/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.15472611]

Summer days edition

Formerly >>15437848

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (Latex)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I search for proofs?
proofwiki.org
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com
>how do I find the source of an image?
images.google.com
tineye.com
saucenao.com
iqdb.org

>where can I get:
>books?
libgen.rs
annas-archive.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>online courses and lectures?
khanacademy.org
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com
www.chemspider.com

Tips for asking questions here:
>attach an image (animal images are ideal, you can grab them from >>>/an/. Alternatively use anime from safebooru.donmai.us)
>avoid replying to yourself
>ask anonymously
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

[Anonymous No.15472730]

>>15472611
uoooooooooooooooooooooh

[Anonymous No.15472735]

someone explain polynomial division to me in a quick manner, I have to integrate rational functions but I forgot how to divide polynomials

[Anonymous No.15472822]

>>15472735
Divide the highest order terms in numerator and denominator. This gives the highest order term in the result. Subtract and repeat.

Example:
>x^4+6x^2+x / x^2+2
>x^4+6x^2+x= x^2(x^2+2) + 4x^2+x = (x^2+4)(x^2+2)+x-8

[Anonymous No.15472830]

>>15472730
this guy gets its

unanswered questions:

math questions:
>>15450783
>>15450795
>>15461884
>>15466432
>>15467161

doctor questions:
>>15440519
>>15455655

/g/ questions:
>>15439513
>>15468878

uncle ted questions:
>>15438453

cool videos:
>>15446899

schizo questions:
>>15450116

assassin questions:
>>15454495

chemistry questions:
>>15456767

solid state physics questions:
>>15461280

weed questions:
>>15464759

thermodynamics questions:
>>15465801

circuit questions:
>>15467742

balloon questions:
>>15468090

poseidon questions:
>>15470142

[Anonymous No.15472886]

>>15472830
>>15466432
I'll be honest, it's hard to read this one because you're making awkward use of the parenthesis. Usually you use them to explicit the order operations should be done in, so the passage [math]xy(y^{-1}) = x(yy^{-1})[/math] is very awkward and very suspicious.
>>15470142
Yeah, correct.

[Anonymous No.15473013]

>>15468090
>I've just started electromagnetics and we're in Coulomb's Law. I'd like to test it, but how would I apply a "known charge" to an object? I was thinking of testing it using balloons.

Well, without a "known charge" you can still test effect of distance on the force.

Also, if you have multiple similar objects able to hold charge (wands, balloons, etc.) perhaps you could assume the relative quantities of their charges without knowing the absolute quantities.

For example:
>charge wand A with unknown quantity
>touch wand A to empty (recently grounded) wand B
Presumably, A and B now hold equal charges.
>touch wand B to empty wand C
Now A has double the charge of B, and double the charge of C. Using these you could explore the effect of relative charges (doubled, quadrupled) even if you don't know the absolute charges involved.

[Anonymous No.15473059]

Is there a specific part of the human genome or group of parts that have been identified that separate us from the rest of the Animal kingdom? If all life on Earth is ultimately related, is there something genetically within us that explains our vastly superior intelligence even compared to our close primates relatives?

[Anonymous No.15473109]

>>15473059
No. You can't point at a few genes and say "these make us human". There are certainly some specific genes that vary greatly between us and other primates but that then ignores all the thousands of others that are slightly tweaked but when combined produce huge differences. Also many, many genes are completely identical but how they are expressed (the functions they perform) can be very different. That's why the number often quoted of us being genetically 99% identical to chimps is extremely misleading.

[Anonymous No.15473236]

could there be a planet the size of Earth or thereabouts that was a moon of a gas giant?

[Anonymous No.15473239]

>>15472611
If I was stranded on a boat without water but had a big jug of vinegar and baking soda could i make drinkable water?

[Anonymous No.15473359]

>>15472830
some janny must have been in a really sour mood to delete a girl in a sundress.

[Anonymous No.15473386]

>>15472611
How hard is arithmetic?

What I mean is, how difficult is it to do arithmetic problems for an average person? I'm trying to do a high school refresher before going to college and I'm realizing long mental arithmetic now is harder than algebra and geometry were for me in high school. Is this normal, or am I retarded? How much should I train my arithmetic to go on into calculus and higher math/computer science?

[Anonymous No.15473405]

>>15473236
Sure. There's nothing in principle stopping an exomoon being that size.

[Anonymous No.15473445]

>>15472611
you jack off to child pornography

[Anonymous No.15473660]

>want to learn high school level physics from scratch to pass the matura exam for it just for fun
>there's no step by step courses online and pretty much no learning materials in my language (Polish)
Am I doomed to use Khan academy? I feel like this course was translated to Polish by pajeets.
Any poles here? Any good textbooks for HS physics (rozszerzona)?

[Anonymous No.15473687]

reposting unanswered questions

math questions:
>>15450783
>>15450795
>>15461884
>>15466432
>>15467161

doctor questions:
>>15440519
>>15455655

/g/ questions:
>>15439513
>>15468878

uncle ted questions:
>>15438453

cool videos:
>>15446899

schizo questions:
>>15450116

assassin questions:
>>15454495

chemistry questions:
>>15456767

solid state physics questions:
>>15461280

weed questions:
>>15464759

thermodynamics questions:
>>15465801

circuit questions:
>>15467742

balloon questions:
>>15468090

poseidon questions:
>>15470142

[Anonymous No.15473832]

According to wiki, Godel's axiom [math]\bf{V=L}[/math] implies the existence of an analytic set of reals which is not Lebesgue measurable.

How to reconcile this with the standard fact that [math]\bf{ZFC}[/math] alone proves that every analytic set is Lebesgue measurable?
(Recall that [math]\bf{ZF}[/math] plus [math]\bf{V=L}[/math] implies choice.)

I guess I must be misinterpreting the terminology, somehow

[Anonymous No.15473949]

>>15473405
And would such a moon be able to hold an Earth-like atmosphere and life, or would the parent planet's gravity fuck with that?

[Anonymous No.15473976]

>>15473949
Nothing would prevent life (in principle) and any atmosphere would not be affected by gravity of the parent (though other factors might). Take Titan for example, it's atmosphere is denser than Earth's.

[Anonymous No.15473999]

>>15472735
https://youtu.be/RPXMBIFG_W4

[Anonymous No.15474026]

>>15473660
yes, lol, are you me? I've been doing literally the same for a week now.
Fuck online resources, they will tie you to a laptop or a smartphone which are unnecessary distractions. The weather is nice, get yourself an actual book and go with it somewhere outside. As for the book, get yourself picrel. They are cheap now because they are from before the reform.

[Anonymous No.15474083]

>>15474026
When I was still in school a popular opinion was that there were no good Polish HS physics textbooks on the market, but there was a good problem book "Zbiór zadań z fizyki, Jędrzejewski, Kruczek", which people praised. The books I used in my school (Operon) were absolutely horrible, and I hold that opinion even when looking inside them today. Maybe modern Operon books are better, but idk.
Picrel are from ZamKor, and I think they are decent. I don't think they publish anymore, but you can still find plenty of used ones in circulation. I was checking out what new books the best high schools are using right now (post-reform), and it was either "Zrozumieć Fizykę" by Nowa Era or "Fizyka" by WSiP, but they are spread into 4 volumes of textbooks and problem books (so 8 books in total) and they are expensive. I can't tell if they're good or not, but in general, I think trusting what best schools use is a good idea.
But honestly, the best way is always to have access to multiple books or resources. Pick one as your main, and use others as supplements when you have a hard time understanding a concept in the main one. My brother has masters in maritime mechanical engineering and he told me he used to borrow books from friends in a vocational school because the same topics were way more approachable in them and it was in general a good idea to start with them, and then go read the same topic in your main one.
Also, for self-study, make sure the problem book has full step-by-step solutions for each problem, and not just answers. The first problem book (Jędrzejewski, Kruczek) I mentioned is divided into 2 volumes, one is for problems, second is for solutions. The ZamKor one from picrel I'm using doesn't have solutions, but you can find them online on 3rd party site "odrabiamy.pl". They're behind a paywall, but I've dumped them with some python magic so I won't have to pay each time I want to check my solutions.

[Anonymous No.15474155]

>>15474026
>>15474083
Thanks. I'll look into it. Any idea how hard Matura for fizyka rozszerzona is? I don't know a single person who had even attempted it.

[Anonymous No.15474156]

I have to solve the limit [eqn]\lim _{n \to \infty} \sum ^n _{k = 1} \sqrt{2 - \left( \frac{k}{n} \right)^2 } \cdot \frac{k}{n^2}[/eqn]
using Riemann sums. How do I do this? I know it's supposed to be some function on an interval such that [math] f(x)(x_i - x_{i-1}) [/math] where x is in [math] x_i - x_{i-1} [/math], but I couldn't get it to this form.

[Anonymous No.15474168]

>>15474156
Start by viewing it from the other direction.
The integral
[eqn]\int_0^1 f(x) dx = \lim_{n \to \infty} \sum_{k=1}^n f \left( \frac{k}{n} \right) \frac{1}{n} [/eqn]
if [math]f[/math] is Riemann integrable over the interval.

How do you have to select [math]f[/math] so that it becomes your limit?

[Anonymous No.15474173]

>>15474155
ah, I actually have that Zrozumieć Fizykę textbook at my house. I remember them being terrible from when I was still at school. Or maybe I just couldn't have been bothered to learn physics, lol. I was always more of a math person. I seem to lack last volume, and their zbiór zadań is split into three expensive books

[Anonymous No.15474177]

>>15474173
Table of content from volume two, but it outlines all materials that's in all volumes.

[Anonymous No.15474178]

>>15474168
Ah, I see it now. Thank you.

[Anonymous No.15474212]

>>15472611
How do you remember basic things after a long gap of not using math? I forgot what a quadratic function was, even though I've made extensive use of it before.
I looked at it again and was able to recall, which was a relief, but I worry that something like this might happen again and I won't be able to recall it. Should I just use Anki or something? Sounds overwhelming to store everything in that.

[Anonymous No.15474220]

>>15474212
Information gets stored in your long term memory when you restudy material that you are just about to forget. Restudy too quickly and you'll forget it quickly too. There's a sweet spot that you should aim for.
Even if you forget some long term memories you'll be able to relearn them quickly + they'll take longer to be forgotten the next time.

[Anonymous No.15474226]

WHY THE FUCK WONT 240U B DECAY INTO PU94 AND ALWATS DECAYS INTO NEPTUNIUM PLEASE WILL SOMEONE EXPLAIN I AM RETARDED

[Anonymous No.15474250]

>>15474226
anon... the only way uranium would decay into plutonium is through double beta decay
and the only isotope of uranium known to do that has a double-beta half-life far, far, far longer than its typical half-life
there's literally no reason to expect it to decay directly into plutonium, ever.

[Anonymous No.15474267]

>>15474250
Thank you, I'm ignorant.
What I was asking I guess is why won't it decay, first into neptunium and then into Pu. However, I now see that it's possible after more research. Thank you, I'm shit at physica except for engineer level stuff

[Anonymous No.15474295]

I bought some chinkshit a while back that came with AAA batteries. Then one day, for no reason at all, it suddenly stopped working and started leaking this rust-orange fluid.
What compound could this be? Are there any common iron(III) batteries that would produce this? Or did HCl come in contact with a steel casing or something?

[Anonymous No.15474412]

>>15474220
That's reassuring. Guess I'll keep reinforcing. Thanks.

