/sci/ - Science & Math

>>10033199
this follows from monotinicity, correct?

supposing the multiverse exists:
which aspects of our reality reflects its matrix?
Gravity and space expansion is a given- but is there anything else?

>>10033214
Yes, well. Think about it like this. The measure of any set can only be non-negative, by definition of a measure. So if the empty set has outer measure X, X≥0. At the same time, the outer measure is defined as an infimum of a set of non-negative numbers (the measure of the covers). Since you found a cover that has measure 0, it means that the infimum (a.k.a m*(O)) must be equal or smaller than 0, since 0 is an element of the set you are trying to obtain the infimum from. Thus, you have X = m*(O)≤0.
Then, if X ≥ 0 and X ≤ 0, it follows that X = 0.

>>10033203

Here where I live (Europe) the way math is taught in high school and school in general is through textbooks and teacher instruction combined with doing numerous problems from the so-called 'problem collections'. Do you have books like these in the Anglosphere? If so, is there a classic problem collection at a high school level that is recommended to any student seriously interested in learning math?

Context: complete brainlet fascinated with mathematics wanting to understand more of it despite liberal arts college education.

So, we just got back a mock exam for a class. The average was 18/50. (We would have received 10/50 if we left the exam blank. Some people basically got a negative score on the grade for just trying to answer questions).

This person left an open ended invite to form a study group. I've never been in one before. Are they effective? What even goes on in a study group? I feel like working alone would be a better use of time. At the same time I got 18/50 on the test so I figure it might be a good idea to change strategies. (I answered one question for +10 and left the 2 other questions blank for +5 and +3).

>>10033284
The effectiveness of them depends entirely on who's in the group.
Working together with others on stuff will always improve your understanding, even if you're the best in the class and just end up teaching everybody the material you will learn it better yourself.
The only risk is that "study" groups often have very little to do with studying, and in those cases it's better to do 4 hours of work by yourself than 15 minutes of work in a group.

>>10033276
Are you Slavic? The only country I know of that has a habit of publishing problem books separately is Russia, but maybe all eastern countries do it that way.
The norm for most western euro/north american countries is that the problem sets are just built into the textbooks in small chunks (i.e. at the end of a chapter there will be 10-20 problems related to the section).
Those kind of problem books exist, but they're almost all targeted at very advanced students preparing for math competitions. If that's what you're looking for the "classic" text among them is probably Paul Zeitz's Art and Craft of Problem Solving.

>>10033307

I'm actually Polish; to be honest I believe these problem books actually do the job. thanks anon.

>>10033296
this. Also try to limit how many people are in the study group. If it's more than 5 people, it's probably going to derail from productivity.

Is there a good youtube series of vids or sth similar that explains equations? In the context of y=x+1, where 1 is where the graph goes through the y plane, shit like that, but only more complex. Like y=(x+2)^3, what does the 2 represent graphically etc. I hope you understand

>>10033307
>>10033339

Publishing books with collection of some Math problems (most popular is stuff from middle school/high school) is a legacy of commnism in East Europe countries atlho I know a few people in Germany to whom translation of these books were recommeneded, to help them with graduation exams (Abitur) and in early Uni.

They do their job as a mean of practice but I'd recommend sites like Khanacademy if you are learning stuff for the first time.

How do I find all integers k such that
[math]5\equiv k \mod k^{2}[/math]

>>10033573
wouldn't the only k that works be k=5?

How do I study effectively without the aid of amphetamines?

I fucking hate studying and it bores me to tears, but I can't afford to make any more failing grades.

Can somebody post the math book flowchart with kuro. It said something about "starting with the math"

>>10033573
The equivalence can only hold if k=5 or k^2 <= 5. For k=1=>k^2=1, everything is equivalent to 0. For k=2=>k^2=4, 5≡1. So it only holds for k=1 and k=5.

I'm interested in Aerodynamics/Electric,Mechanical,Computer Engineering/Micro Biology but my family is knee deep in debt and i'll have to pay it off most likely and I won't be able to go to College for awhile if i work a retail job. I've just started looking into apprenticeships for CNC machinery since someone recommended me it and would anyone here have any recommendations on a job i should go for?
I have little to no experience with the topics I listed but I'm hoping to get my foot into the door somewhere to learn.

>>10033203
PLEASE HELP ME
How do I calculate the work made on a body by a force given by F(v) = -160(kg/s)*v ????????
This is on a parachute, the guy weights 80kg and the starting velocity is 50m/s
I thought something like pic related bu i am too retarded

>>10033603
nevermind I found it.

>>10033676
please i have a test tomorrow at 8 and it is already 10:21 in the night

"Let [math]G[/math] be an abelian group with [math]n[/math] elements, and [math]p[/math] an integer such that [math]n[/math] and [math]p[/math] are coprime. Proof that for every element [math]a \in G[/math] the equation [math]x^{p}=a[/math] has a solution in [math]G[/math]."

I already solved that problem showing that under those conditions, a homomorphism [math]f:G \longrightarrow G[/math] such that [math]f(x)=x^{p}[/math] has to be bijective, so of course every element [math]a \in G[/math] must have an element in the domain that gets mapped to it.

However, I found a much shorter proof, which basically just states that since [math]n,p[/math] are coprime, then (because of Bezout's identity) there exist integers [math]x,y[/math] such that [math]xn+yp=1[/math]. That means that [math]a^{1}=a^{xn+yp}=(a^{n})^{x}(a^{y})^{p}=(a^{y})^{p}[/math], and of course then the solution to our equation would be [math](a^{y})[/math]. Since [math]G[/math] is a group and [math]y[/math] is an integer, it's clear that [math](a^{y})[/math] is an element of the group. What irks me about this solution is that it's much shorter and also doesn't even need the fact that [math]G[/math] is abelian in the first place (as far as I can see at least), whereas it was necessary to have [math]G[/math] be abelian to proof that [math]f[/math] was a group homomorphism. Is this last proof correct at all? I feel like I'm missing something, it's weird that part of the hypothesis could be dropped and the result would still hold.

What the fuck is the Sum: S (dx/dy) dx
seriously what the fuck physics

Is this the right way to roughly calculate moles or is this completely wrong? 20L of HNO3 at 68% concentrate is 13.6L or 13.6kg divided by the mole weight of 63g gives me 216mol. Is that close? I know I have to take the density difference between it and the water to get an accurate result.

>>10033738
if water averages 1g/cm^3 and nitric acid is 1.51g/cm^3 and its 68% in 20 litres is that 13.6L so do I just times the litres by 1.51? Someone pls help.

how do i git gud at math?
I suck at calculus, algebra, trigo

What is the boiling point of testosterone?

