>14980471 post. Specifically:
The part in pink and orange (which are similar).

>>14973844
I have been working more on Maid Parade. I made the Gemini renderer a lot more performant. My goal is make the code as nice as possible and add javadoc comments.

Somebody told me add IRC and linked me IRC docs, so probably I will do that. After this is complete I should have a nearly master level ability to make sockets based communications technology.

Also I think I can write a CC0 VOIP implementation with tricks involving UDP.

>questions
Is there a reference document for Signal? How it's protocol works? Would Signal be a good choice to implement or is there something nicer?

I won't accept suggestions related to interacting with Discord. I refuse to use, install or interact with Discord for any reason.

Thank you /sci/entists for reading my post.

>>14974123
>What are the uses of non-classical logic in math
basically none
>modal logic
has some uses in formal verification of important shit like CPU designs, e.g. CTL*. Most of it is stupid bullshit though
>many-valued logics
no legitimate use except as a thought experiment gone wrong
>fuzzy logic
was the "big thing" in AI like 30 years ago and in "big data" before "big data" was a term, totally discredited now, to the extent I'm surprised you have heard of it

>>14977215
>temporal logics
Interesting in theory, and gratifying to learn about, but there is no depth to it. If you want to reason about computation, dynamic logics are a bit better, but still not very deep. It's a general problem with "logics" that the initial idea is really really interesting, but there isn't much to do with it in terms of proving theorems or extending the theory in a way that doesn't make it retarded. A general problem with mathematics, really, but "logics" have it worse than average

Is there any method to learn even basic rudimentary physics, without the equations? It would make my scifi much more enjoyable.

What is the difference between force and momentum? I do understand the difference that one encompasses acceleration while the other is velocity when it comes to the equations. However, let's say if I push someone at a fixed velocity, wouldn't that also be force? even though, force is defined as acceleration.

>>14981087
The most you could probably allow yourself to go is skipping the mathematical proofs behind shit and only resulting to formulas, which is more or less about the level of an engineer perhaps.

I don't get this proof. I understand the arguments, but I don't see how it leads to the conclusion. Why does U being a neighborhood of [math]x_0[/math] disjoint from Y lead us to conclude that Y is closed? It's not necessarily the complement of Y, right? Couldn't it be the case that the complement of Y is not open, and it just has U as a subset?

>>14981213
You want to prove that X\Y is open.
A set is open if every point in it is an inner point.
A point x0 is an inner point of the set X\Y if you can find a neighborhood of x0 that's fully contained in X\Y.

>>14981213
Call [math]x \in X \setminus Y[/math]'s [math]U[/math]
(as constructed in the proof) [math]U_x[/math].
Then [math]X \setminus Y = \bigcup_{x \in X \setminus Y} U_x[/math], which is an union of open sets.

>>14981116
Force is the net change in momentum.

Basically, momentum is a state that the body possess, and you use force to change that state.

>>14981164
>the level of an engineer perhaps
rent free

If you've got [math]x_{n+1}[/math] as an expression in terms of [math]x_n[/math] of some sequence, is there a general way to find out what [math]x_n[/math] (in terms of [math]n[/math]) is?

>>14981652
No. You also need to define an initial value(s). Think of the factorial expression: [math]x_{n+1} = (n+1)\ x_{n}[/math]. It's meaningless unless you also say that [math]x_0 = 1[/math] otherwise it could be something else entirely.

>>14981652
no, that's an extremely hard problem

[eqn]\lim_{n \to \infty} \left( \frac{1 + \sqrt[n]{n}}{2} \right) ^{\frac{n}{\ln{n}}}[/eqn]
How to evaluate this using basic ln/exp properties? I can't figure it out

>>14981781
it's
[math]\sqrt{e}[/math]

>>14981878
Yes, but how do I actually find/prove that?

>>14981894
Squeeze theorem. With the AM-GM inequality you can bound
[eqn] \frac{1 + \sqrt[n]{n}}{2} \geq n^{\frac{1}{2n}} [/eqn]


[eqn]\left( n^{\frac{1}{2n}} \right)^{\frac{n}{\log(n)}} = \sqrt{n^{\frac{1}{\log(n)}}} = \sqrt{e}[/eqn]

[math]
+ : \mathbb{R}^2 \to \mathbb{R}^2\\
+ : (a, b) \circ (c, d)\to (a + c, b + d)\\
* : \mathbb{R}^2 \to \mathbb{R}^2\\
* : (a, b) \circ (c, d) \to (ac, ad + bc)
[/math]
Let R be the ring [math](\mathbb{R}^2, +, *)[/math]. I have to find all nilpotent elements in R. I believe, the only nilpotent element is (1, 0). Am I right? Do you see any other nilpotent elements in this ring?

>>14981918
Why don't have to define a term for the "upper bound"? Maybe the result is greater than sqrt(e)?