[Anonymous No.15474424]

I have a potential [math]V_{ij}[/math] that only depends on the distance between two point masses. Meaning it is [eqn]\vec{F}_{ij} = -\nabla V_{ij}(|\vec{x}_i - \vec{x}_j|)[/eqn] where the [math]\nabla_i[/math] is the partial derivative in respect to [math]x_i[/math]. I have to somehow show that such potentials lead to forces that satisfy Newton's 3rd axiom and that fulfill the property [math]\vec{F}_{ij} \times \vec{x}_{ij} = 0[/math].

The book says this is an easy task but I just don't see it. Can you guys please help me out. Thanks.

[Anonymous No.15474435]

test

[Anonymous No.15474516]

>>15474424
> show that such potentials lead to forces that satisfy Newton's 3rd axiom
That is trivially shown by the fact [math]F_{ij} = F_{ji}[/math]

> fulfill the property [math]\vec{F}_{ij} \times \vec{x}_{ij} = 0[/math]
Use the cross product formula and the fact both vectors are parallel (the angle between them is zero).

[Anonymous No.15474540]

>>15474516
I think you mean F_ij = - F_ji, right? The thing is I have to somehow derive this identify from the formula with the nabla operator? And who do you know that the force and the distance Vektor x_ij are parallel?

[Anonymous No.15474543]

>>15474540
Btw. the task gives me a hint. It says I have to use the chain rule for differentiation. Maybe this help I don't know.

[Anonymous No.15474552]

>>15474540
>>15474424
I forgot an "i" there

[Anonymous No.15474563]

>>15474540
Yeah, that was a typo, they would be opposite. The gradient going from i to j is the negative of going from j to i.

> And who do you know that the force and the distance Vektor x_ij are parallel?
Because that's the definition of F_ij. The force acting along the vector x_ij

[Anonymous No.15474575]

>>15474543
> It says I have to use the chain rule for differentiation
ah, should have said that earlier. they want you to expand the nabla in terms of the partial derivatives and some basis vectors.

[Anonymous No.15474591]

I want to find the sum of the earth's gravitational force for a very long object. I can assume that the concentration of the object is constant. Is this integral [eqn]\int_0^m \int_{r_{0}}^r -\frac{GM}{r^2}\, dr\, dm[/eqn] the correct approach? If not, how could you calculate this?

[Anonymous No.15474595]

>>15474575
Hm okay. Not sure if you saw this >>15474552. In a way, I can't really expand anything, because there is only one partial derivative.

[Anonymous No.15474598]

>>15474155
>Any idea how hard Matura for fizyka rozszerzona is
You have access to all the past exams and grading instruction sheets online, so you can check them out yourself.
I don't have much experience with the advanced physics Matura exam, I've barely seen a few exams. But it's not like I'm starting fresh. I have roughly covered the whole HS material and I've been through a college-level physics course. But I'm a bit rusty, I have a few holes to fill here and there and I'm definitely lacking in the amount of problems solved. So my goal is more to ground my knowledge than to learn from scratch.
But I have a lot of experience with the advanced math Matura exam. I'm actually a tutor and I've prepared people for that exam with pretty good results.
The reason I'm brushing up on physics is that people want me to tutor them in physics too, because there is a desperate need for people who can teach physics, even in those schools that are supposed to prepare for that exam.
Physics has a reputation for being the hardest Matura exam, and people are definitely afraid of it. Not a lot of people take it, even in the schools that are supposed to prepare for it, and when they do, the scores aren't amazing either. But the material isn't really that much harder than math, imo not at all, and the amount of material is actually a lot smaller.
I went through all the Matura Math exams since the first one in 2002 multiple times with a lot of people, so I'm fairly familiar with that one and the math curriculum. I think that with physics, you only need to solve a small fraction of the number of problems you need for math, which demands an industrial amount of problems (in thousands) to solve.
Personally, I think I could solve most of the Matura physics exam, but it would definitely take me too much time. And it looks like the problems in that exam are time demanding.
So the real problem IMO not the difficulty, but:
1) textbooks are in general shit
2) you're basically on your own

[Anonymous No.15474603]

>>15474591
Maybe I should give you an explanation for what this is supposed to be. I have to calculate the gravitational force that would be exerted on a space elevator.

[Anonymous No.15474643]

>>15474595
You do realise that doesn't make any sense right?

[Anonymous No.15474659]

>>15474643
Well, I did. But that's unironically how they wrote it. They just defined [eqn]\nabla_i = \frac{\partial}{\partial \vec{x}_i}[/eqn]. So I don't know.

[Anonymous No.15474665]

>>15474591
>>15474603
Nothing that complicated. Just use r for the center of mass of the object. However for a space elevator you also have to consider centrifugal force which will counteract against gravity so that formula wouldn't be correct in reality.

[Anonymous No.15474677]

>>15474665
Couldn't the centrifugal force also be calculated using the object's center of mass?

[Anonymous No.15474681]

>>15474659
That's a weird ass notation but I guess they mean implied indices since it wouldn't be a partial derivative for a 1D system.

[Anonymous No.15474689]

>>15474677
I don't think so since it increases with height so at some point the effective gravitational force would switch from down to up.

[Anonymous No.15474706]

>>15474689
But isn't that exactly what would you could expect? I mean the space elevator is meant to be a geostationary satellite.

[Anonymous No.15474717]

>>15474706
Yes, exactly. But that means all the forces acting on the elevator isn't purely due to gravity.

[Anonymous No.15474744]

>>15474717
Okay, the way I would do it is to calculate the center of mess r_0. And then go on to determine the gravitational and centrifugal forces using r_0 and finally add them up. This would then give me the force acting on the object.

I should mention that this elevator is built on the equator, of course. This way the forces would be parallel and only there oriented absolute values would matter.

[Anonymous No.15475442]

How does he get eq 12? If I sum I1+I2 from eq 11 the term of rj^2 for example doesn't disappear, am I retarded?

[Anonymous No.15475460]

>>15475442
[eqn]r_j^2 = r_{1j}^2 + r_{2j}^2 + r_{3j}^2[/eqn]

[Anonymous No.15475540]

What’s the essential book/course or whatever that’ll prepare you for calculus 2 ? In under 3 months preferably.

[Anonymous No.15475880]

So we've known this is how sound works and this is what computers interpret to play sounds for awhile, right? Are there any people that work backwards, making a sound waveform and then seeing what sound it makes? We've been using digital sound long enough that surely someone's kind of figured it out.

[Anonymous No.15475954]

does a continous function on a bounded interval have a countable set of positive (or negative) subsets in the reals?
I believe it does, but I am not sure. Another question is if I can pick a smallest one for any continous functions (I think the first question implies this one)

[Anonymous No.15476072]

>>15475460
I'm retarded indeed, thanks a lot anon

[Anonymous No.15476080]

>>15475880
Aphex Twin and others generated sound from photographs years ago. You should be able to do it yourself with a program called Metasynth.

[Anonymous No.15476132]

>>15475880
You could work backwards since an audio waveform visualization is calculated using a fast Fourier transform, just applying the reverse FFT and you will get you the original data back. However in reality that doesn't work because the visualization uses bucket sampling to put frequency ranges within specific buckets and the graphical representation isn't updated in real time but averaged a few times a second. So you have lost a lot of the original audio data which you can't recover. It would be like compressing a 32bit 192kHz FLAC file to an 8bit 8kHz mp3. How closely it matched the original audio *shrug*

[Anonymous No.15476171]

>>15474598
>because there is a desperate need for people who can teach physics
True. I do remember having problems finding tutors for physics back in high school. Another opportunity would be to make some kind of Matemaks-esque online pre-recorded course and promote it on forums like Wykop. There's only a handful of these courses for physics on the Polish web and most of them are ridiculously expensive.
>I think that with physics, you only need to solve a small fraction of the number of problems you need for math
That's reassuring. I have some experience with advanced math matura and it was an insane grind.

[Anonymous No.15476244]

Basic stats question. I have a set of samples from P(X). In some of these samples, Y is true, and in the rest, Y is false. How do I tell whether the distribution P(X|Y) differs from P(X) in a statistically significant way? And how do I quantify the statistically significant difference?

[Anonymous No.15477310]

Why is the size of an amplifier inversely proportional to its frequency?
I've seen some massive C-band amplifiers but the Ku/Ka band ones were significantly smaller.

[Anonymous No.15477358]

How to prove that the union of first and third quadrant is connected?

[Anonymous No.15477379]

>>15477358
Find a connected set [math]A[/math] and a continuous function [math]f[/math] such that [math]f(A)[/math] is the union of those quadrants. It might be easier to find if you consider polar coordinates.

[Anonymous No.15477638]

[math]S=k_blog\Omega[/math]
where Omega is the number of the microstates of the system; which is, all the possible current configurations of all the N atoms/particles which correspond to the current macrostate (with a certain p, V, T)
then, my book says that each macrostate is associated with an infinite number of microstates; in fact any system is associated to [math]\infty^{2f}[/math] microstates, where f is the number of degrees of freedom of a system.

What does "degree of freedom" mean for a system? And why is there a 2? Is it because a system (perfect gas) only has 2 independent variables at any given time?

anyway, it goes on saying this which i didn't quite understand:
so each state(not clear if micro or macro, i think macro) is a point in an inf^2f dimensional space; then, we divide this space in a certain number of very small cells, each of hypervolume [math]\tau[/math]; then, we assign each cell to the corresponding state. This representation allows us to calculate [math]\Omega[/math] using combinatorics; note that the value of [math]\tau[/math] influences the value of omega and therefore of the entropy, (and we can't make it infinitely small or S would be infinite and useless). What we can prove is that if tau changes, omega changes by a factor (as in the factor times omega), and since there is the log in the formula this means that the entropy changes by an addictive factor; what this tells us is that classical statistical mechanics can't determine a constant of the entropy, which we will have to use quantum mechanics for.

Alright so, I got the general idea but didn't really understand much and this book can't go into much depth since it's just a thermodynamics book, where can i learn more about this last paragraph? And I don't get it, can't we just use the fact that the entropy is 0 at T=0K to calculate the constant at any given state?

[Anonymous No.15477723]

>>15476171
>Another opportunity would be to make some kind of Matemaks-esque online pre-recorded course
Back in the day when universities started to publish and open their courses online and MOOC became a thing, I also thought it would push learning into another dimension by eliminating the need for a physical teacher from the process. Don't get me wrong, I still think they're great, the more high-quality easily accessible materials the better, but I don't think they're revolutionary at all. And especially not in regard to getting rid of a teacher from the process.
You gave an example of "Matemaks". But I had literally dozens of people who came to me for tutoring after they tried learning from his videos. The problem is, people completely misunderstand (and underestimate) the role of teachers and how to utilize them. This was something that Plato understood and he made a brilliant argument against reading books in his Dialogues (yea, he argued reading books make you dumb). This is a bit of tl;dr, and I don't have the energy to repeat all his arguments. I had a thread on some board about it a few years ago, unfortunately, I can't find it in the archives.

[Anonymous No.15477739]

>>15477638
A degree of freedom is some parameter that is used to describe the physical state of a system. For an ideal gas that would be a particles momentum in the x,y,z directions. I'm not sure where that 2 comes from desu. Maybe they are also counting a particles position as well as its velocity?

> can't we just use the fact that the entropy is 0 at T=0K to calculate the constant at any given state?
No because that isn't true for some real-world systems, it is possible to have multiple states with the same minimum energy (degenerate quantum eigenvalues).

> where can i learn more about this last paragraph?
Maybe trying reading up on von Neumann entropy.

[Anonymous No.15477784]

Is this correct? A and B are commutative matrices.

[Anonymous No.15477904]

>>15477784
yes.

[Anonymous No.15477975]

is it true that if two funcions have the same value in the same point and they have the same derivative in that given point, then they have the same values in their immediate (infinitely small?) enviroment?