>>10033840
>What is the boiling point of testosterone?
1488 K.

>>10033853
>1488 K
https://www.youtube.com/watch?v=tFAHOgCjbJY

>>10033853
1488

I see what you did there.

Did I do this right?

>>10033702
dx/dy you brainlet

anyone know where I can find the transition energy(from the ground state) and magnetic quadropole moment for all 2+ states of 44Ti?

What's the name/notation for the derivatives of a function f:R^n -> R where by derivatives I mean the vector [df/dx1,df/dx2,...df/dxn]?

>>10034008
If [math]f:X\subset\mathbb{R^{n}} \longrightarrow \mathbb{R}[/math], then the vector of partial derivatives [math][\frac{\partial f}{\partial x_{1}},\frac{\partial f}{\partial x_{2}},
...,\frac{\partial f}{\partial x_{n}}][/math] would be the Gradient of f at a point of [math]X[/math]. The notation is usually [math]\nabla f[/math] or [math]\nabla f(x_1,x_2,...,x_n)[/math], if it's at a particular point.

>>10033698
Anyone, please?

>>10034073
Thanks, for some reason I thought gradient was a scalar.

Those of you that work and study, how the fuck do you manage to have lives outside of this? I'm on fucking holidays and am still studying in most of my downtime so I don't get raped when classes start again.

>>10034193
They don't.

Just keep doing you, man.

what does it mean if I can answer elementary algebraic questions through intuition alone and no real thought put into them

assuming you have a proof that gcd(a,b)=p1^min(alpha1,beta1)...pk^min(alphak,betak) would you be able to solve the lcm somehow using the gcd-lcm relation

>>10034262
Yes, just observe that min(a, b) + max(a, b) = a + b

I'm trying to calculate nh for optimal allocation for a stratified sample. For the question, it lists to assume that the cost of sampling wihtin each stratum is the same. Would this make Ch and ch = 1?

>>10033203
I think every question on /sci/ is quite stupid

How do I evaluate this integral? I've tried substituting a number of things but can't get any to work.

>>10034917
Have you tried u substitution for what's in parentheses? You'd have to write sin from cos, but that's straight forward.

>>10034934
I'm left with this which doesn't seem a whole lot better.

>>10034956
You need cos^2 in your square root and you substituted cos

>>10034956
>>10034965
After fixing that, you'll have a quadratic in your square root. Then you can try an Euler substitution.
wikipedia.org/wiki/Euler_substitution

>>10034109
Gradient maps a scalar field to a vector field, i.e.
∇ : (R^n->R)->(R^n->R^n)
Divergence maps a vector field to a scalar field:
∇· : (R^n->R^n)->(R^n->R)
Curl maps a vector field to a vector field:
∇× : (R^3->R^3)->(R^3->R^3)

Is there any problem if I use pirated shit to do research and stuff? Uni doesn't provide the tools

>>10033203
Can the pressure coefficient for incompressible be written as the ratio of the static pressure (p) (where Cp is being measured) to the stagnation pressure (po)?

>>10033594
get your shit together.

Sleep early and wake up early. Read and do exercises during the day when your brain is active. Afternoon do work that doesn't require much brainpower. Work out.

Recognize that learning takes time and you have to respect that.

Any engineer wanna help me out with something?
I'm an EE undergrad student who wanted to do something with DSP, but I've heard entry level jobs are typically hard to get in, so I'm rethinking what I want to do. What are some jobs that are lax on entry level requirements?

>>10035253
no. you're only required to cite the work properly, not to own a legal copy of it.

>>10035284
what are you even asking? the definition is right there in the image you posted

>>10035295
Why doesn't it cancel out the freestream static pressure (Pinfinity) at the end?

>>10034917
What are n_t and k? Context of the problem may simplify or bring additional expressions for variables to simplify.

>>10035310

>>10033573
k^2 can only divide k-5 if k^2<=|k-5| so there are very little cases to check like >>10033636
did.

>>10033573
k^2 can only divide k-5 if k^2<=|k-5| or k-5=0 and then it's easy.

>>10033698
>>10034090
I feel like the second method is correct, at least it's the first thing that popped into my mind when I read the question. And if you only need G to be abelian to prove that it's a group homomorphism, there's no problem really. The fact that the equation always has a sloution just measn that if there is a group homomorphism f(x)=x^p that it is then surjective.

I get very sleepy when I'm reading textbooks. What should I do? I'm not a all nighter and I do have a good sleep.
Maybe it's the textbook, the text is so boring and long, I don't really like it.

>>10035369
consuming less penises may help

>>10035375
Shut up, I'm not a faggot

>>10033504
there's only 3 (or 5) things you can do for plane curves.

If y=f(x) is some function, then y=f(x-c) is the same function, shifted c to the right (ie, in the x-axis direction).

If y=f(x), then y=f(cx) is the same function but enlarged by a factor of c in the y direction.

I wrote 3 (or 5) because you can do the same for y instead of x, so you add two more.

The final one is a rotation of the graph. This one is a bit more complicated in terms of what you need to know, but basically, if you have a function y=f(x), you have a vector (x, y) for every point pertaining to the curve. If you use the rotation matrix on the vector, then you can rotate the graph.

So essentially, y=(x+2)^3 is just y=x^3 but shifted 2 to the left

>>10033698
i dont understand what your problem is

Burger here, I need help. I'm tired of being a brainlet. My public school experience was shit and I didn't learn much. Can I please get some book recommendations? Just basic math/science/general. I'm tired of being ignorant.

I'm trying to find a formula for a line that tracks this scatterplot. Fine-tuning the variables for the formula is not a problem, but I'm not even sure what kind of formula would give me the kind of line I want here. You can see that when X is < 1 it follows a somewhat different pattern than when it's > 1. Even below 1 you can see that it's somewhat different in the lower half compared to the upper half. It also starts to slope off somewhere at 1.8.

How did they compute the maps for continental drift?
Background: There is an online "world generator" software which is extremely skilled at generating supercontinents, and only supercontinents. The next step is obvious.

I'm a software engineer by trade, don't be afraid to spook me with concretely described algorithms

>>10035402
Community college helped me with this. Since it was fairly cheap, I was able to fail and retake classes at my leisure and eventually all of the bits and pieces of the sciences started to come together. I even got admitted into a professional program.

Drugs helped as well.

what am I doing wrong? I assume I'm supposed to turn the question into a probability mass function then do the mean and variance, but I can't seem to get the right answer. Here was my solution...

