/sci/ - Science & Math

Unanswered questions:

Mathematics questions:
>>14974095 [Commentary in >>14974130 regarding unanswerability]
>>14976138
>>14976877 [Yes.]
>>14979004
>>14979143 [Yes, it's a dumb question.]
>>14985992 [Answered in >>14986135 but I'm sure anon would probably appreciate more concrete advice regarding the class he's probably taking rather than an actual answer]
>>14986497
>>14987245

Physics questions:
>>14979513
>>14980611 [I could have sworn someone answered this. Probably jannied.]
>>14986103
>>14986251

/g/ questions:
>>14974153
>>14984382

Geology questions:
>>14974182 [Technically answered but could probably benefit from a better answer, see >>14974537]

Stupid questions:
>>14974888
>>14978138
>>14979063
>>14979485
>>14980251
>>14980745
>>14982896
>>14982828 [Answer this one so I can add them to the pasta.]

Why is it so difficult to find a tenure track, full-time job teaching community college? You basically need a doctorate and a current full-time position somewhere else. It barely pays more than HS teaching in my area; both are government financed. What gives? Weak union, greed? I just want to teach people who actually care about academics.

>the first time I did an MBTI I got ESTJ
>some time later I got ENTJ
>just got ENFP
What's even the point of MBTI if it's not stable though time?

Hello anonymous,
I have to prove that if a sequence [math]a_n[/math] has both of these properties:
[math]\displaystyle lim _{n \to \infty} a_{n+1} - a_n = 0 [/math]
and
[math]\forall _{ \epsilon > 0} \exists _{N \in \mathbb{N}} \forall _{m,n > N} |a_{3m} - a_{3n}| \leq \epsilon [/math]
then it has a limit. I know the second one means that a subsequence 3n has a limit, but I have no idea how to tie these two together. Any tips?

>>14991632
How far off is a random [math]a_n[/math] from some [math]a_{3m}[/math], anon?

>>14991632
If you want a hint, read the other anon's reply. If you want a big hint, read till (3). If you want the solution, read the whole thing.

>>14913335 >>14914024
forgot to thank you btw, so better late than never

How TF should I study calculus based physics ? I find it extremely difficult. I have a good grasp over AP calc AB and BC. Also please share few tips for organic and physical chem

>>14991894
I was thinking of showing that [math]|a_n - a_m| < \varepsilon[/math] and then using the equivalence between convergent and Cauchy sequences, but using it at the very start on the subsequence works too, I guess.

>>14991324
same reason why people treat astrology the way it is babe
personality changes over time and for some it changes based on the environment

someone pls give me a hint for this one. I notices that setting [math]x_n = \sqrt{a}[/math], you also get [math]x_{n+1} = \sqrt{a}[/math], but I doubt this alone proves it.

Is the uvw-method useful outside of contest math? Keep on seeing it brought up on stackexchange for lots of inequalities

>>14991245
Good work, i might suggest few things added to the pasta for the next thread:
>https://archived.moe/sci
This is an additional /sci/ archive, it doesn't have search enabled but contains threads not found in warosu because warosu was down some time ago.
>https://proofwiki.org/wiki/Main_Page
A nice collection of mathematical proofs

>[Answer this one so I can add them to the pasta]
Khan academy?

>>14992004
[eqn]\lim _{n \to \infty} x_{n+1} = \lim _{n \to \infty} x_{n}[\eqn]

>>14992004
Generally you can solve these with monotonicity

>>14991961
I suppose so.
Thanks.
>>14992034
>This is an additional /sci/ archive, it doesn't have search enabled but contains threads not found in warosu because warosu was down some time ago.
Eientei has imported a third party dump that includes posts from that period. It's also searchable.
That dump didn't have thumbnails, tho, which is inconvenient but eh.
>>https://proofwiki.org/wiki/Main_Page
Where would you include it in the pasta?
>Khan academy?
Really basic and well known tbqh.
But I should probably still add it for next thread.

is it just me or are american textbooks really dumbed down? I read (not all to be fair) Stewart's and Spivak's calculus, Strang's intro to Linear Algebra and they were all unnecessarily long, while managing to also not be rigorous and exhaustive. One thing I especially hate is when the author starts talking about a subject by giving definitions that are sort of true but also not really the point

eg I just read Strangs chapter on eigenvalues/eigenvectors/eigenspaces and at the end the reader sort of might understand what an eigenvalue is supposed to be but rigorous definitions are never given (but there's a ton of useless stuff and every 5 pages could be summed up into 1 without losing any information)

Are those books meant for high schoolers? I dont know what an high schooler is supposed to study in the us.
Not trying to shame US education just want to see if Im the only one who got this impression.

>>14991942
do more exercises
please elaborate what specifically you find difficult, is mathematical concepts or physical concepts or the connection between them?
also what kind of physics (Newtonian mechanics, thermodynamics, quantum mechanics?)

why are categories memed so hard? Currently reading through Aluffi and they seem like a fairly useful generalization

>>14992090
The US education system is terrible. Someone who only graduated high school in europe or asia knows more math than an american STEM graduate.

>>14992004
Positive numbers are closed under addition.

>>14992041
>[eqn] \lim _{n \to \infty} x_{n+1} = \lim _{n \to \infty} x_{n}[/eqn]

>>14992090
>Stewart's calculus, Strang's intro to Linear Algebra
Those books are supposed to be for low iq students. Hoffman for LA, and Rudin for Analysis, are the actual American books for those topics.

>A category is said to be small if [math]\operatorname{Ob}(\mathcal{C})[/math] is a set
so what's an example of a category where it isn't a set?

>>14992082
very cute wemi <3

>>14992090
took me a month to go over limits and start derivatives, with prof leonard i did calc 1 in 3 weeks with doing tons of practice while full time uni

Show that 2+3=3+2
Is this proof valid?
Assume 2+3<3+2
therefore
2+3-3<3+2-3
2<2, which is a contradiction,
similarly assume 2+3>3+2 and arrive at contradiction 2>2,
thus by contradiction we have proved 2+3=3+2

>>14992191
How do you get from
2+3-3<3+2-3
to
2<2
without assuming that 2+3=3+2?

You should probably do something like
2 + 3 = 2 + (2 + 1) = 2 + ((1 + 1) + 1) = 2 + (1 + (1 + 1)) = (2+1)+(1+1) = 3 + 2
But what a valid proof is depends on your definitions of "+", "2" and "3".

>>14992191
>2+3-3<3+2-3
This step assumes that 3+2-3 = 3-3+2, so it's logically flawed.

>>14992215
>>14992218
i don't get how adding/subtracting the same number on both sides of an inequality isn't allowed.

>>14992082
>Where would you include it in the pasta?
add something like
>>Where can i find a mathematical proof for X?
>https://proofwiki.org
Or whatever else you find more appropriate.
I was thinking this might be useful for someone to search in to find a proof for an exercise or a problem before asking here.

>>14992247
It's the rearranging part. You're trying to prove that 2 and 3 commute with respect to addition. In your third step in your proof, right after therefore, you assumed that [math]2-3 = (-3) + 2[/math] which is probably not an assumption you can make given the theorem you're trying to prove.

>>14992103
Classical mechanics, electrostats and mainly the derivation of equation. I personally don't feel the concepts are tough but the questions which are based on multiple concepts are pain in the ass
(Books recommendations like David morin?)

Btw any tips for physical chem and organic chem?

>>14992265
Yes i get what you're saying. What i'm asking is whether there's a rule that prohibits if a<b then a+1<b+1, that's basically what i assumed, any relation to said commutativity was entirely coincidental.since the sign < still remains.

>>14992191
>Is this proof valid?
From what axioms?

>>14992108
>why are categories memed so hard?
Troon anecdotes.
>fairly useful generalization
Of what?
>>14992153
The category of sets.
>>14992250
Sounds good.
The pasta is pretty close to the character limit tho, no promises.

>>14992297
Generally since the real numbers form an ordered field this is true. So if [math]x,y,z \in \mathbb{R}[/math] and [math]x < y[/math] then you also have [math]x + z < y + z[/math]. I don't know how far along you are in your course though, it seems like you're construction the natural numbers or something. Thus I have no idea if you have defined the order < yet and if you have checked some of the basic properties already.

>>14992274
hmm for analytical mechanics my uni used Douglas Gregory which doesn't have any limericks so it's probably inferior, this Morin book looks very instructive
I think very few people really "get" classical mechanics the first time, after finishing the course I read Landau's Mechanics (which is terse and really light on exercises btw so not a good first pick imo) and finally felt like it clicked for me

>>14992311
Assume that 2+3 is a and 3+2 is b, taking this >>14992297 assumption and replacing it with
if a<b then a-3<b-3, i fail to see how the proof is invalid. You can see how your claim about me assuming some commutativity in my proof becomes coincidental?

>>14992324
>if a<b then a-3<b-3
Where is the contradiction? Maybe [math]a-3<b-3[/math] really holds?

1927 characters including the previous thread link.

>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
z-lib.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

>>14992330
If we evaluate a and b then it doesn't. 5-3 is not less than 5-3.

>>14992353
How do you know [math]a = b = 5[/math]? If you already know it then why are trying to prove it using the inequality thing.

>>14992360
nice catch, i see now i can't escape the self reference

>>14991324
>online psychological tests
>>>/r9k/
>>>/soc/
>>>/b/

>>14991324
tbqh you probably just matured

Am I studying the right thing
I ant to learn how to do pic related is this the right video.
Also when why does the tutor only use 4 of the 5 points for the rectangles.