I don't have much of a formal education in stem, stuff like this just fascinates me, that's part of the reason why I'm phrasing my question so poorly.

to me it seems obvious that it's true but I can't "prove" it I guess? I'm aware that it's likely that my assumption is wrong but if it is, I'd like to know why (please explain it as simply as possible), because that means that my intuition about calculus is completely wrong.

in my mind my assumption is what implies that two funcions are completely the same if they have the same derivative for every point and if they have a point where their values are the same. also if I apply basic algebra, it seems to work out but I'm not sure if I messed something up.

f(x0) = g(x0);
f'(x0) = g'(x0) => lim h->0 (f(x0+h)-f(x0))/h = (g(x0+h)-g(x0))/h


(f(x0+h)-f(x0))/h = (g(x0+h)-g(x0))/h

f(x0+h)-f(x0) = g(x0+h)-g(x0)

f(x0+h) = g(x0+h)

[Anonymous No.15478002]

>>15477975
>is it true that if two funcions have the same value in the same point and they have the same derivative in that given point, then they have the same values in their immediate (infinitely small?) enviroment?
No. Consider
[eqn]f(x) = 0 \\
g(x) = x^2[/eqn]
For those functions
[eqn]f(0) = g(0) = 0 \\
f'(0) = g'(0) = 0[/eqn]
But those functions have different values for every [math]x \neq 0[/math].

[Anonymous No.15478018]

>>15478002
thanks, it's clear that I am wrong but I don't understand why
are the h's not the same on both sides of the equations of my "proof" or algebra just doesn't apply here?
I don't understand where I'm going wrong.

[Anonymous No.15478037]

>>15477975
>and they have the same derivative in that given point
its true if they share *every* derivative at that point, and if both functions are analytic. in that case the functions are actually equal to each other.
https://en.wikipedia.org/wiki/Taylor_series
https://en.wikipedia.org/wiki/Analytic_function

[Anonymous No.15478053]

>>15478037
wouldn't this mean the following:

f(x) = x^5 g(x) = x^1000

all of their derivatives are the same (=0) in 0 as far as I know


if the nth derivative is 0, it implies that their n-1th derivative are the same in 0+h which would imply that their n-2th derivative are the same in 0+h+h all the way for every point of the original function

again, I know I'm probably wrong, I just don't know where I'm going wrong

[Anonymous No.15478055]

>>15478053
>all of their derivatives are the same (=0) in 0 as far as I know
fifth derivative of x^5 is 5! and 1000th derivative of x^1000 is 1000!

[Anonymous No.15478066]

>>15478055
AH, THANK YOU SO MUCH
I don't know how I missed that part
I think I'm on the right path now to understand this but I'm still confused a bit

[Anonymous No.15478067]

>>15478066
its nice that youre curious about this stuff, anon. consider reading a book on real analysis, maybe rudin.

[Anonymous No.15478074]

>>15478067
yes, It's pretty nice thinking about stuff like this, math is amazing but science is not my cup of tea if I'm being honest
I tried reading books on mathematical topics that I should already be familiar with to test the waters but it didn't work out too well.
I used to do well in math back in school but it's really hard to learn when I don't have a teacher, just a book.
is there a way to get more efficient at learning from books or should I just "force it" until I get better?

[Anonymous No.15478085]

>>15478074
read a couple paragraphs, then try to explain/summarize what you just read to an imaginary person. you can have it be a cute girl if you want, but girls are bad at math so you might want to imagine an asian one.

[Anonymous No.15478119]

>>15478085
alright, that's what I will be doing

[Anonymous No.15478130]

The distance x covered by a particle in one dimensional motion varies with time t as x2 = at2 + 2bt + c. If the acceleration of the particle depends on x as x^-n, where n is an integer..find n.


I do have the solution, but can not understand it properly...can any anon here explain the solution step by step pls ?

[Anonymous No.15478133]

>>15478130
It's x^2 = at^2 + 2bt + c

Sorry for error

[Anonymous No.15478187]

>>15478133
First differentiate twice to get
[eqn] x \dot x = a t + b \\
x \ddot x + \dot x^2 = a[/eqn]
Since you need to eliminate [math]\dot x^2[/math] it would the wise to square the upper equation and then eliminate [math]t[/math] from it.

[eqn] x^2 \dot x^2 = (a t + b)^2 = a^2 t^2 + 2 a b t + b^2 = a(a t^2 + 2 b t + c) + b^2 - ac = a x^2 + b^2 - ac \\
\dot x^2 = a + (b^2 - ac)x^{-2}
[/eqn]

With this you can easily solve the other equation for [math]\ddot x[/math].

[eqn]\ddot x = (a - \dot x^2)x^{-1} = (a - (a + (b^2 - ac)x^{-2}))x^{-1} = (a c - b^2) x^{-3}[/eqn]

[Anonymous No.15478341]

why are they prioritizing space travel over medicine? are they planning on sending mortals into deep space?

[Anonymous No.15478381]

You are studying a gene (one locus) that is 100 bp in length. There are three alleles in the diploid population: A, B, and C. You are using the restriction enzyme called Ritzy1. There is no restriction site in allele A. Allele B has a restriction site 20 bp from one end, whereas allele C has a restriction 50 bp from one end. PCR is performed on members of the population, and products are digested with Ritzy1. Name the genotypes showing only one band? Two bands? Three bands? Four bands?

[Anonymous No.15478566]

Any medfags ITT?
Actually scared at the moment, last two times I've taken a shit there's been blood, not massive amounts, but enough to make you go "oh shit"
From what I've read it's most likely hemorrhoids (bright red, no pain, no excessive amounts), but I'm already deathly scared of any interior problems with the human body

[Anonymous No.15478577]

>>15476171
Also, I've been looking up some resources and there is this guy "Flipping Physics" who seems to have nice stuff (in video format tho).
I haven't seen many of his videos, but he impressed me because he's literally the only guy who explained a topic that every other resource just ignored, hand-waved, or couldn't explain correctly: https://www.flippingphysics.com/energy-systems.html
Might be worth checking his stuff

[Anonymous No.15478725]

>>15478566
it's incredible how much nightmarish stuff can happen to your ass without causing sepsis or dying

[Anonymous No.15478775]

>>15477723
>You gave an example of "Matemaks". But I had literally dozens of people who came to me for tutoring after they tried learning from his videos
His course isn't some magic stuff. You still need to do a lot of exercises to really understand any given topic. And he does indeed repeat that many times in his videos, and it's why he records video solutions and step by step explanations for each exercise/task that he gets his hands on.
But you are right about teachers. But it has to be one on one session, I don't find classroom teachers to be very valuable. They can put your train of thought on the right track, or you can ask them questions about anything to dissect any niche nuance. Pre-recorded video lessons are more like textbooks, but you are using more senses (hearing) to get a grasp of the material, which makes them more digestible than books, but they are still not as good as teachers.
IMO a good way to learn effectively right now when you can't afford regular tutor sessions is using chat-GPT + textbooks/video lessons. Chat-GPT is surprisingly good, at least in case of explaining programming concepts. I haven't tried using it to explain me physics/math concepts/nuances yet.

[Anonymous No.15478888]

How do i prove this?

[math](\forall x \in R)((\forall y \in R)(xy = x) \Rightarrow a = 0) [/math]

I'm confused about the universal quantifier on x, when this is only true for when x is 0.

Also i can only prove this for y = 0. 0 is a real number, so let y= 0, giving x(0)=x, which gives 0=x.

But what about 1? 1 is a real number, so let y=1, giving x(1)=x, which is true. But this doesnt prove x=0.

And then something like let y=2 gives x(2)=x which is false, and i cant manipulate it into being x=0.

[Anonymous No.15478889]

>>15478888
sorry i meant
[math](\forall x \in R)((\forall y \in R)(xy = x) \Rightarrow x = 0)[/math]

[Anonymous No.15478912]

>>15478888
Let [math] y = 0 [/math]

[Anonymous No.15479075]

>>15478187
Thanks anon, any resources which contain more these tyoe of questions?

[Anonymous No.15479161]

>>15478775
>You still need to do a lot of exercises to really understand any given topic.
With any teaching resources, be it books, videos, in-person lectures or tutoring, you need to settle on who your target audience is first.
You need to have a good idea of who they are, and then adjust your material and shift your focus accordingly. With a teacher, there is a feedback loop between the students and the teacher, and they can do that dynamically. With one-sided resources like books you have an open loop and you need to assume that in advance. This is the reason why can't we have just one perfect book on supposedly the same subject.
The problem with Matemaks is that he's always assuming his audience is struggling beginners. This is a good thing if you want to have accessible materials to hop on a random topic. But not so much if you want to treat them as a regular teaching course, because he's focusing too much on basic stuff taking his time, there is no assumption of student progression and you end up using way too much time on the easy stuff. Learning is about efficiency and time management, and this is where a teacher comes in. You can try to figure out everything on your own, and sure, you will do it, but it will take you much more time. I recently had a small issue that took me 2 days to figure out, which I could probably resolve in 15 minutes if I had anyone to ask. You could argue it's worth it, but we are mortal after all. And it's better to use that time on something more appropriate for you. It's not just about the quantity of the problem, but also their quality. But you can't really tell what's appropriate and what's not without someone who knows his stuff.
But even though his materials are designed for an audience of any random struggling student, there are always some implicit assumptions about what you already know, which you might not necessarily be fulfilling. A teacher should be able to catch that and guide you to the necessary prerequisites.

[Anonymous No.15479170]

>>15478775
>But it has to be one on one session, I don't find classroom teachers to be very valuable.
oh, but they can be, with a very simple trick - be ahead of the material by studying it on your own, and come to the classroom with questions prepared that popped up when you self-studied the material
>Chat-GPT is surprisingly good, at least in case of explaining programming concepts. I haven't tried using it to explain me physics/math concepts/nuances yet.
Maybe with programming. I tried it with physics but it just repeated after textbooks which was a problem in the first place. A friend of mine tried asking it to solve chemistry problems and he said it spews just a bunch of nonsense

[Anonymous No.15479205]

Can any anon here explain me the equations of motion with more intuition ? Like why do we integrate dx with with limits xi and xf to dt with limits t= 0 and t= t ? And how does it result in getting the equation for uniform motion ?

I have already seen the 3blue1brown calculus video but still can not interpret the use of it in physics

[Anonymous No.15479269]

>>15478381
Please respond. Quizlet says

>Homozygous A and C will have one band, Homozygous B will have 2 bands, Heterozygous A B, B C will have 3 bands, None will show 4 bands.

but ChatGPT says homozygous C is 2 bands..

[Anonymous No.15479471]

what do sabine and others like her define free will to be? I don't get it; she spends a long time ranting how free will doesn't exist and then claims that you can make your own decisions and that making decisions is different from free will.

[Anonymous No.15479482]

In presenting the lack of a supremum of p^2<2 for Q, why does rudin go through the trouble of constructing one rather than simply taking the arithmetic mean of p^2 and 2 to show that no maximum exists?
i.e [math]A=\{p\in \mathbb{Q}:p^2<2\}\\
k=max(A) \implies k^2<2\\
k^2+2<4\\
k^2<(k^2+2)/2<2[/math]

Hence violating the fact that k =max A. Is it merely that he wants to construct an algorithm that tends to root 2?