(a)
0 components | P = irrelevant
1 components | P = (0.96 + 0.89) / 2 = 0.925
2 components | P = 0.96 * 0.89 = 0.8544

mean = 1 * 0.925 + 2 * 0.8544 = 2.6338 (must be wrong, how can the mean be more than the total parts in the system?)

(b)
variance = 1^2 * 0.925 + 2^2 * 0.8544 - 2.6338^2 = -2.594 (obviously wrong, V(X) can't be negative)

>>10035742
what world generator?

It is my understanding that space is expanding (even speeding up), therefore galaxies within the space are likewise expanding (away from each other). If this is true, how is that the Milky Way and Andromeda are expected to collide in the distant future?

Please correct me wherever needed. I thank you all.

>>10033816
Do your homework.

Is there any board in 4chan or thread where I can ask a question related to philosophy?

>>10035802
previously this website but it looks broken now
https://donjon.bin.sh/code/world/
Well, it's GPL'd code so people should be able to run it on their local machine anyways.

>>10035819
while it is true that the distances between points in space are increasing, the rate at which they are increasing is proportional to the distance between them. Some stars and galaxies are moving away from us faster than the speed of light, but the planets for instance do not seem to be noticeably effected. Andromeda just happens to be close enough to us that the expansion of space will not prevent collision, but it will certainly delay it.

>>10035798
>1 components | P = (0.96 + 0.89) / 2 = 0.925
Think about what you are doing here. Does it make sense that, despite the approval rates being so high, it is so likely that only 1 component will meet specifications? That's over 90% chances that 1 component won't meet them. As a hint, whenever you pick a piece, in order for X=1, the only possibilities are:
-the piece you picked will meet the specifications and the other won't
-the piece you picked won't meet the specifications, so the next one has to

>>10035798
nvm, I'm dumb. it's 1 component meets spec, not 1 component in system. So X = 1 should be 0.96 * 0.11 + 0.89 * 0.04 = 0.1412

recomputing mean value yields 1.85, and recomputing variance is 0.136

Why is a moon base a stupid idea as of this decade?

How far are we from humans being able to power their bodies solely from the electrical grid? Like envisioning some kinda implant that filters your blood through and spends energy to activate all the little ATP particles or whatever, I don't know the specifics honestly that's why I'm asking here but I think it would be hella cool if I could just ram a USB cord up my ass and not have to worry about eating for a while yanno? So what you think, 10 years, 20 years, 100 years, what?

>>10036027
Oh yeah, and speaking solely of calorie needs, not stuff like other nutrients that would obviously still need to be replenished

Just wondering if Chemistry or Pharmacology gets mathematically harder than pic.

Volume concentration (from ideal gases mixture, Nm3 standard)
Is it the same as the mole fraction?

please explain la

>>10036077
Square both expressions.

>>10035850
>>>/his/

Whats a treat for a common house spider? I read they eat their webs to regain protein and that pollen gets stuck to it and its calorie dense. Can I sprinkle powdered sugar on there and make it a cotton candy web for them?

>>10036080
(x+1/x)=√40
x^2+2+1/(x^2)=40
x^2+1/(x^2)=38
(x^4+1)/x^2=38
x^4+1=38(x^2)'
(x^2)^2+(1)^2=(x√38)^2
x^2+1=x√38
x+1/x=√38

And that's about as far as I can go

>>10036120
Square BOTH expressions. Not just the first equation.

>>10036123
(x+1/x)^2=√40^2
x^2+2+1/x^2=40
x^2+1/x^2=38

(x-1/x)^2=x2-2+1/x^2
38-2=36

Thank you

>>10035855
Makes sense, thank you for taking the time to respond

>>10036128
you fucking idiot

>>10036088
give them common house insects they can produce the web from the nutrients attained therein. Don’t give wild animals random synthetic substances it can be hyperglycemic or worse poisonous to them.

>>10036193
Please explain, I legit thought I got the answer

How the fuck do turbines work in incompressible fluids? Let's say we have a round pipe with constant cross-sectional area, volume flow in must equal flow out because the fluid is incompressible. If we place a turbine in the middle of the pipe it extracts power from the flow by slowing down the liquid, so that the power is equal to change in flow KE before and after the turbine, but now the volume flows are different? I dont get it.

Why i am only good at mental math, ok at understanding math, but absolutely shit at explaining math and math theory? Btw I've never really done anything outside of math at high school level (I'm still preparing to chose major to sudy)

>>10035284
>>10035302

>>10036335
compare how often you do math by yourself and how often you explain it to someone. teaching is a skill that needs to be learned and practiced, and everybody sucks at first.

>>10036352
But I'm better at first thing (understanding by self) then the latter (explaining it to others)

>>10036352
>>10036354
Sorry, i read it wrong

>>10036352
I'm just a bit anxious that if i pick any major of connected to math I'll be only able to calculate and nothing else

Hey folks, I'm using R to do stratified sampling of that famous forest cover-type data. Anyways, I've come to a problem when calculating standard error. My fourth stratum is getting a 0 for all sorts of spruce /fir coverage. So, plugging that into a sqrt in a SE formula returns NaN. What should I do about this?

>>10036510
nvm, used different standard error formula.

I was supposed to send an email until 12 today. Now it's 15:11. Is there any way I can fake the time sent or something to pretend I sent it before 12h but due to the email service fucking up they have received it just now?

>>10033698
Hey you stupid fucking mathematician cunts would it fucking kill you to write out a goddamn sentence, with actual fucking words, once in a while explaining what the fuck it even is that you just fucking did or what the fuck I'm supposed to actually do with your stupid fucking abstract mathematical objects? I know you have some sick fetish/obsession with trying to explain everything with just numbers and symbols and using the least amount of words possible because you were probably such a fucking socially awkward weirdo your whole life that now you need to try and prove you're better than anyone at all making your fucking ideas unnecessarily obtuse and inaccessible to anyone but your snide little mathematician friends, but the only reason we keep you on the payroll is to come up with tools for us to use to solve real problems. Sure we let you dick around with your insanely nonsensical 97 dimensional semicuspidal manifolds or your hyperbolic triangles without embedded eigenvalues or whatever the fuck it is you assholes are doing all day. But that's just to keep you little shits busy so you don't bother the rest of us with your fucking bullshit periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves. Jesus Fucking Christ. All I'm asking for is ONE (maybe 2) sentences explaining what the fuck this shit even represents. You can blame it on me. Tell your math buddies I snuck it and wrote 'words' while you weren't looking. Just please, for the love of god, tell the rest of us what you are doing and what you want us to do.

Can someone help me understand what this is saying?
>Because fy is continuous over a small rectangle containing the point (0, 1), there is a unique solution around x = 0, namely y = (x + 1)3/2
where is this coming from? What am I missing? How do they establish whether f_y is continouous over (...) and what does that really mean?