>>14994050
https://www.youtube.com/watch?v=YTKQswb60Pw

As mentioned several times in the base wiki article
https://en.wikipedia.org/wiki/Tuberculosis
Tuberculosis is less likely in the developed world, but particularly it is far less prominent in the US specifically. This is despite Canada having plenty of tuberculosis relatively, especially in its native population. In the US the natives also have more tuberculosis than white people, as do other minorities, but not as dramatic a difference. Socioeconomic status plays a big role obviously, but even so, western Europe used to be lousy with tuberculosis until modern healthcare. However, even now that drug-resistant TB has been around for half a century while the whole world has better medicine than Europe did 200 years ago now, the developed world still has low TB especially among white people, but the US has extremely low TB among all groups even native, even though Canada has plenty of TB. It's not just TB striking weakened immune systems in cold climates because it's very bad in China, India and Africa still, and Russia also did incredibly well for a while with TB and even now is relatively free of it. It's not geographic isolation, because Canada has plenty of it.

How exactly does the US have so little TB, and how exactly do white people have so little TB when they used to have so much of it, and in general why do specifically white Americans have one of if not the lowest incidence of TB anywhere in the developed world despite our old people being fatter and thus weaker immune systems than most countrie, and multiple-resistant TB existing?
Did we develop some sort of genetic resistance moreso than Europeans, somehow?

I can't figure this shit out.

>>14994080
wrong channel. medicine is not /sci/
>>>/x/

>>14994088
What drove you to shitpost this?

>>14991217
>Crying Loop
A lot of times I have a problem with a lot of bad memories and then start crying. Memory somehow loses form and then can't remember the memory and stop crying. Later somehow bad memories come again and start crying more. I don't know is it the same one as before or not because I can't remember the one before. Between events I can't remember crying and maybe become happy so it makes a wave with a lot of being sad and crying. I am writing this directly following crying and I am sure it is not the first crying of today and I can't remember why was I crying? I don't know how many times this loop has happened or what starts it or what it contains?

>Anti-Clown Hell Box
I am in Clown Hell. It is a big jail run by Evil Clowns. Clown Hell has mean tricks like crying that can derail my tasks. I have to immune myself to Clown Hell without becoming a Hell Clown myself inside the Clown Hell. If I can't do this I will have problems making technologies for the maid. I might get a big cardboard box and spend my time inside the box with nothing but a computer and the book vampire maid from touhou told me and tape pictures of maids to the inside of the box so the only things I see are the Science Computer and the Jech book and a lot of maids in the box and nothing else so whatever is causing crying either can't operate because nothing makes a bad memories or I discover it is one of those three things. The box has to be big enough to stand in and walk in place some but no bigger probably. Anti-Clown Hell Box can also have some music playing.

How can I better mitigate the problems caused by living in a Clown Hell?

Thank you /sci/entists for reading my post.

can everyone stop shitposting and answer my question

>>14994139
this isn't what mentally ill people post like btw, your feigning is cringe

Is there an explanation for why some people are just worse at math? I have a lot of symptoms of Asperger's and ADHD and even though I'm smart and could benefit from using math it takes me longer than usual to understand

>>14994191
Caring about irrelevant details that are beyond the current difficulty being taught
For example
5^0 = 1
I asked my teacher and she said don't worry about it but it still bugs me years later.

>>14994235
Do you ever learn those details?

>>14994244
Yes. In Analysis you learn all of those weird conventions.
Spoiler: They are all just that, conventions.

>>14994235
Isn't that just e^0

>>14994191
>even though I'm smart
if you were so smart, you'd know that ADHD is not a real mental disease

This /sqt/ has already started off real low quality I see

Just failed my real analysis midterm. It's unironically over. FUCK math, this shit is impossible.

>>14994139
Get a nasal spray and replace the fluid with a mixture of PE-22-28, NSI-189, and DNSP-11. Snort it whenever you feel sad.

>>14994298
I don't know what this means at all. Thank you for telling me though.

Are there any mathematical formulas that represent an ideal money supply relative to an economy (gdp, frequency of transactions, etc)?

>>14993813
That's the point, shouldn't a personality test at the absolute least stabilize at ~19 years of age?
>>14994148
I don't think anyone here really cares or knows much about medicine.

I get the impression the US has a very low demographic density compared to most countries, which might affect disease transmission.
Demographic concentration on occupied land, that is, so obviously you can't just hold the number up to Canada's or Russia's where most of the country is snow.
>>14994268
Buy a lucky charm and bring it to the next test.

>>14994268
No you're just worthless

>>14994268
>this shit is impossible
for YOU

have to catch up in my group theory class about direct product so going to ask some questions to make sure im getting stuff.

Q:How many elements of order 15 are in Z30 ⊕Z600?

I think the answer is one

let g be in G=Z30 ⊕Z600=Z3⊕Z25⊕Z8⊕Z5⊕Z2

then |g|=15 iff lcm(|g3|, |g25|, |g8|, |g5|, |g2|)=15 (where gi is in Zi).

this is true iff |g3|, |g25|, |g8|, |g5|, |g2| are all in {3, 5} or are all in {1, 15}.

this is true iff only we have |g25|=15 and all other equal to 1.

is this the right approach to this type of question?

>>14994470
oops i think i am missing one extra Z3 in the direct product but my answer stays the same

>>14994470
Weird notation in general.

>this is true iff |g3|, |g25|, |g8|, |g5|, |g2| are all in {3, 5} or are all in {1, 15}.
Obviously false. They all need to be in {1, 3, 5, 15}, and either one of them equals 15 or one is in 3 and another is in 5.
>this is true iff only we have |g25|=15 and all other equal to 1.
Nonsense. I have no idea how did you come up with this, redo the logic.

>>14994470
It's wrong. Those statements
>lcm(|g3|, |g25|, |g8|, |g5|, |g2|)=15 (where gi is in Zi)
>|g3|, |g25|, |g8|, |g5|, |g2| are all in {3, 5} or are all in {1, 15}
are not equivalent.

>>14994504
am retard ty. now it seems like i have to count a bunch of shit though no?
the first case (one being 15) is easy enough since Z_25 is fixed, but the other case seems like a somewhat involved counting process, no? because i have 3 cases for each possible place of element order 5

>>14994528
[math]Z_{25}[/math] doesn't have any elements with order 15, anon.

Is it harder to walk in the opposite direction of the Earth's spin.
Why or why not?

>>14994530
>>14994530
thank u got it

am I really this retarded?
why does (3 - ( - 2 )) result in +5?

>>14994627
Yes, that's pretty retarded. What is 3-2? What is 3+2? What is -(-2), or the opposite of (-2)?

>>14994630
hold on, what is retarded?
the image ie (3 - ( - 2 )) = +5?

>>14994627
two minuses make a plus

2x+3y=12
what is the biggest product x^2+y^2 equation can equal? help

sorry for ESL english

>>14994627
what is the distance between +3 and -2 on the real number line?

>>14994745
can you rephrase your question?

>>14994745
Use DeepL, you ESL retard.

>>14994929
>what is the distance between +3 and -2 on the real number line?
whoooooa its 5!

>>14994745
x^2+y^2 has no upper bound. Its lower bound on 2x+3y=12 is 144/13 at x=24/13, y=36/13.

For f(x) = a^x, if a > 1, then is the limit of f(x) as x tends to infinity always infinity?

>>14995130
yes

>>14995130
Do you know the Bernoulli inequality?
[eqn]a^x = (1 + (a-1))^x \geq 1 + (a-1)x[/eqn]
By the archimedian axiom for every K there is an N such that for all x>N
[eqn](a-1) x > K-1 [/eqn]
which implies that
[eqn]\lim_{x \to \infty} a^x \geq \lim_{x \to \infty} 1 + (a-1)x = \infty[/eqn]

About a month ago I recall an anon asked about how to prove that
[eqn]f(i,j)=\dfrac{(i+j-2)(i+j-1)}{2}+i[/eqn]
is one-to-one and onto. Another anon answered that it requires certain properties derived from the fact that [math]f(i,j)[/math] follows certain pattern. Does anyone know what the properties and pattern are?

>>14995181
That proof...was beautiful.

Linear algebra homework, what am I supposed to be understanding here that I'm just not getting? I feel like I don't even know where to start.
I'm mostly just confused by the notation p(0) -p(1)t etc. Like they give us p(t) is the standard basis, so what is this T(p) = p(1)t shit?

I feel like a fucking monkey in this class who only knows how to follow algorithms to find inverses/determinants/diagonalize etc but once I have to actually understand what I'm doing I'm fucked

>>14991217
if a 30hz light was set up next to another 30hz light and they alternated on/off would that be perceived as a 60hz flash?

>>14995130
[math]a^x = \exp (x \log a)[/math]
If [math]x[/math] goes to infinity so does [math]x \log a[/math] and hence so does [math]\exp (x \log a)[/math]
>>14995270
p(0) is just the polynomial evaluated at 0.

>>14995322
So T(p) is just effectively [math]1 - 4t - 4t^2 + t^3[/math] and plugging in for p(t)? That's it?

braindead moment

>>14995270
If you choose a basis like for example [1,t,t^2,t^3] then you can write T into matrix form

[eqn]\begin{pmatrix} 1 & 0 & 0 & 0 \\ -1 & -1 & -1 & -1 \\ -1 & -1 & -1 & -1 \\ 1 & 0 & 0 & 0 \end{pmatrix}[/eqn]

>>14995337
Yes.