[Anonymous No.15479484]

>>15479471
>free will
>>>/x/

[Anonymous No.15479489]

Why are homeless people cold?
I notice that homeless people are cold even when it is not cold outside and I know it's the result of sleeping outside
But I can't make the connection, of course they would be cold when it's cold but even at noon when it hasn't been cold for hours they are still cold
Is their body temperature low or is it just a sensory thing?
It happened to me once when I went camping and then I started noticing that every homeless person during autumn, winter and early spring looks really cold during most of the day, you can see it in their body language, their skin and because they are wearing too much clothing

[Anonymous No.15479491]

>>15479482
How do you know that number is a square of a rational?

[Anonymous No.15479494]

>>15479491
I see, thanks a lot

[Anonymous No.15479496]

>>15479471
If you are deprived of all stimulus in a void and you can't even feel your own body you can still make choices
Thus free will exists

[Anonymous No.15479531]

How many frequent Touhouposters does this general have? 1? 2? 3? Is the poster who answers questions the same one as the one who asks questions? Or are they just all part of a secret group that uses this general as their outpost?

[Anonymous No.15479578]

>>15479205
Bump

[Anonymous No.15479585]

What is the most minimalist proof to the fact that [math] \sqrt{n+1} - \sqrt{n} [/math] strictly decreases as [math] n \in \mathbb N [/math] increases.

[Anonymous No.15479586]

>>15472611
Does there exist (or can I make) a stirrer that's like a magnetic stirrer bar, but is isolated from the plate and is radio frequency controlled?

[Anonymous No.15479670]

>>15479531
It's actually all just me.
Even you are just me, asking myself a stupid question.
In fact, I don't even know why I'm bothering to answer myself.

[Anonymous No.15479673]

>>15479585
>If only it were possible to take a derivative of this function to evaluate the slope!

[Anonymous No.15479677]

>>15479586
In theory, yes. You could make an enclosed plastic object with a motor turning a heavy metal weight inside. The motor being anchored to the housing would result in the whole case rotating the opposite direction as the weight (at reduced speed) and there's no reason you couldn't also enclose a battery and an RF circuit.

[Anonymous No.15479679]

>>15479484
>I'm an NPC, therefore so is everyone else.

[Anonymous No.15479690]

>>15479585
The most? Dunno.

[math](\sqrt{n+1} - \sqrt{n})(\sqrt{n+1} + \sqrt{n}) = n + 1 - n = 1[/math]
Clearly [math]\sqrt{n+1} + \sqrt{n}[/math] is strictly increasing, hence [math]\sqrt{n+1} - \sqrt{n}[/math] is strictly decreasing.

[Anonymous No.15479705]

>>15479690
Nice thanks.

[Anonymous No.15479717]

If velocity is given as function of postion

V = √10+8x
V^2 = 10+8x

Now if we differentiate it-
2V*dv/dx = 8

How come it is dv/dx, shouldn't the differentiation be just 2V ?

[Anonymous No.15479741]

>>15479717
You'll need that [math]\frac{dv}{dx}[/math] once you start doing integration and partial derivatives. I can't really explain why, but what
you should eventually learn is that you have to specify what you're differentiating against what.
In some cases you might have a bunch of different variables lined up in an equation, but you'll only have to differentiate a specific one. The one you pick will have to be pointed out so as to not get mixed together with undifferentiated terms.
Then once you have to reconstruct the original function from its derivative (with respect to a specific variable), you'll have some idea of what to look for.

The general idea to keep in mind is to point out the fact that you're dealing with a derivative, that is to say, a rate of change, and not with a "whole" function.

[Anonymous No.15479755]

>>15479741
Hmm, trying to get the idea....does it mean we get the dv/dx cause we're are differentiating with respect to x and not with v ?

[Anonymous No.15479758]

>>15479755
Yeah, that's more or less it.

[Anonymous No.15479772]

>>15479758
Thanks anon, any tips on how to go through calculus-based physics ? I have only taken algebra based physics as of now. Our reference book is University physics by young and fredman

[Anonymous No.15479794]

what is the most modern and fleshed out book that rigorously defined a base logic and uses it as the foundation of mathematics.
I looked at Dirk Van Dalen's Logic and Structure, but it starts off with a preconceived notion of sets, instead of starting with logic, and then defining sets using that.

[Anonymous No.15479815]

>>15479772
The usual recommendations for Physics classes apply (spot the key variables being used, get a rough mental picture of elements involved, sketch out the situation, write down the relevant formulas).
Generally, it's good to try to understand equations first mathematically and then physically. Try to think of what might be changing (is it a division of space? is it time?). Once you've got that down, find a way to perform the applicable calculus-related operation (either differentiation or integration). After that, it should all be algebraic variable manipulation.

[Anonymous No.15479896]

>>15479815
Thanks, I face problems while doing integrating based questions..like how should I get the idea of when to integrate ?

[Anonymous No.15480122]

>Given [math]n[/math] consecutive natural numbers, show that only one of them is divisible by [math]n[/math]

my idea is to write the [math]n[/math]-th term as [math]T_i = k+(n-i)[/math] and then prove that [math]n|T_i[/math] for only one value of [math]i[/math], but I have no idea on how to proceed

[Anonymous No.15480125]

>>15480122
I meant [math]i[/math]-th term, sorry

[Anonymous No.15480144]

>>15480122
Take any two distinct numbers [math]T_i, T_j[/math] and consider their difference.
If those numbers leave the same remainder after division by n then their difference is disible by n but [math]|T_i - T_j| \in \{1,2,...,n-1 \}[/math]. How many of those numbers are divisible by n?

[Anonymous No.15480186]

>>15480144
none. but I still don't get it, how will the difference between two distinct numbers in the sequence help me?

[Anonymous No.15480223]

>>15480186
If a number divides two different numbers it also divides their difference.

[Anonymous No.15480227]

>>15480223
I think I got it. thanks anon

[Anonymous No.15480254]

Bros, I can't tell if my formula for numerical derivative is optimal.
I'm using n sample points and the best I can do is kill the error up to and including the nth derivative of the taylor expansion.
Since I have a choice of n sample points and n weights, I would expect to be able to do better (up to 2n derivatives).
[math]p(x)=\prod\limits_{i=1}^{n}(x-r_i)=x^n +c_1 x^{n-1}+ \dots +c_n\ \ (r_i\neq0,\ r_i\ distinct).\\
\sum\limits_{i=1}^{n}f(x+{1 \over r_i}){r_i^n+c_1 r_i^{n-1}\over p'(r_i)}\approx f'(x).\\
Error\ starts\ at\ f^{(n)}(x)\ when\ c_1 \neq 0\ (f^{(n+1)}(x)\ when\ c_1 = 0).[/math]
Am I missing something? Perhaps a fancy non-linear combination can do better?

[Anonymous No.15480508]

How far can the average person swim without dying? Like just swimming into the ocean until they drown due to exhaustion.

[Anonymous No.15480533]

>>15480508
The thumb is on the wrong side of her hand.

[Anonymous No.15480566]

>>15478912
but how does that prove it for all x?

[Anonymous No.15480612]

I have an EE exam, pretty basic stuff but I haven't been able to properly do the work all semester and as a result, I'm unable to work out a large number of the q's and there are no solutions provided for the practice paper.

Is there something I can do or some place I can go to get aid for this short of a tutor? (Am too poor for tutor).
The questions are intentionally phrased in unusual ways from our regular coursework I suppose to weed out people like myself from people that genuinely know everything.

I'm not retarded so bruteforce is an option but I'd rather have guided solutions than aimless dicking around

[Anonymous No.15480623]

>>15480566
Are you sure that isn't a typo because that notation doesn't make a lot of sense? I'd expect that to say "there exists an x" instead of "for all x".

[Anonymous No.15480639]

I graduated in stem roughly 10 years ago. Lately I have found I need to take a very extensive 16 hr exam if I expect any more substantial increases in pay.

I'm worried my ability to study but also take exams has diminished since I'm not doing it on a monthly basis anymore.

How do I re establish good practices?

[Anonymous No.15480676]

>>15480623
i feel the same, it says for all x. maybe it is being tricky where the antecedent is false for all x except 0, making the implication true?

the contrapositive makes a lot more sense to me: for all x, if x != 0 then there exists a y such that xy != x.

in this way i understand finding a single value of y, eg any value other than 1.

but in the form i gave, it is confusing.

for all x, if for all y, xy=x, then x = 0.
i guess in this case it still works because for any value of x other than x = 0, the antecedent is false, so the implication is automatically true?

[Anonymous No.15480684]

>>15479772
>Thanks anon, any tips on how to go through calculus-based physics ? I have only taken algebra based physics as of now. Our reference book is University physics by young and fredman
When I teach this, I show the calculus-based proofs to my students, but I don't make them do much calculus. I've noticed this is true for most of my cohorts as well.
You need to be able to understand the operations you are seeing. Basic calculus concepts will be your friends.

[Anonymous No.15480688]

>>15480508
>How far can the average person swim without dying? Like just swimming into the ocean until they drown due to exhaustion.
The "average" person? Have you looked at the average person recently? I'm betting most of them couldn't swim across a bath tub.
Strictly speaking, however, a person can typically sustain only about fifteen minutes of moderate-energy output without their body beginning to switch from burning glycogen to burning fat, resulting in muscle cramping if they aren't in good shape, so that's your magic number for the "average" person today. They can swim across a slow river, but not a fast one and not a reservoir without serious risk of drowning.

[Anonymous No.15480703]

>>15480566
0 can be the only possible value since it is the only one consistent with y = 0, and it also consistent with every other value of y.

[Anonymous No.15480707]

>>15480676
I'd be more inclined to think it's just an ugly notation stating x is real. Also if you move a bracket it would make more sense.

[math](\forall x \in R) (\forall y \in R) (xy = x) (\implies x = 0)[/math]

[Anonymous No.15480733]

>>15480707
>bracket
Ask me how I know you're from the UK.

[Anonymous No.15480740]

>>15480733
> round brackets
> square brackets
Ask me if I work as a coder.

[Anonymous No.15480769]

What's wrong with the proof? This is from Velleman's

[Anonymous No.15480815]

>>15480769
The proof is showing that [math]\forall y \in \mathbb{R}\ \exists\ x \in \mathbb{R}[/math] i.e. for every y you can pick an x that satisfies the equation.

That isn't what the theorem stated. It says for some fixed x, y can be an arbitrary value (which is clearly nonsense).

[Aureliano Buendia No.15480873]

>>15480815
Thnx. I was surprised because the proof seemed correct (which now turned out to be the case). The problem was that its not aligned with what the theorem stated.

[Anonymous No.15481017]

>>15472611
why are all living things (most of them at least) symmetrical

[Anonymous No.15481155]

Can anon recommend me some books or other materials that deal with euler-lagrange equations and/or lagrangian mechanics ?

[Anonymous No.15481160]

>>15472611
Is it possible to compress two integers with a maximum value of 8 into 5bits?

[Anonymous No.15481248]

>>15480533
I don't think it's Remilia's hand that's smushing up her own face anon.
>inb4 but the wristband and the nails
Yeah it's weird but it's probably Flandre.
>>15480688
Wew what the fuck.
>>15481160
Depends, does order matter? If it does, you can't, otherwise you can.

[Anonymous No.15481253]

>>15481248
>>15481160
>Depends, does order matter? If it does, you can't, otherwise you can.
Actually, my bad, that's for [math]1, \ldots, 8[/math] or if "maximum value of eight" doesn't include 8 itself.

[Anonymous No.15481340]

If A and B are matrices and m_A and m_B are minimal polynomials. Can you conclude m_A = m_B, if m_A(B) = 0 = m_B(A)?

[Anonymous No.15481348]

Are hints in books like Rudin optional?

[Anonymous No.15481366]

>>15480684
Is their any video-lectures or PDFs of similar types of proofs which will be useful for undergrad physics students? Can you share ?