Got bumped out of a university for financial reasons recently while working toward a second engineering BS (Industrial I have, was working on Mechanical). I very much enjoyed thermodynamics and want to continue self teaching down that track. Book related from thermo2 course I just left behind. What track of books/sources should I pursue if I considered the topics in the book easy to pick up?

>>10036671
It's Picard's Theorem. Your DE class should've covered this like Week 2. The rest is just leaving out the details of solving a separable DE.

>>10033203
What math fields are the best middle ground between interest in field and making a good wage? Can apply to CS too.

>>10036556
Maybe there's a time zone setting you can change to trick it into thinking you are hours behind.

Maybe it does this by ip address location so go via a proxy.

>>10036724
it probably doesn't.
also the receiving email server doesn't care when you sent it.
it'll record the date it received the email.
winding back the clock on your email server will just show the timestamp being earlier on your side and that's it.

Recommended textbook on differential equations for a brainlet engineering student? (So no fancy maths background, proofs, all that stuff, required)

Is this correct /sci/?

>>10036862
Consider the fact that for any finite a_n, a_n < |a_n|

>>10036885
Small edit because I couldn't be bothered to look up the TeX guide, I used the < symbol for "less than", but I mean "less than or equal to"

>>10036862
Second part yes. First part no. You are saying just because [math] \lim_{n \to \infty} a_n^8 = 0 [/math] that means that [math] \sum a_n^8 [/math] converges. That's not true, see harmonic series. What you actually care about is that eventually, [math] a_n^8 = |a_n^8| < |a_n| [/math] and the series converges absolutely by comparison.

>>10036862
>>10036890
Ok, I need to make a correction about my statement. The proof of the second part is correct, but what you conclude is wrong. It is not that [math] a_n [/math] must be absolute convergent for [math] a_n^8 [/math] to be absolutely convergent. (Consider the series of [math] \frac{1}{n^{\frac{1}{4}}} [/math].

It is just that conditional convergence of [math] a_n [/math] does not imply convergence of [math] a_n^8 [/math].

why is the glue in a glue stick so fucking weak and what's the alternative for gluing paper? like if you reuse postage stamps it always look shady because you have to put tape on the edges of the stamp because the glue stick sucks

and why doesn't the normal laundry program without "extra rinse" wash properly? we have a a fancy washing machine that is only a year old and the laundry comes out with a ridiculously strong fabric softener smell when you don't put the extra rinse option, and the extra quick program doesn't allow extra rinse so it's pretty much useless

>>10036722
If you're just going for an undergrad degree, focus on applied math and stats courses.

If you're going for a graduate degree, don't worry about it. No one hires PhD's for what they already know.

I'm trying to find the component of gravitational force directed towards the center of the sphere in this problem:
http://web.mit.edu/8.01t/www/materials/InClass/IC_Sol_W07D3-6.pdf

From my diagram, I'm getting mg/cos(theta), but the link above and a few others give it as mgcos(theta). I've been trying to understand where I went wrong for ages. Please help me not feel like a retard.

>>10037115
when you break a force vector down into components, neither of the component vectors should be larger in magnitude than the total force. The component vectors should be orthogonal to each other as well as the vector sum should be the original force vector. We can use a right triangle with the sine and cosine functions, but it is important to remember that the original force vector must always be the hypotenuse

>>10037186
Ah, thanks a lot. I hope something nice happens to you.

How much energy would it take for Mercury to become completely tidally locked to the sun?

>>10036057
bumping for my question.

>>10036057
>harder
>er
>implying scientific notation is hard
Just drop out.

Someone explain me once and for all why it makes sense current flows from + to - but electrons move from - to +. What is current but the flow of electrons.

>>10037288
Historical convention before subatomic particles were standardized "positive" and "negative" as they are today. Three options:
>Cope
>Convince everyone in the world to change it
>Give up
Lot of braniacs chose the first

>>10037288
the directional flow of energy is irrelevant as long as it's understood that energy flows down a gradient in potential energy (aka voltage)

I'm not exactly sure how they go from the right-hand side to the bottom here. I see that they're going from [math] \langle \alpha | a \prime \rangle[/math] to [math]\langle a\prime|\alpha\rangle[/math], but don't you generally need to take the conjugate when you go from bra to ket space? Is the conjugate here generally equal to the non-conjugate? [math]|\alpha\rangle[/math] is just some arbitrary ket here spanned by the eigenkets {[math]|a\prime\rangle[/math]}

>>10033203
Anon I could not help but notice your png was not optimized.
I have optimized your png.
your png is now optimized.

>>10037340
Without iCCP chunk.

>>10037288
current is the flow of charge, not electrons, while the movement of electrons is usually (but not always) what causes the flow of charge, it literally does not matter whether we consider it a positive flow of charge in one direction or a negative flow of charge in the other. The term used for the flow of electrons in a conductor is called "electron drift velocity" and it is generally extremely slow. In an ordinary circuit, when I close the switch charge will move from the positive terminal to the negative terminal almost instantly, while it may take multiple years for an electron to move from the negative terminal to the positive terminal.

The concept that "the standard convention of current is backwards" is a meme that needs to die

>>10037266
So I take it doesn't get any more "Difficult"?
I understand it but I've never taken chemistry or calculus, So I'm having to teach myself.

>>10037374
of course it will be more "difficult" than literally middle school math, but it is common practice for chemists to print out a graph cut it out and weigh it on a scale rather than taking the integral.

>>10037374
Scientific notation is very basic stuff, not just for chemistry but any field that uses numbers, so it's not a point of reference for any Chem topic. That being said, chemistry is not hard by any means unless you're an absolute brainlet.

Here's a dumb question.Is TeX somehow not working for anyone else? Everything is being left with math tags.

>>10037397
It's not working for me in Chrome but I checked it in IE and it works. Maybe some add-on is interfering.

>>10037399
>Chrome
Wearing the slave collar. Though Firefox is only slightly net better.

>>10037288
> why it makes sense current flows from + to - but electrons move from - to +.
Because electrons are negatively charged.
> What is current but the flow of electrons.
In a solid conductor, only electrons can move. In a gas or liquid, you have positive ions moving in the direction of current and negative ions and/or electrons moving in the opposite direction. In an ion beam, the current might consist solely of positive ions moving in the direction of current.