>>14981964
>I believe, the only nilpotent element is (1, 0). Am I right?
[math](1, 0)^n = (1, 0)[/math], no? How would it be nilpotent?
Any element of the form [math](0, b)[/math] should be nilpotent. Anything with the first coordinate non-zero has non-zero first coordinate for all powers, so those are the only nilpotents.

>>14982007
Oh, you're correct. I confused definitions. Thank you.

>>14981975
You can find upper bounds with different inequalites. Like if you use the convexity of the function [math]x \to a^{\frac{1}{\ln(x)}}[/math] for [math]a>1[/math] then Jensen gives you

[eqn] \left( \frac{1 + \sqrt[n]{n}}{2} \right)^{\frac{n}{\ln(n)}} \leq \left(\frac{1}{2} + \frac{1}{2} e^{\frac{1}{n}} \right)^n \to \sqrt{e}[/eqn]

an sum that I need to calculate involves some array of coefficients that use an empirical formula
b*cot(b) = constant
how do I even find the all of the b, realistically I probably only want the first 15 but idk how to do this shit

>>14982058
>array
I remember what it's called now. an eigenvector. shows you how little I know of math

>>14973844
I have a problem where my mood can change in unexpected big ways for no reason. Usually that mood is some kind of happy. Low-energy happy or sometime high-energy happy. Usually change is instantaneous and no warning but sometimes I feel it coming.

I am starting to feel the arrival of high-energy depression which is the worst one I think because it causes depression and I can't sleep through it because depression has a lot of energy behind it.

Depression wastes my time. How can I prevent high-energy depression? In the past I tried vitamins and rigorous physical exercise but it didn't help.

I don't want to take any pills.

>>14982097
A rope should work well

>>14981781
[math]a_n = \left(1+\frac{n^{1/n}-1}{2}\right)^{n/\ln n} [/math]
Define x such that,
[math]\frac{n^{1/n}-1}{2}\equiv x^{-1}\implies n/\ln n = \left(\ln \frac{x+2}{x}\right)^{-1}. [/math]
As n goes to infinity so does x.

So [math]a_n\rightarrow e^{1/2} [/math]

>>14982113
Oops copy paste error, I deleted a line
[math]\log a_n = \frac{\log (1+x^{-1})}{\log (1+2x^{-1})}=\frac{x^{-1}}{2x^{-1}}+O(x^{-1})\rightarrow 1/2 [/math]

>>14982097
hot/cold showers, sunlight, exercise like jogging/swimming and self-made orange juice

>>14982123
>sunlight, exercise
Seconded.
I'd also say that shaving improves my mood, but that's just the whole cleanliness-effect.

You know how the government adds fluoride to water, iodine to salt, etc?
From a fantasy point of view, would stuff like that make any sense as a strategy to exterminate vampires/other species of man-eating cryptids through biomagnification?

>>14973844
can vinegar, sodium acetate or co2 pass through dialysis tubing? or only some? I only care about the co2 passing

>>14982289
It's fantasy. The answer can be whatever you want it to be.

>>14981652
Write them in terms of [math] x_0 [/math] and figure out the pattern.

What are some free lecture/course websites? I used to be enamored with coursera back in the day.

>>14981708
Would an inequality, like [math]x_0>0[/math], also suffice for an initial "value" or does it have to be an equality?

why would you ever use \includeonly in latex?

>what's the point of studying linear algebra?
How would you answer this to an undergrad? I tried saying something about how it's used to make computers know how objects in space behave but desu I don't know neither. I just think it's neat

>>14982918
theres none. teaching algebra to a scientist or engineer is like teaching a guy how to repair a car engine who only wants to learn how to drive a car.

>>14981652
In general, x_n doesn't have a closed-form expression in terms of x and n. Specific types of recurrence relation may have a closed-form expression. Finding one is much like integration or solving differential equations, i.e. check whether the recurrence fits a pattern for which there is a known solution.

>>14982918
Depends on which major is asking? If natural science, then everything differentiable function is locally linear. Several things can to simplified into a linear problem. It's also used to make geometry algebraic.

>>14982289
In Logan, mutants were exterminated by spiking the water supply.

>>14982925
This is /sqt/, not /stupid answers thread/.

>>14982918
>How would you answer this to an undergrad?
In what subject? An undergrad in history or literature doesn't have much use for linear algebra. It's fundamental to most engineering disciplines, though. Linear algebra is studied because linear systems admit mechanical solutions; Ax=b => x=A^(-1)b, dx/dt=Ax => x=ce^(At). And non-linear systems can be linearised, i.e. their behaviour in the neighbourhood of a point is approximately linear, which provides a basis for numerical solutions.