[Anonymous No.15481397]

>>15472611
I'm teaching myself coding as he's I can and realized I'm deficient in hardware and general computer knowledge. Basically the sort of things you'd call the office IT guy to setup like putting together workstations, minor repairs, and connecting devices. Is there a good book or resource that would cover that?

[Anonymous No.15481406]

>>15481340
Yeah. They can't have different degrees, otherwise we have a contradiction, and if they aren't equal you can subtract one from the other to get a nonzero polynomial [math]p(x)[/math] with smaller degree than either such that [math]p(A) = p(B) = 0[/math], a contradiction.

[Anonymous No.15481408]

Consider  the matrix that you get when canceling the i-th row and j-th column of a (finite) matrix A. Would you say, it's trivial that Â^T is the matrix that you would get when canceling the j-th row and i-th colum of A^T?

[Anonymous No.15481428]

>>15481408
nvm I don't need this crappy argument anymore lmao

[Anonymous No.15481604]

>>15481253
It doesn't include 8 itself, I'll store values 0 through 7

[Anonymous No.15481673]

How can I prove by induction that [math]19|3^{2n+1}+4^{4n+2}[/math]?
I think I know how to do it without using induction, but I don't know how to use induction on this

[Anonymous No.15481704]

>>15481673
For [math]n=0[/math]
[eqn]3^{2n + 1} + 4^{4n + 2} = 19 \in 19 \mathbb{Z}[/eqn]

Now assume that [math]3^{2n + 1} + 4^{4n + 2} = 19k[/math] then
[eqn]3^{2(n+1) + 1} + 4^{4(n+1) + 2} = 9 (3^{2n + 1} + 4^{4n + 2}) + 247 \cdot 4^{4n + 2} = 19 (9k + 13 \cdot 4^{4n + 2}) \in 19 \mathbb{Z}[/eqn]

[Anonymous No.15481706]

>>15481704
thanks anon

[Anonymous No.15482077]

is it correct to write [math] I(a_1,\cdots,a_s) [/math] as [math] I((a_i)_{i\in\mathbb{Z}\cap[1,s]}) [/math]?

[Anonymous No.15482140]

>>15482077
No and most people wouldn't get it at first.

[Anonymous No.15482146]

>>15482077

the order of the sequence would be ambiguous and the arity of I would also be unclear

[Anonymous No.15482163]

i need some guide to learn basic mathemathics, lectures or some torrent with a course, books to but i would prefer the first options

[Anonymous No.15482166]

>>15481155
chapter 6 onwards of Taylor's Classical Mechanics textbook

[Anonymous No.15482266]

>>15482163
khan academy
>>15482140
>>15482146
Is there a more compact way of writing [math]I(a_1,\cdots,a_s)[/math]?

[Anonymous No.15482412]

>>15482266
You can make [math] I(a_1,\cdots,a_s) [/math] into
something like a vector, perhaps [math] I(\vec {a}) [/math]
where [math] \vec {a}=(a_1,\cdots,a_s) [/math].

The indexing of the components is well known
to be the positive integers [math] s\in\mathbb{Z^{+}} [/math]
and therefore need not be said. However, you need
to state where each [math] a_i [/math] comes from
(integers, reals, etc.).

[Anonymous No.15482481]

>>15482412
ehh I think I'll stick with [math]I(a_1,\cdots,a_s)[/math], the vector notation for this case seems a little awkward.
>you need to state where each [math]a_i[/math] comes from
I've ommited it here, but in my notes it's said that they are from a ring [math]A[/math]

[Anonymous No.15482520]

How do I calculate the error if I average multiple blood pressure readings? It says it's +/- 3 for each measurement. So if I were to take 3 and average them what would the error be?

[Anonymous No.15482528]

>>15482520
There are two possible approaches to this, depending on context.
If the error limits are "hard" boundaries, a blood pressure like 108 could be 105 through 111, but absolutely not 107 or 112. In that case, you do two averages, first for BP1-3, BP2-3, and BP3-3. Then for BP1+3, BP2+3, and BP3+3. These two averages will give you the absolute lower and upper limits for the result. Find the midpoint between them, then the offset to either side, and you have your average with its possible error. THIS IS RARE.

More often, it is assumed that we are talking about something like a 95% confidence interval, meaning there is only a 5% chance that a blood pressure of 108 is off by more than three units. In that case, your average is simply the average of the three BP's ± 3/√3. The 3 in the numerator is because each individual BP was ±3. The denominator 3 in the square root was because there were three blood pressures being taken. Read about "Standard Error" to learn more about this.

I hope that makes sense.

[Anonymous No.15482557]

>>15472611
how accurate is this?

[Anonymous No.15482561]

I have about a week to learn the theory about gaussian processes and using them in machine learning. What are the topics I should quickly freshen up on before and what resources are best for the theory of gaussian processes? Is there a gold standard book/reference?

[Anonymous No.15483083]

(x^2)+(1^2) = 0
For x is Real
>Hahahahahhahah

[Anonymous No.15483143]

Consider the differentiation as a linear transformation. The functions [eqn]f(x) = ae^{\lambda x}[/eqn] are the only eigenvectors of this transformation, right? Both a and lambda are elements of C, of course.

[Anonymous No.15483223]

Can you use the convention 0^0 = 1 in a proof, if you declare beforehand that this is how you are going to use it. Or is the term 0^0 something that you should avoid at all costs?

[Anonymous No.15483234]

>>15483223
It's fine. Think of it as another assumption before the proof.

[Anonymous No.15483252]

>>15483143
Yeah. Haven't you studied ODEs already? [math]y' - \lambda y = 0[/math] is first degree linear homogenous hence the solution space is one-dimensional.

[Anonymous No.15483365]

>>15480254
You can sort of hack an extra n sample points if you assume f is holomorphic and real on the real line.
[math]Let\ q(x)=p(x)\bar{p}(x)=x^{2n} +2Re[c_1] x^{2n-1}+ \dots\ \ (r_i\neq0,\ r_i,\bar{r}_i\ all\ distinct).\\ 2Re[\sum\limits_{i=1}^{n}f(x+{1 \over r_i}){r_i^{2n}+2Re[c_1] r_i^{2n-1}\over p'(r_i)\bar{p}(r_i)}]\approx f'(x).\ (x\ real,\ \bar{f}=f)\\ Error\ starts\ at\ f^{(2n)}(x)\ when\ Re[c_1] \neq 0\ (f^{(2n+1)}(x)\ when\ Re[c_1] = 0).[/math]

It feels like a cheap hack since evaluating f at complex inputs requires essentially twice the work anyways and it doesn't work for irl numerical problems.

[Anonymous No.15483465]

>>15472611
anybody know where i can find some good books on the science behind fabrics and leather?

i ask /fa/ but they are all just coomers

[Anonymous No.15483534]

Do you believe in God? If not what is your reasoning?

Here's my shitty reason as to why God doesn't exist or at least why there is no god in Abrahamic religions:

God is omniscient, omnipotent, Omni benevolent etc

There are all traits humans crave on some level

Putting these traits into a human makes them God. Therefore God is a human creation

[Anonymous No.15483537]

>>15472735
It's division in base x

https://www.explodingdots.org/island/I6

[Anonymous No.15483559]

Am I absolutely retarded or does a subspace containing an isotropic vector imply that it is degenerate?
If [math]W \subset V, W[/math] - non-degenerate, then [math]W \bigoplus W^\perp = V[/math]
But if [math]v \neq 0 \in W, h(v,v) = 0 \implies v \in W, v \in W^\perp \iff v \in W \cap W^\perp \neq W \bigoplus W^\perp [/math]

But I was asked to prove that for [math] \dim V > 4 \exists W_1,W_2 \subset V, W_1 \neq W_2, \dim W_1 = \dim W_2 = 3[/math] such that they're both non-degenerate and [math] v \in W_1 \cap W_2, v \neq 0, h(v,v) = 0 [/math] which makes no sense to me because they both must contain an isotropic vector so I don't see how they can possibly be non-degenerate.

Sorry for shitty latex.

[Anonymous No.15483562]

New to this board, overall I'm not impressed because I've not seen anyone's home labs.

[Anonymous No.15483606]

>>15483562
the equipment i use is too expensive for personal use.

[Anonymous No.15483714]

>>15483606
fair enough

[Anonymous No.15483752]

>>15483562
If people could afford home scientific labs that amounted to anything, then Science PhDs wouldn't be begging for grants.

[Anonymous No.15483827]

>>15472611
i experienced numbness in my mouth, numbness in my lef arm, i had blurred vision and felt like i was about to pass out
i went to the er because i was afraid i could be having a stroke
they did a tomography, a blood sudy and a psychatric test
everything was right
i happenned again two weeks later
they did another blood test and a electrocardiogram
everything was perfectly fine again
i was told it was a panic atack but it couldnt have been, i was so relaxed i was joking with the nurse
i have been feeling my mouth numb a lot since and i experienced shortness of breath and my hand shaking after i got out of the bus once
i take lithium and eroquel and it gets worse when i dont sleep and when i dont take the seroquel because i didnt sleep but the psychatrist said i cant be that
i cant go back o the er because they already did every study they could, i had very little exercise since i started college 2-3 months ago and i believe it could be relaed

[Anonymous No.15483848]

>>15483559
You've skipped enough context for the question to be incomprehensible but Minkowski space is non-degenerate and has isotropic vectors.

[Anonymous No.15483917]

mathlet here, I don't understand the proof given here by mathlove:
https://math.stackexchange.com/questions/1738963/how-to-find-whether-equation-of-angle-bisector-represents-the-obtuse-or-acute-an
can u help me with this? It primarily pertains to proving the condition if a1a2 + b1b2 is +ve or -ve , then u gotta use +ve or -ve sign respectively when finding the obtuse angle bisector and the opposite sign for acute angle bisector.

[Anonymous No.15483928]

Are artificial proteins (enzymes etc.) that perform precise, hand-picked functions ever going to be a thing? The prospect has me giddy as a 4-year-old who'd just found out about mining trucks

[Anonymous No.15483937]

>>15483534
The greatest arguments against any Abrahamic religion, in my opinion, is that their beliefs are all contradicting. For example, if God is omnipotent, then could he commit suicide? If no, then he is not omnipotent. If yes, then he is not immortal. You can come up with many such contradictions, if you can play off these attributes of God.

[Anonymous No.15483960]

>>15483917
Which part don't you understand? The explanation for the condition is given at the end of the proof.
[eqn]\cos{\theta} = \sqrt{\dfrac{1 - f(a,b)}{2}}[/eqn] Depending on the sign of function (i.e the sign of [math]a_1 a_2 + b_1 b_2[/math]) the angle will be greater of less than 45 degrees which determines if the bisector angle is obtuse or not.

[Anonymous No.15483973]

>>15483534
Wipe all of humanity's memories and it books and all other forms of stored knowledge. The religions, gods and holy texts we know today would never be recreated but all the science we know would still be the same and eventually rediscovered. Facts and truth cannot change.

[Anonymous No.15484004]

>>15483534
>>>/r/atheism

[Anonymous No.15484006]

>>15483960
>Which part don't you understand?
\cos\theta=\frac{\left|a_1\left(\frac{a_1}{\sqrt{a_1^2+b_1^2}}-\frac{a_2}{\sqrt{a_2^2+b_2^2}}\right)+b_1\left(\frac{b_1}{\sqrt{a_1^2+b_1^2}}-\frac{b_2}{\sqrt{a_2^2+b_2^2}}\right)\right|}{\sqrt{a_1^2+b_1^2}\sqrt{\left(\frac{a_1}{\sqrt{a_1^2+b_1^2}}-\frac{a_2}{\sqrt{a_2^2+b_2^2}}\right)^2+\left(\frac{b_1}{\sqrt{a_1^2+b_1^2}}-\frac{b_2}{\sqrt{a_2^2+b_2^2}}\right)^2}}

[Anonymous No.15484013]

>>15483960
the cos theta part

[Anonymous No.15484024]

>>15484013
That is just the dot product rule giving the cosine between two vectors. If you plug in the two lines involved you will get that equation.