>>10037385
>>10037392
Thank you for the replies. Chemistry seems like there is just a lot of rules to learn but so far it's comes off as quite easy.
Hopefully I do well when I start study.

t. 125iq-ish brainlet

hi /sci/, I had some really bad health problems and stress that made me take a 2.5 month break from math because I couldn't focus for shit

I just started doing math again today, and it's just some remedial math shit (basic math by lang, books by sheldon axler and some other books written in my language), should I relearn everything? did it really matter that I took 2.5 months off from it? starting from scratch feels like a huge pain in the ass and I fucking hate precalculus, I just wanna be done with it and more to better stuff

I know how to solve the problems but it feels like I forgot some of the proofs for the babby-math "theorems"

What are some of the most abstract/general books on (real) Analysis?
Like developing Analysis just on sets with a topology instead of a metric/norm or even inner product.

>>10037437
>Like developing Analysis just on sets with a topology
There's a whole field of study for this. It's called "topology".

>>10037337
I guess what I might really be asking is if the eigenkets of some observable are orthonormal and their eigenvalues are real, does that necessarily mean that for some ket [math]| \alpha \rangle[/math] composed of {[math]| a \prime \rangle[\math]}, [math] \langle \alpha | a \prime \rangle = \langle a \prime | \alpha \rangle [\math] ?

>>10037446
fail

>>10037446
I guess what I might really be asking is if the eigenkets of some observable are orthonormal and their eigenvalues are real, does that necessarily mean that for some ket [math]| \alpha \rangle[/math] composed of {[math]| a \prime \rangle[/math]}, [math] \langle \alpha | a \prime \rangle = \langle a \prime | \alpha \rangle [/math] ?

Fixed I hope otherwise I'm drinking bleach

Can the Re() function not be applied to an infinite sum?
My complex analysis homework asked me this question: https://i.imgur.com/v4u8JjZ.png.. I started doing doing this: https://i.imgur.com/t0yyTk2.jpg, but got stuck on the new series I obtained. Also using a graphing software showed that it was clearly not the right answer anyway. I used an another method and got the problem right, but I'm still confused by the outcome of my first attempt. Re(z_0+z_1+...+z_n)=Re(z_0)+Re(z_1)+...+Re(z_n), right? Why shouldn't the same be true for an infinite sum? Or did I mess up somewhere else without realizing?

>>10037517
Never mind, I graphed it again and this time it was right. Must have messed up the first time.

>>10037454
Ok I think I got it, was just misunderstanding notation.

>>10037397
It's the ad blocker. (We should add this to the sticky or something.)

Anybody a mature student here? Is there a point to starting a degree at 25+?

>>10037597
>Is there a point to...
Nah bruhh.
t. Camus

>>10036075
help

>>10037597
plenty of people restart their careers in their 30s
if you're not going into software development in silicon valley it'll never come up as an issue for you.

How do I use latex? Gimme the 101
All i really want is fractions and exponents
also how do i post it? format wise

>>10037615
underrated post

>>10033203
>A diminishing sequence of fractions doesn't converge because we can map any such sequence to a divergent sequence.

Is this true? Is analysis a lie?

>>10037759
What does this even mean? If you don't have any restrictions for the function then you can map any sequence into whatever the hell you feel like and it will tell you absolutely nothing about the original sequence. Only sequentially continuous functions preserve convergence, so if your function isn't sequentially continuous then it doesn't matter what sequence it gets mapped to.

>>10037769
Forget mapping. The idea is simply that a sequence of fractions that is said to converge to zero never reaches zero. The difference never converges to a point, since infinity never happens. Therefore analysis is a lie. Calculus is a lie.

>>10033203
is wolfram alpha obvious to teachers? like are they going to notice if i get answers+steps to get to those answers from there? What is your experience with this anons? I am trying my best to work through problem sets honestly but occasionally i get stuck and my tutoring center is very difficult to get into and my teacher has limited office hours so its hard not to just look up the answers since i'll need to know for exams and group work in class.

>>10037805
It really depends how much you are copying.
If you copy the entire solution from there I can tell with basically 100% accuracy that you did that. If you copy most of the solution, I'd say 80% of the time it's obvious.
Copying 1 step will only stand out if you do it repeatedly and the rest of your solution is so shit that I can see the difference in quality of writing. And if it only happens once or twice per problem set I will assume you got stuck and needed a hint from somewhere, which is fine.
If you just copy the answer and write the solution yourself I cannot tell and I really don't care if you did this.

>>10037805
you should know what the answers mean and how to simplify the steps, wolfram alpha does it in a way that makes it easer for machines, not particularly elegant or legible.

How do I do #2 /sci/? I multiplied by the conjugate and I found that c is greater than that mess, but I'm not sure how to find what c is precisely equal to.

If i wanted to shoot a rocket and break orbit,would i need a permit or what paper work would i need to do so?

>>10037979
>I multiplied by the conjugate
That's literally all there is to it. After that just compare what you get to the second inequality and check which value would be the most convenient for c.

>>10037997
do it lol, it's not like they can stop you after the rocket is launched...

>>10037997
You would need A LOT of clearance from several authorities.
>>10038010
>what is shooting it down

>>10038010
Broke and i don't have that much knowledge about rockets yet.

>>10038017
>what is shooting it down
it's a fucking rocket, how the hell are they going to shoot it down?

>>10038000
So I get |a-5|\|sqrt(a) + sqrt(5)| < c. I'm not sure what to do with this? Sorry for brainlet

So if you traveling at the speed of light you can't see anything because you are going the same speed as light, and it cant catch up to you, but what if you going towards that light? wouldn't it makes you see the light even quicker, where is my thinking flawed?

>>10038032
If you multiply times the conjugate you get:
[math]|\sqrt{a}-\sqrt{5}||\sqrt{a}+\sqrt{5}|<c \varepsilon |\sqrt{a}+\sqrt{5}|[/math]
[math]|a-5|<c \varepsilon |\sqrt{a}+\sqrt{5}|[/math]
[math]|a-5|<(c|\sqrt{a}+\sqrt{5}|) \varepsilon [/math]
Notice that also, because of the second inequality, we know:
[math]|a-5|< 1 \varepsilon[/math]
I left that 1 there as a hint.
Once you notice what is the convenient value for [math]c[/math], proving that it fits perfectly into [math]0<c<1[/math] isn't all that hard.

>>10038049
Where you assume an object with mass can follow null geodesics.

>>10033203
This is not homework and it's not for a personal project either, I'm just curious what the best way to solve this programming problem is

Basically you have a graph that shows the latest 30 seconds of network activity. Suppose the graph only shows upload speeds. You want the graph to automatically zoom in and out based on the activity in the graph. So you need to keep track of the min and max and zoom based on those values. But how do you update the max and min quickly?