>>14982889
If there is a closed form, then it can be written as:
[math] f(n, x_0) [/math]
You don't need to find the precise value of [math] x_0[/math] for this.
Now if [math] f [/math] only depends on [math] x_0[/math] insofar as its sign, then the sign is the only thing that matters. Example:
[math] x_{n+1} = \operatorname{sgn} x_n [/math]

this is a solution to a green's function question.
what the fuck is happening here? how did they get it the values for A_1 and A_2 from that

can someone please give me a hint for this exercise?

>>14983044
When proving an equivalence you have to prove two seperate implications
>If x is rational then its q-ary expression in any base q is periodic
>If x's q-ary expression in any base q is periodice then x is rational
Which of the two implications do you have trouble with?

>>14983038
Your question needs more context.
What is "equation (1)"? How is it related to A1, A2, etc.

>>14983062
Does it? I just want to know how they used the jump condition on the expressions for A_2 and A_1 to get the new ones

>>14983072
>Does it?
Yes, for example no one would know how G is related to A1 and A2 if you hadn't posted this image. Have you tried differentiating the expression for G(x; \xi) and then imposing the "jump" condition mentioned earlier?

>>14983056
I just got an idea so I'll get back to you later. I originally had issues with the latter implication.

>>14983088
No but I am now more confused.

>>14983108
Confused with what? For both [math] x < \xi [/math] and [math] x > \xi [/math] you can compute [math] \frac{\partial G(x; \xi) }{\partial x} [/math]. The difference of these two derivatives at [math] x = \xi [/math] should be [math] \frac{1}{\xi^2} [/math]

>>14983114
because the difference for me is 15/xi^2

>>14982397
>can vinegar, sodium acetate or co2 pass through dialysis tubing?
The answer is yes for all of them. CO2 is present in solution as carbonic acid.
Most diffusion dialysis tubings have holes large enough for molecules larger than 1 kD (kilo Dalton) to pass through, unless you're using a special kind of dialysis tubing.

>>14973844
I want to remove some rust from my stainless steel pocket knife. How do i figure out an appropriate anode and current (or voltage?) to use for the reaction?

>>14983215
Looks like a calculation error because I'm getting 1/xi^2 for the solutions they've written down. Did you forget to include the [math] 3\xi^2(A_2(\xi) - A_1(\xi) [/math] part in your calculation while computing the difference?

>>14982828
Bump.
I checked the /sci/ wiki in the OP and most links
>require an account
>are outdated
>link to deleted/private videos
My best option is simply searching '<course/topic I'm interested in> lecture' or 'basics' or some derivative, huh. I already grabbed a few classes off youtube. Lots of different 'big name' schools to choose from, and hope you gambled properly.

>>14983263
>I want to remove some rust from my stainless steel pocket knife. How do i figure out an appropriate anode and current (or voltage?) to use for the reaction?
You want the minimum voltage that produces any meaningful effect, or bubbles will form that result in pitting.
Honestly it's better just to use a rust-dissolving acid, such as muriatic acid from a pool-supply store. And be careful with that stuff: use eye-protection, gloves, and adequate ventilation.

How the fuck do I self study Signals and Systems? What kind of math should I revisit to ace this topic? Are there any sites available that have practice problems for topics like the transforms? Almost every textbook filters me once I get to the transforms, I learn best with example problems.
I have a course on this next semester, there's only 1 professor in my campus that teaches it and he's supposedly so godawful that you have to teach yourself the material.

Lets say that a coin flip has 0.5 to land heads and 0.5 to land tails. Each flip is an idependent event. Lets say I flipped heads 9 times in a row. The coin flip is still 50:50 heads or tails. But, I wonder what are the odds that I'll flip heads again. Flipping ten heads in a row has a (0.5)^2 chance of happening, but a single coin flip is still 50:50. So what are the odds that head will flip? Are "will flip" and "will flip again" even the same question?

>>14983791
> I wonder what are the odds that I'll flip heads again?
> Each flip is an independent event.
You answered your own question. If each flip is independent it's irrelevant what happened before.

what is the weak force?
i tried to read a bit about it but i don't really understand how it fits with my model of what the other forces are. it seems to be related to atomic decay, and the carrier of the force is one of two bosons.

but i don't know what it "does".

like, the strong nuclear force. what it "does" is keep hadrons together, and keeps atomic nuclei together. an attractive force "pulling" on quarks to keep them together, or "pulling" on neutrons and protons to keep them in a nucleus, whatever.
makes sense, i get it.

electromagnetism. carried by the photon. you can "feel" the attraction or repulsion like with magnets, and that makes sense to me when i use that comparison with respect to the strong nuclear force. like how a hadron might be kept together in the way that opposing magnets might be kept together.

and gravity, an attractive force, shit with mass stays near other shit with mass.

these three forces "feel" similar enough in my mind with how they work, and i can accept that they can do different things and have different properties, fundamentally there is some sort of attractive shit going on underneath.

but the weak force doesn't fit in the same box, in my mind. it just describes how shit decays?
maybe my understanding of the extent of the other forces is too narrow and so i'm imagining a box in which they all fit which is not correct.

why is it a "force" on the tier of stuff like the strong nuclear, gravity, and electromagnetism, instead of "just being a thing that happens when shit decays"?