[Anonymous No.15484047]

>>15484004
No stupider question than the existence of God.

[Anonymous No.15484054]

>>15484024
can it be done without vectors? Also y is there no c1 & c2 in the dot product(numerator)?

[Anonymous No.15484058]

>>15484024
oh wait, cuz they're dimensionless scalars?

[Anonymous No.15484078]

>>15484054
> can it be done without vectors?
no idea

> Also y is there no c1 & c2 in the dot product(numerator)?
Because the (unit) vectors do not depend on the c's.

[Anonymous No.15484101]

I've spent hours trying to prove that if x < y, then y < -x. No matter what i try, nothing works.

I can't even derive a contradiction if i try a proof by contradiction by assuming x < y and y>=-x.

I just get x > y and x >= -y, which i know intuitively must be false but i cant prove it.

What am i doing wrong?

[Anonymous No.15484106]

>>15484101
i just get y > x and y >= -x i mean, which is its a contradiction but i just cant prove it

[Anonymous No.15484119]

>>15484101
>if x < y, then y < -x
uhhhhhhhh
did you make a typo there, or...?

[Anonymous No.15484120]

>>15484101
What the fuck are you talking about? Let x = 1 and y = 2.
> 1 < 2
True
> 2 < -1
False

[Anonymous No.15484127]

hey /sci/ any biologists here? i recently noticed my blood clots way too fast (within 20 seconds of a open wound) and i have no clue why. it wasn't like this before as it would previously take a few minutes so i don't think its genetic hypercoagulation, my diet has been pretty unhealthy recently so i think that may play a factor?

[Anonymous No.15484129]

the implications *if* the many worlds theory of quantum physics is correct are scary
you basically cant die from your perspective, until the odds of your death reach 100%
but from your perspective everyone else around you will die normally
so at some point, you become a celebrity for old age and people begin to question why you don't die, eventually they will figure it out, the the universe or timeline they are on revolves around you, and that from their perspective they will also meet the same fate
a fate of becoming increasingly sick, burning with pain, suffering from dementias, unable to pass on
but mathematically, can the odds of you dying ever truly hit 100%? maybe only when the sun swallows the Earth, or the universe ends. you might have thousands of years suffering with agonising pain and dementia until technology can enhance your mind and body and restore you. or maybe they can never fix you.
aren't you scared? isn't many worlds theory worse than just a nothingless void after death? and no matter how hard you try, if it's true, you can't escape it.

[Anonymous No.15484130]

>>15484101
I'll try it directly. First, x < y. Negate both: -x > -y.
Then, x > -x > -y so therefore x > -y. Divide by -1
on both sides to get -x < y or equivalently, y > -x.

Maybe the conclusion is a typo like >>15484119 said.

[Anonymous No.15484132]

>>15484120
>>15484119
oh no

i've made a terrible mistake and wasted hours

i was trying to use this in a different proof but wanted to make sure i knew how to prove it

[Anonymous No.15484135]

>>15484130
thank you for trying anon, it wasnt a typo

i think i was taking x > 0 --> -x < 0 and x > y --> -x < -y and trying to combine them

[Anonymous No.15484169]

>>15482557
very. there's nothing genetic going on when the sperm cells are piercing the ovum, the mechanism is just a series of basic chemistry reactions and virtually the same between all mammals. the zygote will never implant on the uterine wall and the pregnancy wouldn't be viable even if it did; but the initial sperm/egg binding has fuck all to do with genetic compatibility
https://en.m.wikipedia.org/wiki/Zona_pellucida
in humans, the glycoprotein ZP3 is responsible for triggering the acrosome reaction that allows the sperm to penetrate the egg's outer shell. that's also the same protein for virtually all primates, ungulates, carnivora, etc. that'd include things like mice, dogs, pigs, orcas, horses, and so on.

also, freya makes hentai; it's all bestiality. not surprised to learn she's a woman, there are a lot of deranged female doujinshi artists.

[Anonymous No.15484178]

>>15483973
I've read this one before and its the most convincing for me.

>>15483937
Hmm interesting that all these paradoxes exist just by looking at gods attributes

[Anonymous No.15484191]

>>15483973
>Humans crave to be omni-benevolent.
What in the fuck have you been smoking?

[Anonymous No.15484194]

>>15483937
>Check out my straw-man!
The biblical sense of "omnipotent" actually just means He is more powerful than any other being.
The bible readily admits several things God cannot do, chief among them being lying and doing evil.
The "God can do anything, therefore he is a paradox" is a fedora canard that no honest theologian buys into. It's the kind of argument you expect from a third-grader.

[Anonymous No.15484238]

>>15484191
Humans don't crave to be good? Or be as good as possible?

[Anonymous No.15484269]

>>15484194
So when your fictional god ordered the murder and rape of children in your fictional story, he was not doing any evil? Anyway, talking about honest theologians is stupid since you will find that real intellectuals have little respect or time for this sham of a field. NTA

[Anonymous No.15484276]

>>15484269
1. that never happened
2. how is that evil? they were asking for it
3. if it was evil, an omnipotent god can simply say, no it wasn't, and make it so
4. unclamp

[Anonymous No.15484292]

>>15484276
Good job outing yourself as a morally and intellectually bankrupt person who should be shunned by civil society. You're representing your ancient desert cult really well

[Anonymous No.15484339]

>>15484004
i like this wemi

[Anonymous No.15484570]

>>15484078
>Because the (unit) vectors do not depend on the c's.
I don't get it. I'm not that familiar with vectors. know any good material or text book for coordinate geometry that covers topics in great depth?

[Anonymous No.15484581]

>>15484292
christcucks are famously spiteful and full of malice

[Anonymous No.15484679]

>>15484570
In the equation for a line (y = mx + c, or ay + bx + c = 0) all the c represents is a shift up or down the y axis. It is only the x and y components that will define the angle between two lines. As an exercise draw some lines on a graph to make yourself understand this.

[Anonymous No.15484681]

>>15484191
What has omnibenevolence got anything to do with the argument?

[Anonymous No.15484756]

>>15484679
can the same formula used for finding cos theta be determined using pic rel? if so can u show the steps? I tried finding tan theta which can in tun be used for finding cos theta, but the expession for tan theta was big and ugly.
>c represents is a shift up or down the y axis.
can u write the equations in vector form? I'm asking this because i find it quite hard to make sense of the fact that 'c' is both y intercept(a quantity related to y coordinate) and as something that is not needed when finding angles . By my understanding, c just represents lateral and longitudanal shift of vectors and not their orientation, am i rite?

[Anonymous No.15484768]

>>15484756
>c just represents lateral and longitudanal shift of vectors and not their orientation, am i rite?
yes. another way of thinking about it shifting the intersect point to the origin (so al the c's are zero). the angle still doesn't change.

[Anonymous No.15484782]

>>15484768
apologies for not posting the pic.
Also, how do i write equations like this >>15483960

[Anonymous No.15485030]

I am [math] \mathrm \LaTeX [/math] expert.

[Anonymous No.15485056]

>>15485030
t.

[Anonymous No.15485078]

https://odysee.com/@thecosmicswitchboard.com:b/the-beings-inside-the-orbs:2

Am I going mad or does the audio in this video sound like it was created by an ai stitching together a woman's voice?

It's really uncanny.

[Anonymous No.15485083]

Assume the minimal polynomial of an infinite matrix has a finite number of linear factors. Is this property sufficient for the matrix to be diagonalizable?

[Anonymous No.15485093]

>>15484194
>omnipotent doesn't mean all-powerful, even though "omni" means "all" and "potent" means powerful
There is a reason the mass used to be held in Latin. If religion is expressed in intelligible terms, people see how it crumbles under the weight of its overblown assumptions.

[Anonymous No.15485100]

>>15484194
>God can't do evil
>>15484276
>oh yes, God also defines what is evil

[Anonymous No.15485282]

Consider [eqn]x\frac{d}{dx}: \mathbb{F}[x] \to \mathbb{F}[x].[/eqn]I have to show that this transformation does not have a minimal polynomial. I already know that {x^n} with n in N are eigenvectors to the eigenvalues n. Therefore I have an infinite number of pairwise distinct eigenvalues. My question is: Are eigenvalues always roots of the minimal polynomial? In finite dimensions, this is true, of course, but I'm not sure if it is in case of infinite dimensions.

[Anonymous No.15485530]

ALL WE HAVE TO DO IS REVERSE THE VORTEX POLARITY OF THE CELL. WHY AREN'T WE FUNDING THIS LIKE HOTCAKES? WE COULD ALL BE IMMORTAL BY TOMORROW.

[Anonymous No.15485573]

>>15485530
it's probably not that easy

[Anonymous No.15485597]

Beginner astronomy shizo here. I want buy telescope and watch moon from my balcony. Can you recommend some good models?

[Anonymous No.15485602]

why does the definition here say that the numerator has the integrating variable in it, when the example does not?

[Anonymous No.15485649]

>>15485602
>why does the definition here say that the numerator has the integrating variable in it
It doesn't say that.
Take a look at the first few lines of:
https://mathworld.wolfram.com/EllipticIntegral.html

[Anonymous No.15485676]

>>15485282
>My question is: Are eigenvalues always roots of the minimal polynomial? In finite dimensions, this is true, of course, but I'm not sure if it is in case of infinite dimensions.
Yeah.
But you don't need to even think about that. If there's a minimum polynomial [math]P[/math], then [math]P \left( x \dfrac{d}{dx} \right) x^n = \left( \sum_{k = 0}^m a_k n^k \right) x^n[/math]. Then [math]p(n) = \sum_{k = 0}^m a_k n^k[/math] can only have finitely many zeroes.

[Anonymous No.15485691]

>>15485083
>Is this property sufficient for the matrix to be diagonalizable?
No, the linear factors of the minimal polynomial need to be distinct at least.
>>15485282
>Are eigenvalues always roots of the minimal polynomial?
Yes, the number of dimensions don't matter for that.
If [math]p[/math] is any polynomial, [math]v[/math] is an eigenvector to the eigenvalue [math]\lambda[/math] of the matrix [math]A[/math] then
[eqn]p(A) v = p(\lambda) v[/eqn]
If the polynomial [math]p[/math] annhilates the matrix [math]A[/math] then the LHS is zero so [math]p(\lambda) = 0[/math] too.

[Anonymous No.15485696]

>>15485649
>Take a look at the first few lines of:
sorry, im still not getting it. what does R(x,y) mean? its my understanding that it would simply be x/y.

[Anonymous No.15485702]

>>15485696
No. It means an arbitrary polynomial in x and y (for instance 1 is a trivial polynomial) divided by another arbitrary polynomial in x and y.

[Anonymous No.15485706]

>>15485702
ah, i see now, i knew i was misunderstanding something like that but the confirmation bias was too strong. thanks fren.

[Anonymous No.15486643]

My electric toothbrush feels heavier when it's fully charged. Is that real or in my head?