For updating the max and min I can think of a O(log n) solution that uses a maxheap and minheap. But is there a better solution (such as one that does it in constant time)?

>>10038017
Who would i have to contact?

Realistically, how far could someone pushing 40 with a 4thish grade level of math understanding (long division/fractions/times tables not memorized) improve by self study? would calculus be possible? beyond calculus?

>>10038123
>long division/fraction/times tables
that's just calculation.
math isn't about being able to do calculations fast, it's about being able to do calculations at all. And correctly. Every time.

you work your way up to basic algebra and geometry, you'll understand how variables work and the kinds of operations you can do to variables.

calculus, as taught in high school, is just advanced algebra with a few more rules and a handful of new concepts.

Really, everything up to calculus is just calculation. Anybody can do calculation. By definition, it's merely the application of well known rules. If you had a limit, it was because you'd suck at figuring out when to apply a rule out of the limited set of rules you have available to you.

>>10038119
The civil aviation authority in your country, for one. Probably the military too

PO4 is phosphate. Is PO3 phosphite?

>>10038123
You could easily go past calc through linear algebra and pick up the basics of set theory and analytic geometry anon. If you have the time and you're past chasing puss and getting wasted with friends then this is a good use of that.
>>10038132
>anybody can do calculation
no

>>10038284
Yes

https://pubchem.ncbi.nlm.nih.gov/compound/phosphite#section=Top

O3P(-3) = PO3(-3)

>>10038287
>>anybody can do calculation
>no

why not?

>>10033203
if our reality is a simulation and we make a simulation
what stop thy infinite simulation paradox?
can the simulation break from too mutch simulation?
are we just codes or have we a transended body(afterlife)?
can we reverse ingenierd the simulation?
can the simulation controle itself?

How do you report the uncertainty in the measurement of a number of counts over a single time interval?

The measurement is some total N counts after an interval of t. The actual rate is unknown but (what I am doing is plotting the PMT output for different voltages

I know that it needs to decrease with larger time, of course. However, what confuses me is that each sample is itself a single observation. What I mean is that if I use a 10s sample then that's still one measurement. I cannot treat the data the same way I would treat an average taken after repeated measurements of something. Otherwise, one could simply just divide the 10s interval into 10, 1s intervals and claim arbitrary certainty, because time is continuous.

Yes, for each data point I only measured the rate once over 10 seconds.

>>10033203
Is picrelated worth reading?

>>10037340
welcome back fren

>>10037437
well, anything on metrizable spaces surely, or topological vector spaces. Go munkres until you get out of babby level

>>10037753
entry level existentialism is overrated

>>10037713
[*math] [*/math] (without the *) and anything inside to make it tex-ed. Fractions are written \frac{a}{b} = [math]\frac ab[/math] and exponents e^{x} = [math]e^x[/math]

check the sticky for a short guide

>>10037791
convergence doesn't mean you reach 0, just that you're close enough to caress it

[math]e^{x hello}[/math]
thanks if this works!

>>10038688
in the reply window there's a button that says TEX, and if you click it you can have a preview

Is it possible for a Taylor series to have a finite value at (or infinitesimally close to) the convergence radius?

If yes can you give an example or papers/textbook about it? thanks

>>10038711
What do you mean? A Taylor series converges at any point inside the radius, diverges at any point outside, and at the radius it can be anything.

For example, the geometric series [math]\sum_{n=1}^\infty x^n[/math] famously has a radius of 1, but the formula associated to the series, [math]\frac{1}{1-x}[/math] has values at every value of x except x=1.

I cannot for the life of me find a counter example here. The question is to prove that bn has a convergent subsequence for any an, or find a counter example.

I know it diverges because if you try 0.1 as an, then it gets larger. I tried letting an = 1/n, but it doesn't show that it diverges. Can anyone help a brainlet here?

>>10038942
try the sequence [math]a_n=2-\frac 1n[/math]

>>10038949
what is your intuition for choosing that?

>>10038942
>>10038949
excuse me, i meant the sequence [math]a_n=\frac1n-2[/math]
>>10038952

>>10038952
factorise the polynomials nigga, especially the bottom one

>>10038955
the latex isn't working for me. Is that 1/n-2 ?

>>10038941
If you look at your example, the series diverges from the left, I'm wandering about a series that have a finite limit at the convergence radius.

Is there any organism that feeds on viruses?
Feeding as in using them as nutrients, not parasitizing them like virophagues do

>>10038963
yes, adblock blocks latex

Does sub additivity of Lebesgue outer measure fail for uncountable collections of sets? Say for instance, the Cantor set? The union of all C_{n} would be computing the outer measure of [0,1] but the sums of each measure tend to 0.

Can someone explain to me how come the higher the OH- in a solution, the higher the pH? Isn't pH (power of hydrogen) a measuring system for ACIDITY?

>>10039135
subadditivity just means there's an inequality, it doesn't imply equality.

>>10039143
pH is defined as the negative logarithm of the concentration of hydronium ions in the solution. So the more hydronium ions there are, the lower the pH, and the more acid it becomes. The pH measure just goes "backwards", lower pH means a more acidic substance. So of course if the OH- concentration is higher (so lower concentration of hydronium ions), then the pH is higher and thus the substance is more basic.

>>10039181
But with Cantor's set wouldn't the following be true: [math]\mu^{*}\left(\bigcup_{n=0}^{\infty}C_{n}\right) = 1 \nleq \sum_{n=1}^{\infty}\mu^{*}(C_{n}) = 0 [/math]?

I want to start at 20 and keep adding 20 to it 31 times (so 20, 40, 60...620)
I came up with:
>(20+(31*20))/2*31
Is there a better way to simplify this? It's been forever since I was in an actual math class

>>10039217
Why the hell are you dividing by 2 and multiplying by 31? That is not right.
Just do 20 + 31*20, or what is the same: 21*32 lol

>>10039217
>>10039294
20*32
sorry

>>10039216
>[math]\mu^{*}(\bigcup^{\infty}_{n=1}C_{n})=1\nleq \sum^{\infty}_{n=0} \mu^{*}(C_{n})=0[/math]

Keep in mind that, by definition, the Cantor set is given by:
[math]{\cal{C}} := \bigcap^{\infty}_{n=1} {C_{n}}[/math]. If you are talking about the sequence that generates the Cantor set, then it has an (infinitely) countable amount of elements (sets).

If you find the union of the elements in the sequence for the Cantor set, all you'll get is
[math]\bigcup^{\infty}_{n=1}C_{n}=C_{1}=[0,1][/math]
That is, of course, because on that sequence you have that [math]C_{1} \supset C_{2} \supset ... \supset C_{n} \supset ...[/math], so the union will just be the set that contains them all. And if you compare it to [math]\sum^{\infty}_{n=0} \mu^{*}(C_{n})[/math], the measure of [math]\mu^{*}(C_{1})[/math] alone is already equal to 1, so the infinite sum will be bigger than that.