>>14984020
it turns quarks into different quarks and leptons into different leptons

>>14984047
does that mean my interpretation of "forces" to require an attractive/repulsive element is wrong?

just using the bit you said there, the weak force being an interaction between quarks or leptons which changes them. it's an interaction sure but is there some sort of repulsive or attractive element, like in the other three forces?

>>14973844
Is it better to take it slow in math education as an undergrad? TLDR I'm considering switching my major from computer engineering to mathematics. And I'm creating my schedule at the moment.

Would taking Calculus 3, Differential Equations, Linear Algebra and Discrete math in the same term be a stupidly difficult combination for a midwit? I'm definitely not a gifted math student but in some twisted way I feel that, in order to prove to myself that I can study mathematics, I must be capable of taking these courses in parallel.

>>14984096
there's overlap with them, but usually each course focuses in on a particular element. like, my calculus courses were focused mostly on the actual fundamentals of how the derivative works, how the integral works, etc.
linear algebra used elements from calculus sure, but the type of matrix math done in linear algebra was not really the stuff i was doing in calculus.
do what you want to do, but first i'd make sure that if there are prerequisites, respect them. like, it would be retarded to take calculus 2 and calculus 3 at the same time, even if you were allowed to. but also don't grind yourself into the dirt to prove some arbitrary metric about your math ability. if you took 4 semesters and literally did only one course a semester, you'd still know as much as if you did all 4 in the same semester. probably more, because of the duration of exposure.
i don't think there's anything special about math where you have to be some sort of genius to get it. some people might pick it up intuitively better, but a competent instructor can teach anyone calculus.

>>14983691
Linear ODEs, Laplace/Fourier transforms (and Z-transform if it includes DSP), partial fraction decomposition, linear algebra, complex numbers.

>>14983791
> Flipping ten heads in a row has a (0.5)^2 chance of happening
0.5^10. But if you've already flipped nine heads, the chance of ten given that you've already got nine is 0.5^10 / 0.5^9 = 0.5.

>>14984112
>if you took 4 semesters and literally did only one course a semester, you'd still know as much as if you did all 4 in the same semester. probably more, because of the duration of exposure.
Yeah I agree, I'm just very confused about how I should go about the next semester or two...

For some background, I was just about to graduate with a computer science associates and transfer to a four year. But at the same time I was considering engineering, so I took this semester to find out if I would have enjoyed CE, and because any change would be much better now as courses are very cheap at community college. But now, I realize that I'm not really interested in the engineering, and I'm still very interested in the theoretical aspects of CS and Math.

Next semester I could graduate with a CS associates and transfer to a four year (where I would like to focus on AI), or delay my graduation again in order to complete an associates in math, then transfer.

I'm still very interested in CS and AI, but I'm also interested in continuing my math education so that I'm more equipped for research in topics like Deep learning..

Maybe the obvious answer is just to study CS, because that is what motivates me to learn math, but I really do not know..

how does redshifting work? red light has less energy than blue light, correct?
so, light traveling across an expanding space has less energy at the end than if it was traveling across a static space.

if you could locally compress a region of space, like, imagine a box of a meter across, and you crushed a kilometer of space into it, then shot a photon across it, does the photon come out more blue on the other end?
or is it only for a photon moving across space being actively compressed? like, if you fired the photon into a 1 meter box, and then compressed space locally in the box to 1 kilometer while the photon was still there, then it exits the box.
then is it more blue? does the distinction matter whether? in my mind it wouldn't matter, since the photon is a discrete thing, but it seems odd that a photon going through a compressed region of space would keep that energy once it has come out. if so, you could create high energy particles by passing them through a locally compressed region of space.
unless the energy comes from the space, but that would mean that the expanding universe is sucking energy from photons traveling through it.

>>14984151
i know what you mean. i went to school for chemical engineering, and changed my major in my third year to computer science. it kind of sucked because i really liked doing thermodynamics and calculus and stuff, but the computer science curriculum had much lower math expectations than chem E.
i'll say, knowing what i know now, the actual title of your degree doesn't matter much except when it does. like, you can absolutely get a job doing AI shit with a degree in computer science, or software engineering, or computer engineering, or physics, or math, or any number of other degrees which are "close enough".
so you can either do it two ways, i'd say. either do the easiest degree which is closest to what you want to do for a career, or, choose the degree closest to what you want while still allowing you to take the courses you're interested in.

i'd recommend you try and apply for some jobs if you haven't. like try to get an internship for the summer if nothing else. maybe january, start really getting your resume and stuff together. you'll see that your degree is honestly just a checkbox to get your foot in the door, nobody gives that much of a shit about it. but you'll also see what the real work is like. i was a year out of finishing a chem E degree, and then i actually did an internship at a factory and it was so unpleasant that i changed my major. what you're expecting work to be like may be different than what it actually is.