Just to make sure I'm not a fucking idiot: the set of all [math]n \times n[/math] matrices with [math]\infty[/math]-Schatten norm (max singular value) [math]\|X\|_\infty \leq 1[/math] is the same as the set of all [math]n \times n[/math] matrices with [math]1[/math]-Schatten norm (sum of singular values) [math]\|X\|_1 \leq n[/math], right? Since if [math]\|X\|_\infty \leq 1[/math] then [eqn]\|X\|_1 = \sum_{i=1}^n \sigma_i \leq \sum_{i=1}^n \sigma_{\text{max}} = n \|X\|_\infty \leq n.[/eqn]

>>14995819
It's not the same, a matrix can have the eigenvalues n, 0.

>>14995850
Wow I'm a fucking idiot. Thanks.

>>14995192
Anyone? Just any clue on how to prove the thing would be appreciated.

>>14995871
Your >>14995192 is basically a shifted version of https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairing_function, and that wiki page has a fairly thorough proof.

>>14992274
For organic chemistry, visualizing the molecule and charge rearrangements is key. People seem to struggle with that.

>>14995966
Checked

I never had problems visualizing organic chemistry; remembering the fucking exceptions and rules were pain in the ass, though. Physical chemistry is way better and closer to physics

Can someone explain why my professor does this differently. On the organic chem tutor video he gets do alone and replaces it in the original problem along with u. My professor seems to take part of the problem and find the same expression when taking the derivative of u, I think.

What scenerarios should I use what in and does anyone have a video explaining my professor’s method

>>14996111

>>14996111
Bad handwriting aside that's just the standard u-subtituion method. Why he uses that and doesn't just cancel the sec's I have no idea at all. That seems retarded.

>>14996111
>>14996121
https://www.youtube.com/watch?v=sdYdnpYn-1o

>>14996111
I don't really know what you're saying. You have u, 1 + sec
the derivative of this is just the derivative of sec which is sectan
so du/u

what specifically is the issue

>>14996130
>cancel the sec
anon.....

>>14996198
in the video

https://www.youtube.com/watch?v=sdYdnpYn-1o

the guy gets dx by itself and then replaces dx in the orginal problem with what dx = equals. So here it would be

u=1+sec(x)
du=sec(x)tan(x)dx

then here is where the methods differ

du / sec(x)tanx(x) = dx

then you replace dx with du / sec(x)tanx(x)
In the original problem. That's how the video does it, my professor instead tries to make du =sec(x)tan(x) and then just replace that with du

Which method is better

>>14996208
the hell do you mean "getting dx by itself" it's just substitution
you choose a u that has it's own derivative in the problem so that it breaks down into an elementary integral

if u = 1 + secx
then,
du = secxtanx dx
both of those are directly in your problem, there's no need to do anything else except directly substitute u as 1 + secx and du as secxtanx dx (in your problem it's with respect to theta but regardless)

I scanned through the video and can't find anywhere that he does the problem so I have no idea what you mean by them doing them different ways. It's such a fundamental basic integral that there's really not any other reasonable way to do it.

>>14996208
>>14996217
maybe you're confused by the movement of the dx

slightly more formally it'd be
u = 1 + secx
du/dx = secxtanx
du = secxtanx dx with separation of variables so you can fully isolate what's in your integrand and directly substitute it out

why you would turn this into du / secxtanx = dx for this problem is beyond me

asking for a sanity check from someone with a better chemistry background.
would it make sense for ethyl acetate to get fucking obliterated by anhydrous acid?
I was distilling ethyl acetate off some salicylic acid i'd extracted after an acid hydrolysis, but i didn't wash the organic layer with base because i didn't want to form any salicylate salts. i figured it would be fine, since not that much water dissolves into ethyl acetate.
but, when i was distilling it, black tar shit appeared along the walls of the flask right at the liquid surface, and as i distilled it all the i was left with some shitty salicylic acid sludge.

what i think happened is that the ethyl acetate / water azeotrope came off first, and the unneutralized and now anhydrous acid did some weird nonsense to the ethyl acetate. is that reasonable?

Help with brownian motion problems, also want to know if someone could tell me how to understand this shit better.

Can someone give me a tip for this one? I tried inserting something for [math]\alpha[/math] and solving for the rational number to no avail and brute-forcing didn't work either.

what are "even" functions?

>>14996227
https://eientei.xyz/sci/thread/14900456#p14903641

>>14996252
Thank you, this makes a lot of sense. I still don't get why Zorich would pose such a question before even introducing limits.

>>14996227
Take
[eqn]\sum_{k=0}^\infty \frac{1}{10^{k!}} [/eqn]
it's well approximated by the partial sums.

>>14996265
Thank you!

>>14996262
Because he wants you to discover limits yourself. The LA book I am using asks to find a closed form solution to powers of Jordan matrices in the chapter that introduced matrix multiplication despite the fact that Jordan matrices aren't introduced until like the end of the book. I like books which give specific version of later topics as exercises.

>>14996271
i also think it is a good way to do it. it feels cool when you get to that chapter and it's like "wait, you already had me do this you fucker, i see what you're trying to do"

>>14996271
>>14996273
Even more based is Knuth who gives unsolved problems as exercises.

>>14996271
> The LA book I am using asks to find a closed form solution to powers of Jordan matrices in the chapter that introduced matrix multiplication despite the fact that Jordan matrices aren't introduced until like the end of the book.
Are you calling triangular matrices Jordan matrices?

>>14996275
Oh right, when you do the Jordan-Chevalley decomp you scale things so that the nilpotent part is cute, nevermind.

>>14996271
yeah it's great once you've got used to abstraction

How do you typeset these slightly larger parentheses in LaTeX? \left( and \right) don't work if the text they encapsulate isn't large itself.

>>14996408
>mathematicians in charge of naming things

What method do i give a python class to be able to compare two instances of it using ">" or "<"?

If you have a group G=Z2⊕D3 and you know G is isomorphic to one of Z12, Z6⊕Z2, A4, D6, how would you go about finding which one?

>>14996473
fuck found it immediately after asking.
__ge__ and __le__ for >= and <=

If some process has, say, a 1 in 10 chance of success, and you randomly choose when to sample the output of the process such that you are only getting a random subset of the outputs, is it still 1 in 10 according to your samples?

>>14996475
i think its not z12 cus z12 is cyclic and G isnt but other than that idk

>>14996408
Use package [math] \texttt{mathcom} [/math] and then use [math] \texttt{ \del[0] } [/math] where you can change 0 up till 4.

Can someone show me how to do this and also tell me what to type in to youtube to get a video of the matarial

>>14991217
There are many subjects that I want to have deep knowledge of, but it seems that I will never have the time to learn even a small portion of them. While college, has helped temporarily extend the period of time when I'm allowed to focus specifically on learning. Its inevitable that will have to start selling my time in order to afford the time to continue education. I'm not anyone special or intelligent, If I were I would find some way to avoid this problem entirely.

But is the trade off worth it? Can you keep pace while working a 9-5? Or do you inevitably lose interest and start to choose spending your time on entertainment or other instantaneous pleasures.

It's depressing to think about the amount of time I will end up spending commuting, attending morning stand-ups, and keeping up with current events just to appear normal and have some way to relate with coworkers. And I doubt that I will have the willpower to continue studying the topics that are important to me now, once I begin a career.. Please tell me I'm wrong...

>>14996629
Look up "Area between two curves".

>>14996498
Yes, assuming probability is independent of other events.

>>14980745
>i dont want any chemicals or lifelong shit
>i just want to take vitamins for life
you deserve to go bald subhuman

>>14991288
>why is free gibs for lyfe so competitive guise

I don't understand refraction

so if I have a glass cube (top) and shine a white light through it, most of the light is not absorbed and passes straight through, but some small amount is and gets re-emitted in all directions by the absorbing atom, and then again that emitted light has a super small chance of getting absorbed. the end result is the magnitude is of light leaving in other directions is so tiny that light effectively only passes straight through the cube. okay

but when I swap my cube for a prism, the light suddenly splits upon exiting for some reason? It's still just as transparent so shouldn't most of the light be coming straight out the other side? where are all these colors coming out anyways, if most of the light is not getting absorbed, then then the atom can't emit in a different frequency or anything like that

>>14996675
>but some small amount is and gets re-emitted in all directions by the absorbing atom
this is a misnomer, it doesn't happen. stop trying to think about photons interactions in materials, unless you understand QED and solid state physics, it will just confuse you. the photons interact with the EM field produced by the atoms and in the end you get the wave picture of light so stick to that.

> when I swap my cube for a prism, the light suddenly splits upon exiting for some reason?
it splits in every transparent material. if you look very carefully at a beam through a cube you would see red and blue at the edges. the angled edge of a prism simply enhances the effect to make a more pronounced.

How do you prove that the following ratios of binomial coefficients are natural numbers for all n?

[eqn] \frac{{16 n \choose 6 n}{31 n \choose 15 n}}{31 n \choose n} \\
\frac{{5 n \choose n}{11 n \choose 5 n}}{11 n \choose 2 n} \\
\frac{{7 n \choose 3 n}{14 n \choose 7 n}}{14 n \choose 2 n}
[/eqn]

>>14996408
use package [math]\texttt{physics}[/math] for saner parenthesis syntax than [math]\texttt{\left}[/math] and [math]\texttt{\right}[/math]

"Max" is the coldest setting for a refrigerator and "Min" is the least cold, right?

Can we recapture the polluents in the atmosphere?

>>14997192
Technically, sure. Just pass all of the air in the atmosphere through a bunch of filters. Realistically though that is never going to happen.