>the sums of each measure tend to 0
I don't know if I'm understanding the question correctly, but I think you are confusing the sequence of measures with the series' sum. Even if the sequence converges to 0 (which it definitely does), the series' sum will still be bigger than 1 just because of that first element.

>>10039294
>>10039296
(20+(31*20))/2*31 = 9920
20*32 = 640

>>10039334
And 640 is the correct answer. What is your point?

>>10039346
640 is neither the last item in the series (620 is) nor is it a simplification of the formula I posted: (20+(31*20))/2*31

>>10039351
You said you wanted to start with the number 20, and add 20, 31 times.
620 is the answer for 20 + 20*30. 30 times.
And your formula is nonsense and has nothing to do with what you propose. And it's not even a formula. It's an expression.
You have nothing better to do than to troll here?

>>10038496
only if you want to learn about discrete mathematics and its applications

>>10039359
Yes, add it and then get the sum of all numbers in the sequence. I thought it was pretty clear from the context, especially given that I provided the working formula I actually wanted to simplify.

I highlighted the number I want in case you are still confused.

>>10033698
>doesn't even need the fact that [math]G[/math] is abelian
Yes it does. a^{ab} = a^{ba} only when G is Abelian.

Can someone explain what exactly they're doing here from 1.3.17 to 1.3.19. I get that they're expressing the middle part as a matrix, but what happens to the a'' ket on the left and a' bra on the right?

>>10039386
If X can be represented as a matrix and <a|X|a'> is a number then you can represent the bra and ket as a row and a column vectors respectively

>>10039383
The property only states that if [math]a,b \in G[/math], then [math]\forall n \in \mathbb{Z}, (ab)^{n} = a^{n}b^{n} \Leftrightarrow G[/math] is abelian.
[math]a^{mn} = a^{nm}[/math] under any circumstance just because [math]n,m[/math] are integers and the integers are commutative under integer multiplication.

>>10039391
Oh ok, I get that the outer product is a matrix and the inner product is a number, I guess what I wasn't sure on is what form the matrix of the outer product takes.
So like here the left a'' ket and right a' bra just form the "skeleton" of the matrix, so to speak? They don't input any information into it themselves, but just provide the form for <a|X|a'> to be expressed across the base kets?

>>10039373
You could have say that from the beggining instead of fucking around. You wanted the sum, o.k.
Your expression is fine, but I prefer that formula in this slightly simplified and formatted form:
[math]\frac{1}{2}x n(n+1)[/math]

where x is your starting number/added amount, and n is the number of times.

>>10039410
They form a possible base in which you can span your wave-function. The bra and ket are elements in the corresponding Hilbert space.

>>10033682
Can a math oriented person please explain why this flowchart culminates in single variable Calculus when the 4th book in the series (Foundations of Analysis) assumes you've taken 3 semesters of calculus already? I assumed the Calc book would be real analysis but it doesn't look like it.

>>10039544
Nevermind, wrong author

prove that

[math]f(\overline{x}) < \overline{f(x)}[/math]

given f is convex

I don't even know how to begin. I've written it out using the definition of arithmetic mean but I can't move further. Any hints?

Did you guys find intro to differential equations hard? I hate calculus and took a 2 year break between taking calc 3 and this class (my final calc based classed before graduating).

Would the class have been easier if I didn't delay it? Like, it seems like it's basically just an overlay on applying calculus so far.

>>10038691
>thanks if
thanks

>>10039554
Does [math]\overline{x}[/math] stand for the arithmetic mean of n values of x in your notation? If so then for an intuition on what's happening, notice that if you have a convex function [math]f:X \subset \mathbb{R} \longrightarrow \mathbb{R}[/math] (say, [math]f(x)=x^{2}[/math]) and pick 2 points [math]a,b \in X[/math], you can draw a line connecting the points [math](a,f(a))[/math] and [math](b,f(b))[/math]. Since the function is convex, the graph of the function [math]f[/math] will always be below the line you drew joining both points, [math]\forall x \in [a,b][/math]. This is a direct consequence of the definition of convexity of a function on an interval (which you should probably proof).

Now, if [math]f[/math] is convex in [math][a,b][/math], then you can evaluate [math]x=\frac{a+b}{2}[/math]. How is [math]f(\frac{a+b}{2})[/math], in comparison to the line that connects both points? What is the relation between the line and the arithmetic mean of [math]f(a)[/math] and [math]f(b)[/math]? You can then generalize if you need to, but the results all follow from the same ideas.

Depending on what definition you are using for a convex function, the result for any 2 points might be proven by simply substituting a single value, but since I don't know which definition you use I'm just guessing.

>>10039326
Oh yeah, I fucked that up proper. Does such a counter example exist for uncountable collections?

brainlet here, why is n (-n) -n^2? why don't they cancel out

>>10039709
n*(-1*n)=-1*(n*n)=-n^2

>>10039709
[math]n^{1} \cdot ( -1\cdot n^{1}) = -1\cdot (n^{1}\cdot n^{1}) = -1 \cdot (n^{1+1}) = -1\cdot n^{2} = -n^{2} [/math]

>>10039722
i see, thank you

>>10039668
Such a thing as "uncountably additive" is very hard to define in a way that makes sense for the purposes we need on a measure function. It can be proven that if you have an uncountably infinite amount of non-negative numbers [math]x_{k} \in \mathbb{R}[/math], [math]\forall k \in K[/math] where [math]K \subset \mathbb{R}[/math], and you also ask that [math]\sum_{k \in K}{x_{k}} < \infty[/math], then [math]x_{k}=0[/math] for all but a countably infinite amount of values of [math]x_{k}[/math]. If you have an uncountably infinite collection of sets, and each of them has a measure [math]x_{k}[/math], you can see that defining an uncountable additivity brings us nothing we can use practically.

The idea of a measure is to assign a non-negative number to a set that can be evaluated and compared with respect to other sets, which is what lets us define the Lebesgue integral and other stuff, so having it be uncountably additive is not really something that helps a lot. If you want a sort of counter example, see that we can pick the open interval [math](0,1)[/math] and have the collection of singletons [math]x_{n}=n[/math], where [math]n \in (0,1)[/math]. Clearly, [math]\bigcup_{n \in (0,1)}{x_{n}} = (0,1)[/math], since by definition our uncountable collection is made up of every single point that is contained in the interval [math](0,1)[/math]. However, all singletons have Lebesgue outer measure 0. So:
[math]\mu^{*}(\bigcup_{n \in (0,1)}{x_{n}}=(0,1))=1 \nleq \sum_{n \in (0,1)} \mu^{*}(x_{n})=0[/math].