>>14984096
i took calc 3, dif eq, and lin al in the same semester, it was fine.
>I feel that, in order to prove to myself that I can study mathematics, I must be capable of taking these courses in parallel.
your gut is 100% correct on this one.

>>14984193
i think it's kind of arbitrary to make the distinction like that. it might feel like a lot of math to take calculus and linear algebra at the same time, but it's not any different than taking calculus and physics at the same time. it's math, sure, but what you're doing in each course is pretty distinct.

>>14984076
> does that mean my interpretation of "forces" to require an attractive/repulsive element is wrong?
Yes and no

In the modern quantum field description a force is an interaction between two fermions mediated by a boson. This results in the classical attractive or repulsive idea of a force for Electromagnetism and the Strong Force (and hypothetically Gravity). An interaction is essentially a transfer of energy and momentum, and possibly some kind of charge. So while the Weak Force doesn't classically behave like the other forces it still affects a change.

>>14984177
Appreciate the advice, I agree I should definitely start searching for some internships. At this point I think that I am so severely detached from reality that I cannot even picture what life could be like after college.

How is life for you now? Did you end up working in anything related to computer science?

why does he use 2x when defining what du is. He said it's because it will cancel out the x in 4x but why not just 4x.

What are the types of waves in nature?
>material waves
>electromagnetic waves
>sound waves aka mechanical waves
any more?

>>14984333
>gravitational waves
>love waves

>>14984333
Heat waves.

how would you define a turing machine so that on input 01^n, it halts on output 01^2n?

>>14984376
>gay waves

>>14984288
nevermind

This is a homework question I have, supposed to be for a coil moving through a magnetic field I suppose.
Given that there's no resistance given, and no magnetic field given, this question is unanswerable as-is, right?

>>14984458
I don't understand any of this but why is 15+5=20 off to the side was that really confusing for a person who's able to do the problem

>>14984333
Ondular waves

>>14984621
sorry, those represent the possible points for the question. 15 for part a, 5 for part b, for a total of 20 points

>>14984155
something something moving away from you at relativistic speeds produces a long, low frequency wave and Doppler shift presents a red shifting a color

>>14984155
> so, light traveling across an expanding space has less energy at the end than if it was traveling
> but that would mean that the expanding universe is sucking energy from photons traveling through it

The perceived red/blue-shift depends on the relativistic Doppler effect, gravity, and the Hubble expansion. Combine that with the fact the energy of the light (frequency and wavelength) depends on the reference frame of the observer and it's not obvious what is going on. The answer General Relativity gives is that energy is not conserved in an expanding universe.

>Since the prizes are the same, it follows that the participant will prefer Gamble A to Gamble B if and only if they believe that drawing a red ball is more likely than drawing a black ball (according to expected utility theory). Also, there would be no clear preference between the choices if the participant thought that a red ball was as likely as a black ball. Similarly, it follows that Gamble C is preferred to Gamble D if and only if the participant believes that drawing a red or yellow ball is more likely than drawing a black or yellow ball. It might seem intuitive that if drawing a red ball is more likely than drawing a black ball, drawing a red or yellow ball is also more likely than drawing a black or yellow ball. So, supposing the participant prefers Gamble A to Gamble B, it follows that he/she will also prefer Gamble C to Gamble D. Supposing instead that Gamble B is preferred to Gamble A, it follows that Gamble D is preferred to Gamble C.
Gamble D has utility u(60*100/90) while C could have u(30*100/90) up to u(90*100/90). If u is shaped like sqrt, the average of the 60 possibilities of Gamble C will be less than D. Why does the expected utility theory strawman have utilities of the form u(dollars) = k*dollars?

Do I need to use the compactness of K for this? I was trying to work with unions and intersections of only two sets to build intuition, but I can't figure out what to do when they're not the same type of open sets as each other.

>>14983044
>>14983091
uh, nevermind. I manage to represent a number that is at one point periodic in a q-ary positional computation system (I think), I just don't quite get how to conclude it's necessarily a rational number from that.

>>14984020
Think of it like an interaction ("force") between the fields. A particle like a neutron corresponds to some complicated oscillation in the quark and gluon fields. The weak interaction means that the quark fields exert a "force" on the electron and neutrino fields so that some of the energy in the neutron oscillation can be transferred into making electron oscillations

>>14985204
The utility of an outcome here is just u(the dollar amount won), so the expected utility is u($100) multiplied by the probability of winning. The shape of u doesn't matter.