What books should I read if I really want to become a genetic engineer? Can I get through a book on molecular genetics with a high school-level knowledge of biology?

Why does my poop smell like mothballs? Or rather my ass, as I opt to wash it out afterwards in the shower rather than wipe. My time is my own.

Can anyone explain tensors?

>>14995949
Thank you.

I want to teach myself maths from the ground up. Is khanacademy still the best starting point?

Can I answer this by just doing the ratio test on the even and then the odd as is (giving 0 and 3)? Or do i have to express a_n as a_2n and a_2n+1 and subsequently change their expressions to match?

>>14991217
Just starting to study analysis, proving that 1 is the least upper bound of the rational numbers such that 1-1/n where n is a natural number.
Assume that 1 is not the least upper bound. Then there is some c such that 1<=(1-1/n)<1+c.
Subtract 1 from all sides:
0<=(-1/n)<c which cannot be as -1/n is negative and can't be greater than zero. Is this right?

>>14997605
Easy, a tensor is anything that transforms as a tensor

>>14992090
>reads a part of a 101 level math book
>"Americans are obviously drooling retards"

>>14992112
And the reason so many foreigners come here for college is..?

what if I had two -200s?
.
-200
x 2
------
+400
-------
.
BUT....
.
-200
-200
------
-400
------
.

wff!!

>>14997953
Greencard.

If G is a Hausdorff locally compact group, is it true that every unitary irrep of G appears as a sub-representation of the left regular representation on L^2(G)? If not, does it become true if we further assume that G is compact?

What's the easiest way to see this?

>>14997953
mcdonalds is great food and the proof is that it's in every country

>>14997987
-200*2 isn't 400.

>>14998043
congrats, under 53mins

>>14996746
okay I've done a bunch of reading and I'm refining my diagram

white light doesn't exist, it's merely a product of the cones in a tight area of our eye all maxing out (like RGB lights). A 'white light' is merely a blast of radiation across the spectrum 380nm to 800nm.

The light separates in the prism because of compton scattering (?). unlike in the cube where the light enters normal to the surface, the prism has the light enter at an angle and so the computed scattering angle differs between the different wavelengths resulting in them diverging. when they exit the prism they are far enough apart to only max out or partially max out 1 or 2 cones in a tight cluster which is why we see the rainbow of colors. I'm guessing that since the atoms of a prism / cube are bonded together, the electron cloud, which is what the wavelengths interact with, sort of blobs together going from spherical to kind of flat-ish which is why the light can enter 'normal' to the surface almost everywhere as opposed to very tiny areas which is also why the prism can decide on a scattering angle after it enters at an angle?

I have the alphabet, A to Z, 26 letters.

If I want to represent all possible combinations (allowing repeats and reorderings), this is easy. Just treat it as a base 26 number:

0 = AA
1 = AB
2 = AC
...
25 = AZ
26 = BA
27 = BB
28 = BC

What if I don't want to allow repeats and reorderings, though? Is there a simple closed-form expression? I want

0 = AA
1 = AB
2 = AC
...
25 = AZ
26 = BC
27 = BD

It's trivial to enumerate, but can I calculate it on the fly?

>>14997953
>choice of college is plentiful, but the Ivies matter obviously...
>party their asses off, or whatever
>get some quick, good grades
>get back to their country and share what they know, or for the flex
typical foreigner college experience, I guess...

>>14998068
Leonhard Euler told you the answer over 250 years ago.. I don't understand why you guys keep making it so hard.. Likely it's driven by your professors and teachers who are equally as misguided if not more so.

>>14994538
No because earth is not spinning, relative to you.

>>14994538
A disc can't spin

so limit ordinals are defined as non-zero ordinals without a successor. I don't get how such definitions are legal. What ZFC axiom allows their construction?

>>14998070
Isn't that just [math]\displaystyle \sum ^{26} _{k = 1} k[/math], since every next letter you are removing an additional letter, e.g. in B, you're removing BA, in C you're removing CB and CA, in D you're removing DA, DB, DC all the way until in Z you only have ZZ since every other letter has been represented as xZ. If you don't want to allow repeats all you need to do is to sum [math]k-1[/math] instead since each letter has exactly one repeat.

Hello i was just wondering about a simple question:

How big is the difference between a 5% drop rate of an item and 7.5%? Asking to see if its worth or not buying an item that boost x1.5 the drop loot

Like for exemple it makes a huge difference after 20-30 kills? Thanks

>>14998360
the probability of getting an item at least once within 30 attempts is [math]1-p^{30}[/math] where [math]p[/math] is the drop rate
if [math]p=5\%[/math], then the probability is roughly 79%
if [math]p=7.5\%[/math], the probability jumps to 90%

>>14998360
>>14998378
I made a typo, should be [math]1-(1-p)^{30}[/math]

>>14980611
>>14991245

Force isn't an entity. It's a mathematical tool to assess the change in momentum, which is a state of a system.

>>14998378
>>14998380
Thanks anon

Do you think its worth it or nop? I also forgot that its not only one item, but 3 other

Basically, all three have 5% rate for me atm. But if i use a drop boost, each will have 7.5%

If i farm it most of the time, worth?

>>14998384
it's a 10% difference, it's not huge but it can matter, it entirely depends on how much patience you have and if you're willing to save the boost for later on or if it's expendable

>>14998360
You have to look at cumulative probability for the mass function of probability.

It's a simple binomial distribution problem.

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

>>14998388
The boost are daily/monthly same price. Thing is for one boss there is a 100% item loot and 1 other 5%, when i kill it i rarely or never get the second one. But other people with the x1.5 dropboost gets often the second item

for me : its 8 kill, 8 item 100% rate (obv) and one item that has 5% rate boosted

For them : its 8 kill, 8 item 100% rate (obv) and 3-4 item that has the 7.5% rate boosted

I do not understand how comes there is such a big difference. Another possibility is that the "free" dropboost you get ingame are fake or even negative and only paid ones works, which makes it 5% vs 10% desu

>>14998416
Oops meant 3.3% (if free boost dont work) vs 7%

How can I do more exercises in a single day? I do about 10 and then get about exhausted.

>>14998522
Of course, make sure to eat enough. Otherwise, try pushing the boundaries just a little bit every day. You'll probably eventually manage to do more every day.
The first few hours you're awake are (for most people) also the ones in which their mind is at its clearest, so try doing it early.

>>14997820
Bump?

Is there a specific term for the elements of a (filter) base in math?

>>14997820
https://4chan-science.fandom.com/wiki/Mathematics

How do I prove that a function is continuous in [math]\mathbb{R}[/math]? I know how to prove that a function is continuous at some point, but I'm not sure how to prove that it's continuous everywhere.
My current approach wrt. piecewise functions was to just examine the point at which the function changes and handwave the rest as "it's composed of elementary functions, so it's continuous ". Is this correct?
Picrel is a function. I just tried to show that for some values of a,b,c it's continuous at -1 and 1 (I came up with [math]b = 0, c = 1, a \in \mathbb{R}[/math] and [math]b = \sqrt{1 + a^2} , c = -a, a \in \mathbb{R}[/math])

>>14998555
>How do I prove that a function is continuous in R?
by definition, [math]f[/math] is continuous in [math]\mathbb{R}[/math] if it's continuous in every point [math]a \in \mathbb{R}[/math], i.e.
[eqn]\forall a \in \mathbb{R}, \lim_{x\to a}f(x) = f(a) [/eqn]
>My current approach wrt. piecewise functions was to just examine the point at which the function changes and handwave the rest as "it's composed of elementary functions, so it's continuous ". Is this correct?
"elementary functions" are not necessarily continuous everywhere, but in your case the function is trivially continuous everywhere but in 1 and -1
you need to show that the limit in -1 and 1 is equal on both sides, to [math]f(-1)[/math] and [math]f(1)[/math], respectively

>>14998318
Sure, if i want the total, it's easy, I can use binomial formula too.

But if I want to go from 26 to BC?

Looks like Donald Knuth covers it in TAOCP though.

Do we go to Gensokyo when we die?

>>14998555
The subfunctions are continuous everywhere, so just check continuity at points where the subfunctions switch.

>>14998546
Thank you. I skimmed it in the past a long time ago and must have missed the intro bit. I will now start my day by doing baby kindergarten maths and work my way to the top.

>>14998607
Holy shit, does this "great job! x more to go!" confirmation thing go away with later modules on khanacademy? Forcing two clicks per question submission is already going to be a drag. I can see why they would have it (for kids as encouragement) but I hope it isn't universal.

>>14998619
nvm I can just press enter. I'm retarded. bye /sci/

>>14991217
I live in America. Can I get in trouble for working on a Computer Program with somebody Serbian in Serbia? Are America and Serbia friends? I don't know anything about Serbia or where it is or what happens there. I just want to know, will the government in America be mad at me or cause me problems if I work with a Serbian on a technology project?

Is there some type of list of people Americans can make technology projects with, without getting in trouble? I don't want to work in a corporation. They would not accept the terms I need and also corporate programming problems are very boring. Also would prevent CC0 releases.

>>14998642
Cooperating with anything the iron curtain encompasses will put you on the FBI's watchlist. For the record, no, Serbia and America are not friends at all. Lots of Serbians are denied entry to America every year. You should move to a neutral country, like Switzerland.

is there a website/program that lets me bend/move/curve a line on an xy graph and then gives the exact and approx functions for the line?