[Anonymous No.15486651]

>>15486643
>My electric toothbrush feels heavier when it's fully charged. Is that real or in my head?
Imaginary. There is a weight difference but it wouldn't be something you could detect due to how incredibly small that weight difference is. You can convert joules to grams if you want. Just use a calculator. Or if you can't there's probably an online converter someplace

[Anonymous No.15486707]

Take an elliptic curve over Q without CM. Then the endomorphism ring of E consists of isogenies defined over an algebraic closure of Q (or C by lefschetz principle)
And this ring is isomorphic to Z.
But how do galois group actions fit into this? For example even just complex conjugation should yield a nontrivial isomorphism of E, but this doesn’t correspond to any multiplication by m map.
Is there something wrong with my definition of the endomorphism ring?

[Anonymous No.15487262]

[eqn]det(A) = 0 \implies \text{A is not invertible}[/eqn]Is this also true for infinite matrices?

[Anonymous No.15487325]

What would happen if I didn’t take all the rabies series vaccinations would the first one be enough to hold me over if I’ve been bit

[Anonymous No.15487350]

Scientifically speaking, what would happen if the Large Hadron Collider theoretically used marbles in place of protons? So basically you would have two marbles going nearly the speed of light in a vacuum and then bang into each other.

[Anonymous No.15487413]

>>15487350
1/2 mv^2 = E_kin, if disregard everything

[Anonymous No.15487417]

[eqn]det(A) \neq 0 \iff \text{matrix A is invertible}[/eqn]Is there such a theorem for infinite matrices A?

[Anonymous No.15487420]

>>15487325
Rabies is weird.

[Anonymous No.15487436]

Consider a complex polynomial p of C[x]. I want to show the invertibility of "A - lambda", given that "p(A) - p(lambda)" is invertible. In the finite dimensional case, this is trivial, because p(lambda) is an eigenvalue of p(A); just apply the contraposition on the statement above and you see what I mean. The infinite dimensional case however is more difficult. This is how I tried to show it so far
>if p(A) - p(lambda) is invertible, then by definition there exists an B such that "B * (p(A) - p(lambda)) = (p(A) - p(lambda)) * B = 1"
>furthermore we can apply the algebraic definition of polynomials and rearrange the term and we end up with
[eqn](A - \lambda) \cdot \left[\sum_{k = 0}^{\infty} a_k \sum_{r + s = k} A^k \lambda^s\right][/eqn]
>apparently the linear factor "(A - lambda)" showed up again, which is why I did this
>if we know remember the invertibility of "p(A) - p(lambda)", we can write
[eqn]B \cdot \left[\sum_{k = 0}^{\infty} a_k \sum_{r + s = k} A^k \lambda^s\right] \cdot (A - \lambda) = (A - \lambda) \cdot \left[\sum_{k = 0}^{\infty} a_k \sum_{r + s = k} A^k \lambda^s\right] \cdot B = 1[/eqn]
>as you can see the problem is almost [!] solved, the remaining issue is to show the commutativity of this
[eqn]B \cdot \left[\sum_{k = 0}^{\infty} a_k \sum_{r + s = k} A^k \lambda^s\right]= \left[\sum_{k = 0}^{\infty} a_k \sum_{r + s = k} A^k \lambda^s\right] \cdot B [/eqn]
My question is can you do that and if so how? If you can't, how else can you show the statement from the beginning?

[Anonymous No.15487457]

>>15487436
btw. I think you might be able to show this using the "Fredholm determinant" and an infinite-dimensional equivalent for rule in >>15487417 here that I found on wikipedia. I would rather not do this, because I don't know the theory behind it.

[Anonymous No.15487459]

>>15487325
you die

[Anonymous No.15487502]

how/why does cancer kill? it spreads around and then what? it clogs blood vessels with itself (tumors) causing organ failure and/or it somehow siphons all water, energy and nutrients?

[Anonymous No.15487506]

>>15487502
Replicates itself everywhere starving out other cells and disrupting homeostasis everywhere in multiple ways. Necrosis is one of the consequences, yes.

[Anonymous No.15487517]

>>15487506
starvation and necrosis it is, thanks
>disrupting homeostasis everywhere in multiple ways
this also makes sense due to cancer's metabolic byproducts if that's what you mean because I heard that tumors thrive in acidic environments and vice versa for alkaline

[Anonymous No.15487530]

>>15487517
Well you're talking about cancers that end up surviving and causing problems for people. Most cancers are spontaneously removed by the immune system and other factors because they fail to survive, a kind of natural selection true of your body same as any organism in any environment. That same phenomenon is why it has been argued in various publications that very early detection of cancer may not, in fact, warrant operating or intervention as most of them may go away on their own. It's a very complicated topic and I am by no means doing it any justice with this summary. When it comes to surviving and thriving cancers, they modify environments such that they are more successful and can't be dealt with by your own body anymore. That of course can include ensuring your immune cells can't survive where they're replicating, among many other factors, and none of these are exclusive or required. For example, just having very poor immune function would be sufficient and tumors will thrive with very little modification to pH.

All that is important since people take a kind of superficial analogy-based flawed reasoning to it and end up falling for things like "changing your body pH with this miracle snake oil". Doesn't work like that. Best thing you can do for your body is exercise and a good diet, as always.

[Anonymous No.15487539]

>>15487530
>>15487517
Sorry I should also mention the modifying part is about initial survival. Of course as they kill off things in your body and crowd out your other cells the pH in its local environment will necessarily change anyway. Just talking about the initial thriving or remission period in case it was not obvious.

[Anonymous No.15487560]

>>15487530
>>15487539
nice read, thanks again!

[Anonymous No.15487626]

>>15487436
If A, B, C are any three operators and if AB = CA = 1, then B = C.

[Anonymous No.15487631]

What is some general advice for proving these types of inequalities? It feels like you need to already know the answer to solve them.

[math]4ba \le (a+2b)^{2} -a^{2}[/math]

To solve this, you use the fact that [math] 0 \leq b^{2} [/math] and then do 0 <= 4b^2, then:
4ba + a^2 <= a^2 + 4ba + 4b^2
4ba <= a^2 + 4ba + 4b^2 - a^2
4ba <= (a + 2b)^2 - a^2

but if you didnt think to start with 0 <= b^2 it would have been impossible to solve this way.

[Anonymous No.15487637]

>>15487631
Why don't you just expand the RHS?
[eqn](a + 2b)^2 - a^2 = 4ab + 4b^2 \geq 4ba[/eqn]

[Anonymous No.15487642]

>>15487631
Expand the RHS
the a^2 cancels
The 4ab cancels between LHS and RHS
There you're left with 0 <= 4b^2 so as long as b^2 >=0 then you're good.
Assuming b is not imaginary, b^2 is always >=0

[Anonymous No.15487706]

>>15487626
[eqn]
\begin{pmatrix}1 & 0 \\ 0 & 0 \end{pmatrix} \cdot \begin{pmatrix}1 & 0 \\ 0 & 0 \end{pmatrix} = \begin{pmatrix}1 & 0 \\ 0 & 1 \end{pmatrix} \begin{pmatrix}1 & 0 \\ 0 & 0 \end{pmatrix}
[/eqn]
What do you mean by operator? AB = CA => B = C is only true if A is invertible, which is not a given unfortunately.

[Anonymous No.15487751]

>>15487626
Are you sure you don't mean BA = AC = 1? Can you link a proof to this?

[Anonymous No.15487764]

>>15487626
Great! Thanks!

[Anonymous No.15487784]

Injectivity is sufficient for the invertibility of an endomorphism, right?

[Anonymous No.15487788]

>>15487784
On finite dimensional vector spaces, yes. On infinite dimensional ones, no.

[Anonymous No.15487790]

>>15487784
No.

[Anonymous No.15487793]

>>15487788
>>15487790
What would be a counter-example?

[Anonymous No.15487802]

>>15487793
The multiplication by x operator on the space of polynomials in x

[Anonymous No.15487806]

how does a DE like this work, where you have two variables? is x a function of z? is z a function of x?

[Anonymous No.15487858]

>>15472611
Hey anon, is there any chart/guide that start from basic algebra and go up to sheaf theory?

[Anonymous No.15487904]

At work I ran a test to find out how much error I had in my measurements. All of these measurements (in dBm) should have been the same. So when I chart my real results do I put error bars +-2.15dBm both ways? Do I call it standard error? Please help. I am not a smart man.
3.38
4.55
3.68
3.32
1.64
0.24
1.56
1.19
1.26
0.68
1.56
3.73
2.91
1.62
0.84

4.55-0.24=4.31

[Anonymous No.15487906]

>>15487904
Forgot to post an unrelated picture. Please enjoy.

[Anonymous No.15487916]

>>15487904
theres a couple ways you could represent the error, you could report the mean and the standard deviation, perhaps with an accompanying distribution plot, or you could create a box and whiskers plot.
>>15487906
this is definitely the weirdest looking 2hu ive seen.

[Anonymous No.15487947]

>>15487906
gemmy picture

[Anonymous No.15488005]

>>15487916
Thank you for your input and your help! That has put me on the path of box plots. I'll get that done. I have a feeling that I'm going to struggle to figure out how likely my results are statistically relevant. I'll be back :(.

[Anonymous No.15488031]

>>15487637
>>15487642
oh ok ty anons i think i was trying to work backwards

[Anonymous No.15488036]

>>15488005
heres a good example i saw when i took stats
>youre a manufacturing engineer at a paint making factory
>the lab boys put some shit in the paint that they think will make it dry faster
>you have to run some tests to see if theyre right
>you create a bunch of samples from the regular batch and a bunch of samples from the new batch, and you see how long it takes for each sample to dry
>because of random variation in the manufacturing process, sample creation process, etc. its expected that there will be random variation in the drying times as well
>the average time it took for the regular batch to dry was 154 minutes, and the average time it took for the new batch to try was 149 minutes
>is that difference significant?
>in deciding if it is, the main factors to consider are the difference in mean, the standard deviation, and the population size
>if the difference is really big (e.g. the new batch dried in half the time), it becomes more significant
>if the standard deviation is really big (e.g. the window for drying time is 30 minutes in either direction), it becomes less significant
>if the population size is really big (e.g. you tested 1000 samples), it becomes more significant
in this example, the null hypothesis is that additive did nothing to the drying time, and the alternative hypothesis is that it did do something. when calculating the significance of results, its listed as a probability. for example, p = 0.04 means "theres a 4% chance that the 5 minute difference in drying time could be chalked up to random variations." you can look up formulas for all of this.
also, this only applies if you assume your distribution of results is normal (https://en.wikipedia.org/wiki/Normal_distribution)), but you can assume it is, no ones gonna call the cops on you.

[Anonymous No.15488051]

>>15487806
>is x a function of z? is z a function of x?
Either one of those would work as long as dz/dx is not 0

[Anonymous No.15488072]

>>15488036
>theres a 4% chance that the 5 minute difference in drying time could be chalked up to random variations.
This is *not* what a p-value is.
If p = 0.04 then, under the null hypothesis, the event of observing a difference which is at least 5 minutes has a probability of 4%.
You might accuse me of pedantry but so many people make mistakes with this that I wanted to point it out.

[Anonymous No.15488079]

>>15488072
not entirely pedantic, thanks for the clarification.

[Anonymous No.15488083]

>>15488051
thanks fren. i think im in way over my head with these elliptic integrals, i might try asking /mg/ for help exactly what im trying to do.

[Anonymous No.15488136]

The vectors with lengths a, b and c are pairwise orthogonal. Is this property [eqn](a + b + c)^2 =a^2 + b^2+c^2[/eqn] true?

[Anonymous No.15488139]

>>15488136
yes.

[Anonymous No.15488141]

>>15488136
It's not

[Anonymous No.15488146]

>>15488139
you need to add the vectors on the right side, then evaluate the square of the lengths. Imagine you'd say (a + b)^2 = a^2 + b^2 for orthogonal vectors with lengths a and b in the 2D case. Of course this is nonsense, and OP posted the equivalent for the 3D case.