Why [math]|a_{n+1} | \leq |a_1 | q^n[/math] and not [math]|a_{n+1} | < |a_1 | q^n[/math]

>>14985363
What's the theorem?

>>14985381

>>14985381
>>14985391
I guess it's just providing a weaker condition. I checked my book and it starts with equality in the beginning as [math] |a_{n+1}|/|a_n| \leq q[/math]

>>14985381
>>14985391
I guess it's just providing a weaker condition since comparison test works with equality as well. I checked my book and it starts with equality in the beginning as [math] |a_{n+1}|/|a_n| \leq q[/math]

>>14985204
>It might seem intuitive that if drawing a red ball is more likely than drawing a black ball, drawing a red or yellow ball is also more likely than drawing a black or yellow ball.
No it fucking doesn't.

>>14982097
maybe you should give anti-depressants a try, son

>>14985449
>It might seem intuitive that if drawing a red ball is more likely than drawing a black ball, drawing a nonblack ball is also more likely than drawing a nonred ball.
How about now?

>>14977126
Shit, electromagnetic fields are difficult.

But for me personally, I try to always keep the big picture perspective in mind while learning or reviewing a subject. That makes actually understanding the problem much easier and quicker. Most of the time, if I can't solve a problem, it's because I was too involved in the nitty gritty of the problem. Don't worry about the calculations or formulas at first; just try to lay out a "flow" of the solution, then addendum with the formulas and finally the calculations.

I need help with proving these 2 questions on set theory.

Prove that the set of non-decreasing infinite sequences of natural numbers has a cardinality continuum.

Is it true that the set of non-increasing infinite sequences of natural numbers has a continuum cardinality?

>>14985469
What does [math]cyc[/math] in [math]\sum_{cyc}[/math] mean? I've seen that a couple of times at this point.

What does [math]cyc[/math] in [math]\sum_{cyc}[/math] mean? I've seen that a couple of times at this point

>>14985204
That's not how expected utility works.
There are two outcomes: winning 100 dollars and not winning 100 dollars. Expected utility is the sum of the probability of each outcome times its payoff.
>>14985268
>Do I need to use the compactness of K for this?
Yes.
>I can't figure out what to do when they're not the same type of open sets as each other.
[math]U \subset X[/math], [math]V = (X - K) \cup \{ \infty \}[/math]
[math]U \cup V = U \cup (X - K) \cup \{ \infty \} = (X - (\overline{U} \cap K)) \cup \{ \infty \}[/math]
Remember that closed subsets of compact sets are also compact.
(Also the question seems to be missing assumptions, I don't think I can assume all compact subsets are closed willy nilly in any topological space)

>>14985514
the issue is I can't tell if my professor actually didn't put enough information into the question or if I'm just stupid and haven't reviewed enough

because as far as I can tell, I would need at least a magnetic field equation given to derive any of the values requested.

>>14985665
You sum over all cyclic permutations of the variables involved.

[eqn]\sum_{\text{cyc}} f(x_1,x_2,\ldots,x_n) = f(x_1,x_2,\ldots,x_n) + f(x_2,x_3,\ldots,x_1) + \ldots + f(x_n,x_1,\ldots,x_{n-1})[/eqn]

>>14985691
>the issue is I can't tell if my professor actually didn't put enough information into the question or if I'm just stupid and haven't reviewed enough
Solve just for the variables first, and then substitute the values in the end to see if enough information was provided. If there is a part where some information is required but you have to assume it to solve further, assume the default values that your professors uses (or as the textbook assumes).

If the profs have enough experience with teaching, they usually give all the required info for assignments, though. It could be given explicitly or implicitly in the question.

>>14982828
Bump.

How do we know the stars and galaxies we see in the night sky are actually there today and haven't disappeared or moved in the thousands, millions or billions of years it has taken their light to reach us?

For me it's farmer walking around the gym while all the cardio nerds and the "I'm only here to grow a butt" squat stacies look at me weird

>>14985929
We don't.

Is it possible to prove there are uncountably many (distinct) functions?

>>14985957
[math] \{ f(x) = rx : r \in \mathbb R\}[/math]

How do I prove a PDE is well posed. I know that we need 3 things: existence, uniqueness, conditional to be satisfied, but given a PDE, how would you prove each one. I'm having a test that covers it so if I could get a concrete example I'd be very thankful.

So let me get this straight:
Photons don't interact with photons.
The electromagnetic force is mediated by photons.
However, photons are not affected by the electromagnetic force (which can be demonstrated by trying and failing to deflect a laser with a magnet or an electric charge.)
So then, how the fuck can photons interact with matter?

Is there a linear algebra book specifically for people with an abstract algebra background i.e. less elementary?