>>14998642
Serbia is a nationalist, anti-American shithole. It's also anti-EU and hundreds of war criminals there have yet to be arrested. There never really was a democratic revolution. I'd also bet that your Serbian boss could scam you without any repercussions. Best to not make deals with these people.

>>14998068
>A 'white light' is merely a blast of radiation across the spectrum 380nm to 800nm.
That is the only thing you got right. Everything else is utter nonsense.

>>14998649
>>14998683
Thank you for telling me. I will avoid interacting with the project or the person. It was not an employment. It was a nice person who has an interesting project which is directly connected to Computer Science topics I like. I was interested because person is nice to me and project is interesting and I would learn a lot of things by contributing. I am not willing to move out of America.

This is the second time this has happened to me and I don't really want a third time. Is there a list of countries where I won't get in trouble if I work with a person from there on a CC0 Math or Computer Science idea? How do I meet a nice American person who likes Computers and Books? Where do I post research and maids? I can't use any social media because it bans me for incomprehensible reasons. It also asks me to login and asks me to accept a 500 page terms of service I have no hope of comprehending. I refuse to even visit Reddit for any reason and I will not use or install Discord for any reason.

I am not sure what is meant by Iron Curtain in this context.

Thank you for reading my post.

>>14998713
Only cooperate with stable EU countries and American vassal states.

>>14998717
Thank you for telling me.

>stable EU countries
Which ones are stable? Also I might be an information hazard to Europeans. They have laws about Thought Crimes like Illegal Opinions and any European who talks to me risks getting messaged and then consequently being in possession of an Illegal Opinion.

>American vassal states.
The only countries I know that have this status are Japan and Germany I don't know anybody from there.

>>14998713
Finland
Norway
Switzerland
Denmark
Sweden
Ireland
Australia
Iceland
New Zealand
Canada
Luxembourg
Netherlands
Austria
Germany
Portugal

>>14998586
>But if I want to go from 26 to BC?
If you have the total it's fairly trivial. Get the first nth letter, find the total sum of n-1 and then subtract that from n. Then all you need is to add the number of the second letter while avoiding all previous letters.
E.g. EF - E is the fifth letter, so 26+25+24+23 and then we also add 2 (since E{ABCD} would be a repetition, so we only have EE and EF) = 100. Subtract one at each step to get this without double letters like EE.

>>14998717
>EU countries and American vassal states
redundant

>>14991217
I just realized that a lot of manifolds are constructed by a) restriction/intersection, or b) quotient. Real projective spaces (and other Grassmann manifolds) are of real space,as are tori, while unitary and symplectic groups are intersections ("specfiically those matrices obeying this relation). SO(3) is a restriction, but it is homeomorphic to RP3 which is a quotient. Here I am specifically talking about "building down" spaces; you can also build them up by taking (in)direct products etc. My question is: do all possible manifolds follow this scheme; if they do not, what exceptions (or other techniques for obtaining them) are there, and if they do, is there a particular structure to it (like my remark about SO(3) and RP3)?

>>14998792
Thank you for telling me. I will save this list.

An aqueous copper sulfate solution should be a bit acidic yes? By mixing it with an unknown aqueous solution that is assumed to have hydroxide in it, would it form a precipitate,?

>>14998859
If we're being literal about it every manifold embeds in [math]\mathbb{R}^n[/math], so they're all restrictions of [math]\mathbb{R}^n[/math]

Practically speaking, there are also topological techniques for manifold construction like surgery, and also spin groups, moduli spaces and random non-generic constructions like spaces of basis for some vector space, and a bunch of other ways that I either don't know about or am not remembering right now.
Algebraic geometry also has blow-ups and probably other stuff, but I'm not sure how often the results of that are manifolds.

>>14998922
That's exactly the thing I'd like to see classified. You're right about embeddings, I realized after posting, but I can't help but thinking about how manifolds can or can not be formed by taking R^n and "folding it in on itself" through certain operations like the quotient.

test
my posts keep getting eaten

>>14997605
this is a condensed matter physics/material science take which ignores co/contravariance (source is De Graef & McHenry)
read an intro level GR textbook for the full picture

Let [math]R[/math] be a commutative ring and [math]\mathfrak{a}_1, ..., \mathfrak{a}_n, \mathfrak{b} \subseteq R[/math] pairwise coprime ideals. Then the product [math]\prod_{i=1}^n\mathfrak{a}_i[/math] and [math]\mathfrak{b}[/math] are also coprime. My proof just takes a pair [math](\alpha_i, \beta_i) \in \prod_{i=1}^n\mathfrak{a}_i \times \mathfrak{b}[/math] such that [math]1 = \alpha_i + \beta_i[/math] for all [math]i = 1, ..., n[/math]. Then consider the following product [eqn]\prod_{i=1}^n(\alpha_i + \beta_i) = 1.[/eqn] If you write it out you get only one term without a [math]\beta_i[/math] and you can only get that by selecting [math]\alpha_i[/math] in each bracket, so said term will be in [math]\prod_{i=1}^n\mathfrak{a}_i[/math]. All the other terms contain a [math]\beta_i[/math] so they are in [math]\mathfrak{b}[/math]. Thus [math]1 \in \prod_{i=1}^n\mathfrak{a}_i + \mathfrak{b}[/math], meaning they are coprime. So that was my proof, but I don't find it really satisfying. Is there a more elegant way to handle that product? Or just a more elegant way in general?

Is it worth studying semi-classical analysis or is it a meme? I know my questions is a bit vague so if anyone could give me a brief rundown of it and tell me in which areas it's largely used I'd be more than happy-

What is going on here in the calculation of m? I dont understand it. Ive tried to draw the signals but I dont understand how you end up with this expression.

Basic linear algebra:
Let [math]V[/math] be a vector space on [math]\mathbb{R}[/math]. A scalar product on [math]V[/math] is an operation [math]< \cdot ,\cdot >:V*V\rightarrow \mathbb{R}[/math] with the following properties: commutativity, bilinearity, defined positive.

My teacher then went on to say that a vector space V with a scalar product is called an Euclidean space and that the standard scalar product is defined as a1b1+...+anbn where a_j and b_j are the elements of the two vectors a, b. So basically in his definition a standard scalar product is what's known as the dot product I guess.

Now, my questions are:
1) Im getting confused because on english wikipedia it uses scalar product and dot product interchangeably, while my teacher defined the dot product as a particular kind of scalar product
2) my teacher talked about "Euclidean space". Is this equivalent to the inner product space? my book also talks about hermitian space but i havent quite understood if it has anything to do with this. thank you

>>14999231
You can just do algebra directly with the ideals.
>>14999521
>1) Im getting confused because on english wikipedia it uses scalar product and dot product interchangeably, while my teacher defined the dot product as a particular kind of scalar product
I'd say your teacher is the one in the wrong.
An inner product is a generic positive definite, bilinear form, which is symmetric on a real vector space and hermitian on a complex vector space.
The dot product and scalar product stand in contrast to the cross product and mean the standard Euclidean inner product on either a real or complex vector space.
>2) my teacher talked about "Euclidean space". Is this equivalent to the inner product space? my book also talks about hermitian space but i havent quite understood if it has anything to do with this. thank you
Euclidean space is a name for [math]\mathbb{R}^n[/math] equipped with the dot product.

How do I show [math] \frac{\partial A_i}{\partial t} = 0 [/math] from [math] \frac{d\vec{B}}{dt} = 0 [/math] using suffix notation?

I tried to take the total derivative of the curl of A but I am messing something up.

Okay, /sci/ whats happening when the lid on a slow cooker has water all around it and causes the lid to lift up and slide around a little bit, and there is a slight suction when I go to lift it off of the slow cooker.

Just curious if there is a name for this phenomenon or whatever it can be labeled as.

Can someone explain what does the 3rd point mean? Is it the same as 4th point?

>>15000624
The 3rd point explains that every cycle is a product of transpositions. The 4th points extends this to permutations in general, not just cycles. This follows from point one where it was stated that every permutation is either a cycle or a product of cycles.

>>15000630
Ahh makes sense. Thanks anon. Btw is there any point to studying Group theory in Linear Algebra?
Most textbooks I checked (Hoffmann & Kunze and Strang) start with systems of linear equation but our uni started with groups & fields and then went to matrices.

>>15000653
It's not totally necessary, because the main subject of study of linear algebra is vector spaces and linear transformations, but it's not like them and groups are totally unrelated so I can see why your uni would do that. I remember that we skipped groups entirely and started with rings and fields. I know books that start linear algebra with determinants, those are all legitimate ways in my opinion. What counts is what you know/have seen at the end of the course.

are medical related questions allowed here?
as in I have an injury and would like advice

>>15000653
Groups are not that important but fields are.
>>15000669
>those are all legitimate ways in my opinion
incorrect

>>15000215
the surface tension of the water is my guess

>>15000653
If all you care about is complex vector spaces, then you have no reason to care about abstract algebra. There are many books (better imo) that does not start with linear equations. For example:
Friedberg, Insel & Spence,
Bhimasankaram & Rao. (favourite)
Some don't talk about it at all:
Axler,
Halmos (both of his books)

Let [math]f: V \to V[/math] be a linear operator on a finite dimensional space. Given a non zero vector [math]v[/math], let [math]\mu_{f,v}[/math] denote the lowest degree monic polynomial that satisfies [math]\mu_{f,v} (f) v = 0[/math], and let [math]Z(f,v)[/math] denote the cyclic space of [math]v[/math] wrt [math]f[/math].