[Anonymous No.15488218]

I'm checking my professor's note on some rigid body exercise. At some points it considers the small oscillations problem. Doing a first order Taylor he comes with this equation:
[math]
\dot{\delta \theta^2}+\left(\frac{\mathrm{I}_3 \omega_3}{\mathrm{I}}\right)^2 \delta \theta^2=\dot{\theta}_0^2 \quad (1)
[/math]
And then he writes: "Since θ(0) = θ0, it must be δθ(0) = 0 and therefore
[math]
\delta \theta(t)=\delta \theta_0 \sin \Omega t \quad (2)
[/math]
donde
[math]
\Omega=\frac{I_3}{\mathrm{I}} \omega_3
[/math]
y donde
[math]
\delta \theta_0=\frac{\dot{\theta}_0}{\Omega}
[/math]".
I don't get how he comes with (2), since (1) is clearly not a second order linear differential equation, and even if that were the case he would be missing the particular solution term.

[Anonymous No.15488224]

I'm checking my professor's note on some rigid body exercise. At some points it considers the small oscillations problem. Doing a first order Taylor he comes with this equation:
[math]
\dot{\delta \theta^2}+\left(\frac{\mathrm{I}_3 \omega_3}{\mathrm{I}}\right)^2 \delta \theta^2=\dot{\theta}_0^2 \quad (1)
[/math]
And then he writes: "Since θ(0) = θ0, it must be δθ(0) = 0 and therefore
[math]
\delta \theta(t)=\delta \theta_0 \sin \Omega t \quad (2)
[/math]
where
[math]
\Omega=\frac{I_3}{\mathrm{I}} \omega_3
[/math]
and
[math]
\delta \theta_0=\frac{\dot{\theta}_0}{\Omega}
[/math]".
I don't get how he comes with (2), since (1) is clearly not a second order linear differential equation, and even if that were the case he would be missing the particular solution term.

[Anonymous No.15488227]

>>15488146
>>15488141
It's just the pythagorean theorem anon. a, b, c are vectors.

[Anonymous No.15488258]

>>15488036
Thank you! I'll keep trying to figure it out. I'm not very bright. Like a dog trying to open a door. But I'll keep at it until I get t.

[Anonymous No.15488287]

>>15488224
Why do you think it needs to be a second order differential equation? Since it's an oscillation then it's likely the solution will involved sin and cos. But you are told the initial condition is zero so it can only involved sin. Then you get terms involving: sin^2 + cos^2 = 1, which tells you what the necessary constants must be.

[Anonymous No.15488360]

>>15472611
What's the regex for

(newline) followed by (any amount of whitespace) followed by (a specific character, say 'a')

[Anonymous No.15488368]

>>15488136
If [math] a_i [/math] are pariwise orthogonal then
[math] (\sum_i a_i)^2 = (\sum_i a_i) \cdot (\sum_j a_j) = \sum_{i,j} a_i \cdot a_j = \sum_{i\neq j}a_i \cdot a_j + \sum_i a_i \cdot a_i = 0 + \sum_i ||a_i||^2 [/math]

[Anonymous No.15488371]

>>15488360
\n\s*a I'd say.
https://regex101.com/r/nm3IDR/1

[Anonymous No.15488375]

>>15488360
>>15488371
On further inspection \s includes whitespace like \n so you may want to exclude that

[Anonymous No.15488379]

>>15488371
Thanks that does it

[Anonymous No.15488386]

>>15488375
>>15488379
Oh I see what you mean. Either way it works well enough as is

[Anonymous No.15488443]

>>15488360
>>15488379
If that's not quite what you wanted try /^[ \t]*a/m

[Anonymous No.15488486]

>>15472611
Not sure if this is an appropriately stupid question for this thread or not. I feel like I could be (probably am) overlooking something stupid obvious, but maybe not. Hoping to get help at least figuring out how to begin attacking this kind of problem.

So, suppose I have some implicit surface, [math]F(x,y,z)=0[/math], with surface normal, [math]\mathbf{\hat{n}}[/math] (for the sake of argument, let's say a spheroid, like the football this kitten is playing with). This surface is allowed to rotated freely about its axes according to some roll, pitch, and yaw described by a rotational transform, [math]\mathbf{R}[/math]. I want to analytically determine or estimate the centroid/center of mass of the part of the surface in space which is facing some particular vector, [math]\mathbf{\vec{v}}[/math].

Computationally, this is very straightforward to handle - I generate a list of points describing the surface and work out [math]b=\mathbf{\vec{v} \cdot \left(R \cdot \hat{n}\right)}[/math] for the points in the list, select the points that satisfy [math]\mathbf{b<0}[/math] (the points facing towards [math]\mathbf{\vec{v}}[/math]), then I can numerically compute the average position of the points in the list. However, the issue is that obviously computation time for this scales linearly with the number of points simulated, so the smoother of a shape I try to model, the longer it takes to compute, and since I'm trying to look at many different shapes in many different orientations, this becomes extremely time-consuming, so I would like to work out if there an analytic solution or approximation.

Differential geometry is a subject I never really got, so I'm unsure if this is something trivial that I just don't know, or something impossible that I don't recognize as such.

[Anonymous No.15488628]

>>15480254
I've generalized to m derivatives and simplified the weights and sample points.
[math]p(x)=\prod\limits_{i=1}^{n}(x-r_i)=x^n +c_1 x^{n-1}+ \dots +c_n\ \ ( r_i\ distinct).\\ \sum\limits_{i=1}^{n}f(x+r_i){D_{z=0}^{m}[p(z)/(z-r_i)] \over p'(r_i)}\approx f^{(m)}(x).\\ Error\ starts\ at\ f^{(n+k)}(x)\ when\ c_m, \ldots , c_{m-k+1} = 0\ and\ c_{m-k} \neq 0.[/math]

Clearly the "best" p is p(x) = x^n - 1 or some re-scaled form of it.
Somehow the sample weights have a nice formula that doesn't require linear algebra.

[Anonymous No.15488669]

So I am having a dumb. If I had an outlet that had 5 spots and I plugged in the exact ammount on the strips by 1 each time how many outlets would I have all togther. So 5 would go to 4 and to 3 etc. Till it goes to 1 and stops.

[Anonymous No.15488726]

How do I make amphetamine great again?

[Anonymous No.15488731]

>>15488669
what?

[Anonymous No.15488735]

>Is it true that atoms are really just bands of standing waves of light and weight is it's dimensional "depth?
>Also is it true that sunspot are singularity points/gravity wells like black holes and all stars do that?

[Anonymous No.15488742]

>>15488735
None of that is true.

[Anonymous No.15488789]

>>15488669
Can you translate this to English?

[Anonymous No.15488923]

>>15488669
5 x 4 x 3 x 2 x 1 = 120
You wouldn't need to plug in the one-outlet strips. They're basically extension cords.

[Anonymous No.15489201]

why is root mean square used in trying find quantities like velocity of gas molecules, voltages, etc. and not say root mean (2n)?
>Root mean square values are more in line with experiment observations bro
Are there quantities in physical sciences that make use of other root mean(n)?

[Anonymous No.15489255]

>>15489201
There are like a dozen different definitions of ‘average’ in statistics, all of which yield answers of the same order of magnitude. Some use RMS, some use most probable velocity, some use expectation value of velocity, etc. I’ve seen arguments break out at conferences over which velocity is the ‘right’ velocity to use in definitions.

[Anonymous No.15489327]

>>15489201
It's a consequence of the underlying physics. For example for an ideal gas you start from the possible configuration of microstates which leads to the maxwell-boltzmann law which gives you a root mean square equation for the velocity distribution.

[Anonymous No.15489614]

Hi anons. Just realized I could graduate faster if I change my degrees to math from cs. I think I'm gonna do it because math seems way more exciting and the department seems way more less stick up the assy.

I swear the CS dept is all about how they can make you a worker drone I hate going into a lecture and being surrounded by 20 year old workaholics it exhausts me, and the math professors are super proud and passionate.

So apparently I need to take differential equations and applied linear algebra... any anons here got advice for that? Been a while since I've done calculus. Ive taken like 2-3 semesters of discrete, so I can take analysis and algebra but those applied classes are still required.

[Anonymous No.15489624]

>>15489614
You will be filtered hard.

[Anonymous No.15489633]

>>15489614
What makes you say that? Sounds pretty good to me if not more work. I'm like 6 classes short of graduating in math, and 2 of them are prereqs and 3 of them are electives.

[Anonymous No.15489712]

>>15488486
First of all, rather than thinking of the rotation acting on the surface while keeping v fixed, you can take it to act on v while keeping the surface fixed by doing a trivial change of coordinates. So let's just leave the rotation aspect out of the problem for now.

You are asking to divide up the surface into regions according to the dot product of v with the surface normal, and then you want to do integrals over these bounded regions in order to get the center of mass.

Here's what you do:
>do a rotation of both v and the surface so that v lies along the z axis (this is not unique since you can do an extra rotation about v).
This leads to a new rotated surface equation G(x,y,z)=0.

>Transform coordinates from x,y,z to x,y,G
For a given value of G there will be more than one z as a function of x,y. But the different choices of z correspond to the regions of the surface that face towards and away from v, so this is exactly what you want.

>Calculate the Jacobian for integrating over x,y at fixed G
This will follow from the coordinate transformation. If I'm not mistaken it is just |dG/dz|^{-1}, but check it yourself. This will blow up at the boundary of region facing v, since the x,y,G coordinate system is ill defined there (the x and y coordinate vectors are linearly dependent), but this should be harmless once you actually do the integrals.

>Do the integrals to calculate the average value of x and y.
This requires you find the correct region to integrate over x and y. It will be bounded by the curve dG/dz = 0.

>Substitute the average value of x and y into the equation to find the value of z.

>Rotate back to the coordinates you want

>Warm up exercise: do all this for the equation of the sphere G(x,y,z)=x^2+y^2+z^2 -1= 0.

[Anonymous No.15489748]

Let [math](X,d)[/math] be a metric space and [math]f: X \to [0, \infty][/math] be lower-semicontinuous, i.e. [math]\lim_n x_n = x[/math] implies [math]\lim \inf_n f(x_n) \ge f(x)[/math]. Suppose [math]f(x_0) = \infty[/math]. Is it true that [math]\sup_{n \in \mathbb{N}} \inf_{y \in X} [f(y) + n \cdot d(x_0, y)] = \infty[/math]?

[Anonymous No.15489784]

>>15489712
>If I'm not mistaken it is just |dG/dz|^{-1}, but check it yourself.
Solve for z(x,y). The Jacobian should be
[math]\sqrt{(1+z_{,x}^2)(1+z_{,y}^2)-z_{,x} z_{,y}} [/math]
where z_{,x} is the partial derivative of z with respect to x, etc.

[Anonymous No.15489789]

>>15489712
>If I'm not mistaken it is just |dG/dz|^{-1}, but check it yourself.
Solve for z(x,y). The Jacobian should be
[math]\sqrt{1+z_{,x}^2+z_{,y}^2} [/math]
where z_{,x} is the partial derivative of z with respect to x, etc.

[Anonymous No.15489904]

Why is energy stored by work done by non-conservative forces irreversible? Does it apply to all non-conservative forces, or only friction? Why?

[Anonymous No.15489983]

>>15489904
>Why is energy stored by work done by non-conservative forces irreversible?
Do the integral and convince yourself
>Does it apply to all non-conservative forces, or only friction?
To all non conservative forces