>>14985992
>given a PDE, how would you prove each one

>existence
Through great struggle.
There are also some general methods, like Riesz representation, open and closed argument, limit at infinity of some other PDE, turning it into an optimization problem, separation of variables, characteristics, etc.
>uniqueness
Constraint counting, shit like uniqueness for harmonic functions.
Stuff like Schrodinger or heat or really time evolution in general is obviously unique whenever it is unique.
>continuous on input
If it's linear, you show it's continuous at zero. Otherwise you struggle.
The way you proved existence might also immediately get you the result.

>>14986122
This one

how the FUCK do I solve this for the two functions

>>14985327
>>14985670
>That's not how expected utility works.
>There are two outcomes: winning 100 dollars and not winning 100 dollars. Expected utility is the sum of the probability of each outcome times its payoff.
Why can we not define outcome as "number of black balls", "probability of drawing a winning ball" or equivalently "expected payoff of the urn". Choosing urns with known balls and known prizes is almost as easy as "Choose $10 or $0". The number of balls can be found in principle. People don't worry about how the outcome "product of two dice" is calculated not observed.
Money is only a means so if I have enough money and I'm not into conspicuous consumption, I won't ever spend the $10 winning and thus expected utility theory is absurd as there's only one outcome "life goes on" -- this is my caricature of Ellsberg. In other words, he adds a step that combines outcomes and sends expected utility theory down there.

I'm supposed to solve these with u-substitution. What do I make u if there's more than 1 x. In a question like e^x^3 is u supposed to be x^3 or e^x^3. If theres parenthesis like (1-2x) is u 2x or 1-2x.

The examples in class were way easier than this it was just like 4 sin(4x)

>>14986230
sry

>>14986230
you have to find out what's the best substitution depending on the derivative
for instance, for 8., notice that if [math]u = x^3[/math], then [math]du = 3x^2 dx[/math] which means your integral simply becomes [math]\frac{1}{3}\int e^u du[/math]

>>14986230
7. substitute [math]1-x^2 = u[/math] and proceed

8. [math]x^3 = u[/math]

9. don't need to substitute anything, really. Straightforward linear function

Does mass accelerate "upwards" in all directions, or is the fabric of spacetime "pulled" by the massive object? I made a pic trying to illustrate what I think, but it could be just me being stupid. If someone can enlighten me better, I'd appreciate it. Not then it can happen that I'm just a retard that didn't understand gravity.

>>14986240
are there any general guidelines, are there any kind of tricky questions my professor might throw at me

how does what I marked in blue disprove the assertion?

>>14986428
forgot to add, the function [math]f(t)[/math] has $a,b,c$ as roots

>the main connective is the only truth-functor occurrence which has one more ' (' than ') ' to the left of it.
how so? This relates to propositional logic btw.

>>14986240
>>14986241
Also what happens to du
The organic lab guy just has it disappear after I simplify it, I would have thought we keep it

I'm trying to prove that [math]\mathbb{Z}[i][/math] is a Euclidean domain. I need help with one step. If I have integers [math]r, c, d \in \mathbb{Z}[/math] such that [math]r < c^2 + d^2[/math] can I somehow get a stricter bound for [math]r^2[/math]. I would need at least [math]r^2 < \frac{1}{2}(c^2+d^2)^2[/math]. Maybe assume [math](c^2+d^2)^2 \leq 2r^2 < (c^2+d^2)^2[/math] and by way of contradiction show that one of those numbers cannot be an integer? I hope someone has an idea for that.

I've been trying this for like 15 minutes and I have no Idea how to get this answer

>>14986428
z-zbar is purely imaginary. Since |z-c|^2 is real, their product is complex.

>>14986578
u=5-3x
du=-3dx
int dx/(5-3x) = -1/3 int du/u = -1/3 ln(u)

>>14986428
[eqn]-(z-\bar z)|z-c|^2 = \underbrace{i}_{\not \in \mathbb{R}} \cdot \underbrace{i(z- \bar z)|z-c|^2}_{\in \mathbb{R}}[/eqn]
A product of a non-zero real number with an imaginary is imaginary.

>>14986544
A little more clarification: [math]r \in \mathbb{Z}[/math] is the remainder when you do division with remained on [math]c^2+d^2[/math] assuming [math]c \neq 0[/math] or [math]d \neq 0[/math]

>>14986640
If you do division in [math]\mathbb{Z}[i][/math] then in general the remainder should be in [math]\mathbb{Z}[i][/math] too.

>>14973844

is there a formula that allows a var nBounces and given the number of bounces will "bounce" a ball from x = 0 to x = length N # of times?

e.g. given a range 0 to 100 and nBounces = 4, the ball moves forward on the X axis and down on the Y as it is released and hits the first bounce at range 40 or something. friction and "bounciness" reduce its x and y velocity so the next bounce is at 70, the next bounce at 90 and the final "bounce" where it comes to rest is at the end of our range, 100.

i've modelled this programmatically but im not sure about the math and relationships that would allow me to input a numBounces and distance and always bounce N times before coming to rest at distance.