I need to show that if [math]\mu_{f,v}[/math] is irreducible and [math]0 \ne w \in Z(f,v)[/math] then [math]Z(f,w) = Z(f,v)[/math]. Attempt: Write [math]w = Q(f)v[/math] for some polynomial [math]Q[/math]. Given an arbitrary polynomial [math]P[/math], we must show there exists a polynomial [math]S[/math] such that [math]P(f)v = S(f)w[/math], i.e. [math]P(f)v = S(f)Q(f)v[/math]. Letting [math]P = SQ+R[/math] where [math]R[/math] is either 0 or has smaller degree than [math]Q[/math], it suffices to show that [math]R(f)v = 0[/math]. By irreducibility, we must have [math]\mu_{f,v} = \mu_{f,w}[/math]. How can I use this to conclude?

Can someone show me how to do this, it says find the derivative but everything is an anti derivative, I almost feel like the derivative would just be the same problem but without the integral as if they cancel out but it can't be that easy.

Why is Tor so slow since few days? Is it a problem with me?

>>15001106
https://www.expii.com/t/differentiating-an-integral-function-using-chain-rule-9183

>>15001106
I've seen you here with these questions multiple times. I'm just curious if you are studying in a high school or self-teaching?

Also, see this: https://en.wikipedia.org/wiki/Leibniz_integral_rule

>>15000754
>surface tension

Can't believe that didn't pop in my head. I appreciate it, thank you.

Did Serge Lang kill himself? Heard rumors of this. Why?

>>14999698
What are you trying to prove, specifically?
That's not true if we just have [math]B = \text{curl} \ A[/math]. You can tell since we can do a gauge transformation [math]A \to A + \nabla f[/math], and then make [math]\displaystyle \dfrac{\partial A_i}{\partial t} \neq 0[/math] (not sure if you mean the divergence or the components but doesn't matter).

>>15001131
>>15000754
>>15000215
Actually it's the water vapor pressure inside the cooker, according to the ideal gas law
PV=nRT

When the lid is closed n and V are constant but T is increasing so higher temperatures increase the pressure so the lid lifts up.

When you try to lift the lid you're trying to increase the volume with n and T constant so the pressure drops and you feel slight suction.

Idk if surface tension of the water plays a role, maybe it also provides a slight suction force? though i'm not sure.

>>15001143
why do you like touhous

Why does the video about gravity have 133 million views? Why are people so attracted to it?
>https://www.youtube.com/watch?v=MTY1Kje0yLg

>>15001144
Thanks for the explanation, this is insightful.

Also, would you say your post number has
>001144
multiple dubs.
would this be considered 3 squared, or 2 cubed, or neither?

^ btw that doesn't have to actually answered, just something I threw in.

>>15001119
Im in college, calc 1

>>15001113
>>15001119
Okay I tried looking it up and I have a new question. Why did the youtube person bother doing any of this and not just replace t with x.

Was he just showing me why we replace t with x

>>15001134
> Later in his life, Lang was an HIV/AIDS denialist. He claimed that HIV had not been proven to cause AIDS and protested Yale's research into HIV/AIDS
Yikes

>>15001146
Remilia is absurdly cute.
I want to pat her head and brush her hair and give her piggyback rides.

>>15001178
't' is a dummy variable and 'x' is the independent variable in the function. Here, due to the nature of limits of integration, the function comes out exactly the same as the integrand, but in general, this is not what always happens.

>>15001204
so if the upper value on an intergral is just x then all I need to do is replace the dummy variable?

How the fuck do you learn physics? Every answer just spawns more questions, and eventually, the teacher will just say: ''well, we don't know that.'' It seems to me like the whole foundation is pretty shabby

>>15001216
I literally posted a link that tells you EXACTLY what to do in every scenario jfc, stop watching gay 30 min over complicated garbage

>>15001197
Makes sense. Always came off as kinda schizo tbqh.

>>15001227
The foundation is held up by a single zenga brick, we're currently trying to find it and pull it out

>>15001242
*jenga

>>15001242
See? Legit questions get meme answers. And we can't even trust you to type it right.

>>15001234
Sorry I just like hearing someone explain it to me, buy yeah your site looks good thx

>>15001227
you are more apt for philosophy than physics.

>>15001216
No, please understand it more fundamentally. Literally look at any HS calc textbook; it should have explained taking derivatives of integrals.

>>15001163
>would this be considered 3 squared, or 2 cubed, or neither?
what? 3 squared is 9 and 2 cubed is 8.
I don't understand what you're saying here, but i would call this triple dubs i guess?

>>15001257
I think he means the probability of 2 and 2 and 2 digits being the same. like the chance of 2 digits being the same, cubed

Why some [math]N[/math]? Isn't the neighborhood of infinity, [math]U(\infty )[/math], defined to be the set of [math]x[/math] whose absolute value is larger than _any_ [math]N[/math]?

>>15001257

I didn't explain it well, and this is probably more of a gag

the 3 represents 3 sets of dubs [00, 11, 44]
squared just represented the n of the same number ie 00 <- 2 of the same number.

but its kind of reversed now.

2 would represent the n of the same number, and cubed would represent how many times it showed up consecutively

from mathematical standpoint it wouldn't make sense, just more of a bullshit gag thing.

>>15001258
This anon is explained it well, basically the chance of two digits being the same, and have it happen 3 times in a row.

>>15001284
Stop reading shitty meme books like Zorich.
>le hecking base
What the fuck is wrong with him?

>>15001284
>Isn't the neighborhood of infinity, U(∞), defined to be the set of x whose absolute value is larger than _any_ N?
That's the empty set, by Archimedes.

>>15001324
don't really mind the bourbakitism
>>15001367
yeah I've reread the previous pages and seem to have misread it. It's really just some arbitrary real number

Will you watch the team's game today? >>15001267

>>14991217
Does anyone know a good book about the Riemann Hypothesis and the Riemann-Zeta function? I'd like something with a good balance between accessibility and technical detail. Readable by a layman. But hopefully one with citations so I can go and read real papers about anything I want to investigate myself.

how do we know the casimir effect is actually from the interactions of virtual particles and not, say, local net charges (a la van der Waals forces or Dispersion forces) on the plates causing an electrostatic attraction (or, hell, even the gravity of the two plates attracting one another as minute as it may be)

Hot take: most of you don't know even the basics about physics, but it somehow strokes your ego to pose as an expert on virgin channel. If you were asked to explaine a simple phenomenal, you'd spill you spaghetti.

>>15001884
bullseye

>>15001884
>you don't know even the basics about physics
Correct.
>it somehow strokes your ego to pose as an expert on virgin channel
Incorrect.
I posted >>15001143 because anon coincidentally asked a question that I could immediately tell was missing context.

My bad if you're actually seething because of someone else.

>>15001227
> Every answer just spawns more questions
That's how most of science works. Physics is kind of special though since most of what you are taught at highschool is wrong.

How do I solve this? I am tried to find the difference between the action before and after the transformation but I cant get zero. I get a exponential term that can't be cancelled.

>>15001163
Actually, you reminded me of the algorithm I came
up with regarding how many of dub, trips, etc that
passed from just the post number. This was what
I did in pic related.

>>15002013
Use u-sub


[eqn]S' = \int_{t_1'}^{t_2'} L'(x',\dot x',t') dt' \\
= \int_{t_1'}^{t_2'} \left( \frac{ (\frac{dx'}{dt'})^2}{2} - \frac{g}{(x'(t'))^2}\right) dt' \\
= \int_{t_1'}^{t_2'} \left((\frac{dx'}{dx})^2 (\frac{dt}{dt'})^2 \frac{ (\dot x(t'))^2}{2} - \frac{g e^{-2\alpha}}{(x(t'))^2}\right) dt' \\
= \int_{t_1'}^{t_2'} \left(e^{-2 \alpha} \frac{ (\dot x (t'))^2}{2} - \frac{g e^{-2\alpha}}{(x(t'))^2}\right) dt' \\
= \int_{t_1}^{t_2} \left( \frac{ (\dot x (t))^2}{2} - \frac{g}{(x(t))^2}\right) dt \\
= S
[/eqn]

>>15002013

[math]
\mathcal{L}(x,\dot{x}) = \dfrac{\dot{x}^2}{2} - \dfrac{g}{x^2}
\\ \\
\\ t'=e^{2\alpha}t \implies dt'=e^{2\alpha}dt
\\ x'=e^{\alpha}x \implies dx'=e^{\alpha}dx
\\
\\ \implies \dot{x}' = dx'/dt' = \dfrac{\dot{x}}{e^{\alpha}}
[/math]

So,

[math]
\begin{align}
S'(x',\dot{x}') &= \int dt'\mathcal{L}(x',\dot{x}') \\ \\
&=\int dt'\ \left( \dfrac{\dot{x}'^2}{2} - \dfrac{g}{x'^2} \right) \\ \\
&=\int e^{2\alpha}dt\ \left( \dfrac{\dot{x}^2}{2e^{2\alpha}} - \dfrac{g}{e^{2\alpha} x^2} \right) \\ \\
&=\int dt\ \mathcal{L}(x,\dot{x})
\end{align}
[/math]

How do I "find" the addition and multiplication tables for a finitie field K with 4 distinct elements {0, 1, a, b}? Is there any method besides guessing?
And why is it only possible to construct a 4-element field with a characteristic of 2 and not e.g. 3

If you spin uranium or some other radioactive source fast enough, will the alpha particles come out of the sides?