>>14986812
nm i answered my question, i needed to reference a library w/ bouncein easing

>>14986227
>is politely corrected on something basic
>goes on a rant about how the theory is actually wrong and his misinterpretation is correct
Literally every single time someone criticizes economics on /sci/.
>>14986544
You're literally trying to show that [math]n^2 < \dfrac{(n + 1)^2}{2}[/math]
Obviously, the answer is "no, that won't work".

If A(t) is a matrix dependent on a parameter t with A' · A^{-1}' = A^{-1}' · A', does

[math]A·(A^{-1}·(A'·A^{-1})·A)'·A^{-1} = A'·A^{-1}[/math]
?

I think it is.

if I understand right, the impulse response can be considered the inverse Z transform of the transfer function.

I believe this is the right transfer function
[math]H(z) = \frac{z+1}{z^2 - \frac{1}{2}z+\frac{1}{4}}[/math]
but it has complex roots and a really strange, whack-ass partial fraction decomposition. There's no entry in my Z transform table like it, and wolfram alpha is spitting out nonsense about it too

I know from my continuous control systems course that this is obviously going to be an oscillatory system from being second order, but I have no clue how to invert this

any ideas?

>>14986167
guess I'm fucked huh?

>stupid questions thread
How far off are we from being able to do body swaps via brain transplants? Or even better, being able to put a human brain inside a cyborg body tailor made to your choice

>>14987387
Do you need to solve the system exactly?
The starting conditions sort of imply that you can just zero the cube term and solve a linear system of pdes to get good results around 0.

>>14987449
I have no fucking clue
all I know is that I'm an engineering major fresh into grad school and I somehow have to get that equation to work in a macro written in a programming language I don't know for a CFD program I started using 6 weeks ago and all of the relevant professors and phd students are absolutely dumbfounded about how the fuck it's supposed to be done

>>14987414
We are not even close so definitely not in your lifetime.

>>14982918
No reason. You can teach students about Gaussian elimination, cross product, and Cramer's rule without teaching them anything about vector spaces and linear maps.

>>14981116
>if I push someone at a fixed velocity, wouldn't that also be force?
No. If you bring a body up to a certain velocity, then the change the velocity undergoes through time is acceleration. There can be an initial momentum (defined by the initial velocity and the mass). Momentum changes every time the object/body has an external force is applied onto it.
If there is no external force applied onto it, since it remains at exactly the same velocity at all times, heading in the exact same direction, then momentum is said to be conserved, which means that the velocity is preserved in proportion to the distribution of momentum among objects inside the system, in accordance to their respective masses, initial positions, and velocities.
Momentum can be stated as the integral of force over time (i.e. [math]I=\int Fdt[/math]).

Are coincident lines considered concurrent?

>>14987487
>>14987487
You have a system of nonlinear ODEs, just use some random numerical method.
>>14990655
>Are coincident lines considered concurrent?
Yes.

BTW that's false unless "the three lines are concurrent" means "concurrent at the same point".
[math]x[/math], [math]y[/math] and [math]x + y + 1[/math] for a simple example.

>>14986592
hmm
Why can I move -1/3 out of int isn't it bound to du, and where do the absolute value lines come from

>>14987339
I get:
(8/√3)·(1/2)^n·sin(πn/3) - 4·(1/2)^n·cos(πn/3) + 4δ[n]
You should be doing partial fraction decomposition in terms of z^-1, not z. That should produce a constant term of 4 => 4δ[n] and terms matching #21 and #22 with ω0=π/3 => sin(ω0)=√3/2, cos(ω0)=1/2 in
https://en.wikipedia.org/wiki/Z_transform#Table_of_common_Z-transform_pairs
Or you can factor the denominator using complex roots to get two terms matching #11 with complex a and complex scale factor; their sum will be real because the a's and scale factors are conjugates.

In the case of a quadratic denominator with complex roots:

A(1/z)^2 + B(1/z) + C

first factor it so that the constant coefficient is 1:

(A/C)(1/z)^2 + (B/C)(1/z) + 1

Matching coefficients against 1-2a·cos(ω0)·(1/z)+a^2·(1/z)^(2)

=> (A/C)=a^2 => a=√(A/C)

=> (B/C)=-2a·cos(ω0) => cos(ω0)=-(B/C)/2a

From there, you can match the numerator against cases 19-22 (and case 1, Z{δ[n]}=1).

>>14991362
constants can be pulled out of the integral and the absolute value is a technicality of the integral because the log of a negative number is a bit gay.

>>14991217
new thread