>>15002152
>How do I "find" the addition and multiplication tables for a finitie field K with 4 distinct elements {0, 1, a, b}? Is there any method besides guessing?
There are many explicit ways to construct fields. All finite fields with the same order are isomorphic so you can just construct any field of order 4 for example
[eqn]\mathbb{F_2}[x]/((x^2 + x + 1) \mathbb{F_2}[x])[/eqn]
Then it's easy arithmetic to calculate the tables.
In general you can construct the field [math]\mathbb{F}_{p^n}[/math] by taking an irreducible polynomial of degree n (it can be shown they exist for all n) and then taking the quotient
[eqn]\mathbb{F_p}[x]/(p)[/eqn]
Here [math](p)[/math] stands for the ideal generated by this polynomial.

>And why is it only possible to construct a 4-element field with a characteristic of 2 and not e.g. 3
Let [math]\mathbb{F}[/math] be a field then [math](\mathbb{F},+)[/math] is an abelian group and you can consider they cyclic subgroup generated by 1. By the theorem of Lagrange it's order divides the order of [math]\mathbb{F}[/math].
Also the characteristic p always has to be a prime number because if [math]p = a \cdot b[/math] then [math](\underbrace{1+1+\ldots +1}_a)(\underbrace{1+1+\ldots +1}_b)=0[/math] and you can't have zero divisors in a field so one of the factors had to be 0 already.

>>15002063
Oh, I see.
I need to account for the t'.
Thank you

>>15002082
Thank you too.
I got luck in older problems when the t' was just [math] t' = t + \alpha [/math] . So always got the answer right.

>>15002152
>How do I "find" the addition and multiplication tables for a finitie field K with 4 distinct elements {0, 1, a, b}? Is there any method besides guessing?
I'm not sure what you mean by "guessing". The obvious method is very methodical and clear cut.

Since [math]1 + a \notin \{0, 1, a\}[/math], trivially [math]1 + a = b[/math], which is how we'll write it from now on.
Since [math]a^2 \notin \{0, a \}[/math], either [math]a^2 = 1 + a[/math] or [math]a^2 = 1[/math]. If the latter, [math](1 + a)^2 = 1 + a^2 + 2a = 0[/math], which violates field axioms.

Then we're done, basically.

>>14994315
What do you mean by "ideal money supply"? You mentioning GDP and frequency of transactions makes me think of the quantity theory of money (more like quantity rule of thumb of money).
>MV = PQ
>M: money in circulation
>V: how many times 1$ is used to purchase goods and services in a given period
>P: price level
>Q: quantity of goods and services
If M grows but Q and V stay constant, then P grows. Meaning increasing the money supply faster than the economy grows generates extra inflation.

That said this rule of thumb is 60 years old and isn't actually being used anywhere. Modern monetary economics takes into account things like market power, inflation expectations (e.g. self-fulfilling prophecies), etc. which the quantity rule of thumb of money abstracts away. Jordi Gali's textbook is often used as an introduction to modern monetary economics but it doesn't have a simple equation explicitly relating money supply and other economic variables as far as I remember.

What are scientific methods to grow your penis length and girth. I've been training with my penis for five months now. I have a daily routine where I stretch my penis in a flaccid state 100 times both in the morning when I wake up and shortly before I go to bed. I noticed that it actually grew larger, but I'm unsure on how to optimize my training. Do any of you have well-founded knowledge on this? Any physicians here, maybe?

>>15002343
>anon rediscovers jelqing
I don't think there are any scientific methods of increasing your penis size backed by peer-reviewed studies.

why do bicycles fall over sideways when slightly turning on ice?

How does someone with a master's get into any type of academic research position, even short-term (expectedly)? I'm not talking about a doctoral program.

>>15002616
They'll fall sideways if you take an extremely sharp turn, even if there's no ice or rain on the road.
t. guy who's fallen down his bike a few times

Trying to prove the orthogonality of the spherical harmonics but I'm getting stuck at this integration by parts. I've already prove that, for two harmonics, [math]Y_{l}^{m}(\Omega)[/math] and [math]Y_{l^{\prime}}^{m^{\prime}}(\Omega)[/math], the inner product between these two is proportional to [math]\delta_{mm^{\prime}}[/math], but now I'm trying to prove that it's also proportional to [math]\delta_{ll^{\prime}}[/math]. I was able to prove this so far by representing the harmonics as state vectors and taking the inner product thusly: [math]\langle l^{\prime}, m|l,m \rangle[/math], but I also want to accomplish this in the position representation of the harmonics.

So far I have:
[math]\langle Y_{l^{\prime}}^{m}(\Omega), Y_{l}^{m}(\Omega) \rangle = \int_{\Omega^2}L_{+}^{l^{\prime} - m}Y_{l^{\prime}}^{l^{\prime} *}(\Omega)L_{-}^{l-m}Y_{l}^{l}(\Omega)d\Omega[/math]
where the angular momentum ladder operators are defined as such: [math]L_{-}=e^{-i\phi}\left ( -\frac{\partial }{\partial \theta} + i \cot{\theta}\frac{\partial }{\partial \phi} \right )[/math] and [math]L_{+}=e^{i\phi}\left ( \frac{\partial }{\partial \theta} + i \cot{\theta}\frac{\partial }{\partial \phi} \right )[/math]

My strategy here is to get [math]L_{+}[/math] and [math]L_{-}[/math] next to each other akin to [math]\langle l^{\prime},l^{\prime} | L_{+}^{l^{\prime}-m} L_{-}^{l-m} | l,l \rangle[/math] through IBP but I'm not sure what to select for my u and dv. Also, [math]\Omega = (\theta, \phi)[/math], [math]d\Omega = \sin{\theta}d\theta d\phi[/math], and [math]\Omega^2[/math] is the surface of the unit sphere.

>>15001227
The answer you're really looking for is that the first principles of every branch of physics are set in such a way that everything else can be defined in terms of what the first principles allow there to be.
There's no turtles at the bottom, no escape from the Matrix, no world outside of the cave, nothing else.
They're all just names for variables and functions that we consistently assign to phenomena that match a certain set of criteria. We use them because they preserve a certain mathematical relation between each other.
There is no scientific answer to any question that starts with "why". There are only answers to questions asking for "how" and "by what means" things come to be, given some constraints that we must either measure or assume if not given.

t. guy who used to read philosophy books and smoke weed

Guys, why does everyone recoomend Arduino to do any robotics projects? Do any real robotics companies use Arduino in their robots?

>>14991217
Anyone got the dover book chart?

>>15002463
>peer-reviewed studies.
that's because science is homophobic. We need more faggots to do the peer review.

>>15002944
>why does everyone recoomend Arduino to do any robotics projects
because it's easy for hobbyist normies to learn

> Do any real robotics companies use Arduino in their robots
No. they will use either ASICs or FPGAs. AVR microcontrollers are really only used in archaic sensor technologies, afaik.

If I'm working in R2 the orthogonal complement of the subspace generated by any given line is always going to be a plane (which is the whole R2 plane), right?
Now if I'm working in R3 does the situation stay the same, regardless of the number of dimensions?
Intuitively, let's say I have a line in R3. I take a point on that line and I want to find the vectors that are orthogonal to that point in respect to that line. In R2 it's easy, it's just the line perpendicular to the starting line, but in R3 I would have infinite lines that make a full 360° rotations around that point. If I do this for any point on the starting line this should generate the whole R3 space, therefore the orthogonal complement of a line in R3 is R3 itself. Does this make any sense?

>>15003177
Nevermind I did the math and apparently the orthogonal complement of a line in R2 is the line itself and the orthogonal complement of a plane in R2 is the origin. I think that the dimension of the subspace plus its orthogonal complement has to be exactly the dimension of the whole space so what I said doesnt make any sense. At this point I think I just don't understand the whole concept of what an orthogonal complement is even though I can do the exercises

>>15003150
So, if I wanna get started in robotics as an absolute beginner should I use Arduino? And no, I'm not doing it just for a hobby, I eventually want to become a robotics engineer in a major company.

>>15003212
Also, I wanna add, that I don't generally want to get involved in the hardware side. I wanna do something with AI that will relate to robotics.

>>15003177
>>15003185
Do you even know what a complement is let alone orthogonal? Because this is an extremely obvious question. I recommend you read that first. I studied it from 1.6 and 1.7 of "Rao, R.A., & Bhimasankaram, P. (2000). Linear algebra." (available on z-lib and libgen), and it does a good job.

But basically:
complement of a subspace is another subspace whose common element is only 0 and
[math] \forall v \ in V \quad \exists x \in S, y \in S^c \quad v = x + y [/math]
Basically, it is another subspace such that you can express every vector in the superspace as a UNIQUE sum of two vectors, one in the subspace, the other in the complement. If they contain a common non zero element, then it can be easily verified that the sum is not unique. In fact, when sums of two subspaces map to unique vectors the sum is called direct. Hence, a complement of a subspace is a another subspace such that its sum with the former is direct and can express every vector in the superspace. Orthogonal complement is a complement that is perpendicular to the subspace. For example in IR2, any OTHER line is a complement to any line, but the perpendicular line is the only orthogonal complement.

Total maths retard here
I'm trying to write a c++ program that simulates a two body system.
As things stand now, I store the cartesian coordinates of the two objects in two arrays. I plan to run a loop that calculates Fg between them every second to get the acceleration through a = F/m.
Then, their respective velocities would be incremented by a.
What I'm having trouble wrapping my brainlet around is describing acceleration vectors. Obviously if both objects were, say, on the x axis, only their acceleration in the x direction would change since they attract each other in a straight line.
But what if they're not? How would I calculate the x and y "components" of acceleration?
I figured asking here was more appropriate than asking /g/ because this is more of a maths question instead of a programming logic one.

Anyone else got a love/hate relationship with math? I've found that it can be hella fun deriving things on your own, but whenever I read textbooks it feels like debugging code where rather than doing a binary search with print() or single stepping, you have N steps and your next step is rand() mod N.

I've had textbooks use things without defining them, or missing "obvious" steps, or being implicit about it, e.g "now we can do X" (because X equivalent to Y). Some books don't even have answers.

It really feels like there's a bunch of connections that are "just there" but good fucking luck seeing them.

>>15003347
Forgot animal pic.

>>15001866
it can't be a simple gravitational attraction because the Casimir force scales as [math]r^{-4}[/math] and not [math]r^{-2}[/math] and more importantly, doesn't scale with the density or mass of the plates at all
the traditional derivation using vacuum fluctuations matches experiment really well, but there seems to be controversy about it for several reasons and some people have proposed a relativistic van der Waals-like origin
I only learned a simplified vacuum fluctuation derivation in an unrelated class (mesoscopic physics) and don't know field theory so I can't really evaluate the merits of the two approaches but the Wikipedia article in this case looks quite good and has links to relevant papers
there seem to be all kinds of subtle connections to speculative theories of gravity as well, which I'm not qualified to speak on

>>15003273
The position of the first body is the vector [math]r[/math], the position of the second body is [math]r'[/math].
Gravitational acceleration on the first body is [math]\ddot{r} = \dfrac{ Gm' }{ \| r' - r \|^3 } (r' - r)[/math]
Flip everything for the second body.
>>15003347
>but whenever I read textbooks it feels like debugging code where rather than doing a binary search with print() or single stepping, you have N steps and your next step is rand() mod N.
Extremely autistic analogy.

>>15003273
the accelerations vectors sum straightforwardly as vectors, that is elementwise
a vector is just an ordered list of numbers with one number for every dimension of the space
so for example (2, 1) + (3, -2) = (5, -2) in 2 dimensions
>their respective velocities would be incremented by a
this is wrong: you are saying that [math]v_{n+1} = v_n + a_n [/math], but in fact the relation is [math]\frac{dv}{dt} = a[/math], which is a differential equation that you must solve by "integration"
the easiest way to do this is "euler integration" where you specify a time step [math]h[/math], and then calculate [math]v_{n+1} = v_n + h\times a_n [/math]
however this approach is flawed no matter how small you take the time step because you will end up with energy leaking out of the system
you should look up a tutorial about verlet integration, it gives better numerical stability for this type of physical problems, you can learn about adaptive time step systems and so on, almost certainly someone has already implemented n-body gravitational system in c++ so you can compare

some fun brainlet-friendly guides:
https://explorabl.es/math/
https://gafferongames.com/post/integration_basics/
https://blog.bruce-hill.com/6-useful-snippets

>>15003273
oh I misunderstood your question
if it's about: how to get the x and y components of a?
you take the difference between the positions of the 2 bodies as a vector, so (x1 - x2, y1 - y2), normalize to unit length by dividing by the norm of this vector, then multiply by the magnitude of a

>>15003588
>this is wrong: you are saying that vn+1=vn+an, but in fact the relation is dvdt=a, which is a differential equation that you must solve by "integration"
>the easiest way to do this is "euler integration" where you specify a time step h, and then calculate vn+1=vn+h×a
I could be overestimating anon but that's literally what he's doing (with time step [math]1[/math]).

scientifically speaking, how smelly would vampire feet be after not being cleaned since the renaissance?

>>15003619
you are right
but of course depending on the scale of the other quantities time step 1 would fuck up the evolution, while a smaller time step would be okay
forgot to mention that the size of the time step matters

So most answers online mention gauss jordan elimination but we haven't been taught that in uni. Are there any other ways to check if a given system Ax = B has no/unique/infinitely many solutions?

>>15003703
Obviously a system is consistent iff the output matrix is the column space of the coefficient matrix.

>>15003712
Yeah I figured it out as soon as I posted it so deleted it. I was jus being dum-dum. Still thanks anon

>>15001144
>When the lid is closed n and V are constant but T is increasing
When T increases, n also increases because more water evaporates. 1°C is raises n_water by 7% (Clausius-Clapeyron) while the ideal gas pressure rises by somewhere between 1/300 and 1/400. Since n_water/n > 0.05 = 1/(300*7%), it's better to assume a constant density than to assume a constant amount of water vapor.

Is proofwiki working for you guys?
It's getting stuck while rendering the Latex on my browser, so I can scroll around but can't click the links.

>>15003818
Nvm it was ublock origin.

On Maple, you can compute the Period Matrix of a Riemann Surface using periodmatrix(f,x,y,opts), which for example they give:

https://www.maplesoft.com/support/help/maple/view.aspx?path=algcurves/periodmatrix
[math]\text{with}(algcurves):[/math]
[math]f := x^4 + y^3 + x^2[/math]
[math]\displaystyle \text{periodmatrix}(f,x,y,\text{Riemann}) = \begin{pmatrix}
1 + \frac{2i\sqrt{3}}{3} && -1 - \frac{- i\sqrt{3}}{3}\\
-1 - \frac{- i\sqrt{3}}{3} && 1 + \frac{2i\sqrt{3}}{3}
\end{pmatrix}[/math]

How do you arrive at the same matrix on Sage?

Let m,n>1m,n>1 be relatively prime.

Let phi: Z_mn -> Z_m ⊕ Z_n be:
phi(k mod mn) = (k mod m, k mod n)

prove phi is an isomorphism

>>15002616
In order to turn under any circumstances, you have to lean into the turn; otherwise you'll fall to the outside of the turn. This is something you do by habit. If you lean into an intended turn but don't actually turn because you lack traction, you'll fall over in the direction you're leaning.

>>15003941
https://en.wikipedia.org/wiki/Chinese_remainder_theorem#Proof

>>15003212
>>15003217
> So, if I wanna get started in robotics as an absolute beginner should I use Arduino?
If you wanna do any advanced robotic design, look into ARM based microcontrollers. Arduino is only good for small and/or hobbyist tier projects.

>I eventually want to become a robotics engineer in a major company
>I don't generally want to get involved in the hardware side.
Robotics is a very competitive field which involves multiple domains of engineering. People working on hardware usually had to go to a formal college and get a degree in mechanical or electrical engineering if you wanna work for a major robotics company.
I think you can self-learn the programming and AI stuff side to get a job, but don't quote me on that. Try contributing to open source robotics projects.

>>15003636
How fragrant is her hair, though?

>>15003976
how would this show the two groups are isomorphic exactly?

There's something I don't understand about blakc holes, I assume my mind has been poisoned by inaccurate popsci descriptions.
Their gravity is so strong that light can't escape, but that gravitational strength doesn't seem to come from their mass, but their density.
there are many stars more massive than blakc holes, and blakc holes have been theorized to be possible at tiny masses.
Why does densely packing mass make gravity so much stronger?

>>15004101
>Why does densely packing mass make gravity so much stronger?
remember that in Newtonian mechanics, gravitational pull is proportional to the mass and to the inverse of the distance squared
the gravitational pull of conventional objects like the Earth and the Sun is limited by the fact you can't get inside, so you will not have a gravitational pull stronger than if you are at the surface
but with the black hole this is different, namely because it's so tiny that it's possible to get extremely close to it without being actually inside it, and remember that halving the distance between you and an object multiplies the gravitational force by 4
of course this is a fairly simplistic answer, the reality is that black hole mechanics fall under general relativity so it can't be accurately described by Newtonian mechanics alone

>>15004110
Thanks, that at least makes intuitive sense, but like you said I feel there may be some spacetime fuckery going on.

>>15004101
It doesn't make gravity stronger, the black hole has the same mass as the star that died to become it.

What happens is that the black hole is smaller, so you can get closer to it, with newtonian mechanics you'd only have to solve the escape velocity for
c = sqrt(2*G*M/r) to find your point of no return.

Which for the mass of the earth means r = 0.009m, as you can tell, the earth is a lot bigger than that, so you can't get within 0.009m of the entire's earth mass, and it would require you to go under the surface, but if you go under the surface, you're now being pulled by the mass in other directions, which weakens the gravitational pull
So to be able to get within 0.009m of the entire mass of the earth, the earth would have to packed a lot smaller.

If for example the Sun was replaced by black hole with the same properties as the Sun, everything for us would behave the exact same way... except the Sun would be black and you wouldn't be able to see anything within 3km of the Sun's center, or escape if you went that close.

This is the only problem on my homework (we are using u substitution to evaluate) where the intergral has an a and b and what's with the (a>0). Not really sure what to with this

>>15004278
Just treat [math]a[/math] as a constant

>>14991217
https://www.youtube.com/watch?v=7XASTUMUaqA
9:15 What does he do there? Can you just set the imaginary part on the LHS equal to the imaginary part on the RHS, I'm confused?

>>15003987
i'm sure it's like roses

>>15004512
Yes you can. If you have two complex numbers
that are equal to each other, we must have the
real parts equal and the imaginary parts equal.

I'm confused about finding the points of intersection, in one example he factors out x^2-x
so
x(x-1) then sets bouth to zero to get 0 and 1
but in this different he just plugs 0 and 1 in make the equation equal

>>15005144
The same factoring can be done for that example too:

[math] x=x^4 \rightarrow x^4-x=0 \rightarrow x(x-1)(x^2+2x+1)=0 \rightarrow x=0, x=1 [/math]

The other factor yields a complex number and can't be used.

Next thread:

>>15004641