I understand the definition of [math]\frac{\partial}{\partial x^j}[/math] as a derivation at a point in a manifold. How can I get the equivalent definition of it as an equivalence class of curves? I suppose my question is how exactly is a local basis defined if you identify the tangent space as equivalence classes of curves?

>>10039808
Your insights are very helpful to me. That counterexample is great too, many thanks.

Hey guys, any analysts (or people who are good at real analysis) here? I need to prove the following function is differentiable at 0 and find f'(0).

[math]f(x)=|x|^{\alpha}|ln(|x|)|^{\beta}[/math], for [math]x\neq{0}[/math], [math]f(0)=0[/math], where [math]\alpha>1, \beta\geq{0}[/math]

I feel pretty defeated by this problem and I'm pretty frustrated by it. Any hints would be great. I have a feeling that f'(0) = 0, but I have NO idea how to bound the natural log part, given a epsilon and delta defining an open ball about 0.

Can I use the fact that [math]\mathbb{R}[/math] is open to prove [math]\mathbb{Q}^{c}[/math] is Lebesgue measurable? Certainty, [math]\mathbb{Q}^{c}\subseteq \mathbb{R}[/math]. Let [math]\epsilon>0[/math], then, [math]m^{*}(\mathbb{R}\setminus \mathbb{Q}^{c}) = m^{*}(\mathbb{Q}) = 0 < \epsilon [/math].

did the big bang explode into all this space or did the space run ahead of the meat of it our of the explody

>>10033203
context: algebra 1, exponents, infinite geometric sequence problem.

"Find the total distance that a super ball travels if it always bounces back 75
percent of the distance it fell. You dropped it from a window that’s 40 feet
above a nice, smooth sidewalk. Assume that the ball always falls straight down
and returns straight up."
i get the basic idea of adding two distances with infinity steps by a+a(r) where "a" represent a given distance and "r" represent the ratio.

got lost here, can't understand the thought process behind it:
The sum of the terms of an infinite geometric sequence where the ratio, r, is a
number between 0 and 1, is found by dividing the first term of the sequence, a,
by the difference between 1 and r:
sum = a/1-r

also, pic related, totally fucking lost:
sum = a(1-r^n)/1-r

please anon, show me the light, don't spare any theorems rules and details/steps.

Kind of a long shot, but is there a book like Sedra/Smith that just covers Parts I and IV from it?

>>10039939
Why don't you take the limit from the right and left and see if they are the same.

>>10038336
bump

>>10039831
the wikipedia article is good https://en.wikipedia.org/wiki/Tangent_space

>>10039963
it is almost by definition that a set being lebesgue measurable implies its complement is (the definition is completely symmetric). Since Q is measurable as it has measure 0, then clearly Q^c is too.

I’m taking pew calculus in community college after almost 10 years out of school and the highest math I took in ha was geometry, how do you solve this problem? I just don’t understand how to solve equations with two variable expononents

>>10040013
Which definition is this?

>>10040028
A set E is Lebesgue measurable if for any set A, [math]m^*(A)=m^*(E\cap A)+m^*(E^c\cap A)[/math] where [math]m^*[/math] is the outer measure

>>10040027
[math]e^{x+5} = 7.2^{x} \implies \ln(e^{x+5}) = \ln(7.2^{x}) \implies x+5 = x\ln(7.2) \implies x = \frac{5}{\ln(7.2)-1} [/math]
Basically, take the natural log of both sides and apply your logarithm rules.

>>10040033
Hm, I haven't seen this before. I'll keep note of it then.

>>10040038
??? what other definition of lebesgue measurable is there?

>>10039969
>don't spare any theorems rules and details/steps.

maybe i exaggerated.
just tell me what topics i have to look into because this book i'm reading using proofs such as "trust me on this one", like holy shit if you're not going to explain something don't bring it up, stressing me out with this shit.

>>10040038
The definition I have in my notes is: [math]A \subseteq \mathbb{R}[/math] is Lebesgue measurable if for all [math]\epsilon>0[/math] there exists an open set, [math]G[/math], such that [math]A\subseteq G[/math] and [math]m^{*}(G\setminus A) < \epsilon [/math]. This is how I was introduced to Lebesgue measure.

>>10040042
meant for >>10040039

>>10040036
Thank you. But what happens to the second x? Where does it go to? That’s what is confusing me because up to this point I would divide by x and it would equal 1 so the equation wouldn’t work

>>10040055
[math]x+5 = x\ln(7.2) \implies 5 = x\ln(7.2) - x \implies 5 = x(\ln(7.2) -1) [/math].
Then just isolate [math]x[/math]

>>10040042
Keep in mind that if [math]A \subset \mathbb{R}[/math] (in your case [math]A = \mathbb{Q}[/math]) is Lebesgue measurable, it is contained in the Lebesgue [math]\sigma -[/math]algebra and by definition of a [math]\sigma -[/math]algebra, if a set is in it, then it's complement must also be it. Then, [math]\mathbb{Q^{c}}[/math] is also contained in the Lebesgue [math]\sigma -[/math]algebra, and is therefore Lebesgue measurable.

What is the difference between vector field and phase portraits? They look exactly the same to me.

>>10040061
Like in X+5 = x ln(7.2), how does the x i capitalized turn into one? I have two exponents in this equation, how do i get one in the end without getting rid of both, that's what is confusing me. Thank you again.

>>10040080
Are you telling me the original problem is [math]e^{X+5} = 7.2^{x}[/math]? If so, the way you have it wrote in your picture is extremely misleading.

If they are different, say [math]e^{a+5} = 7.2^{b}[/math], we could define one in terms of the other [math]a+5 = b\ln(7.2) \implies a = b\ln(7.2)-5[/math], but not much else can be done.

>>10040089
No i just capitalized it when i wrote kind of like to highlight it because it was the x that you subtracted in your response and then turned into a -1, and that is what i don't get how i have two x at the start but end up with one .

>>10040073
A vector field is just a function that maps vector to points in space/the plane/[math]\mathbb{R}[/math]. A phase portrait is a tool supposed to describe dynamical systems. Usually with vector fields, sure, but they usually also need curves, depending on what system they try to describe. Basically you can use vector fields to partially describe phase portraits, but the latter are mostly just a particular application, and use a bunch of other tools as well.

>>10040111
Also meant to post 'maps vector to points in space/the plane/[math]\mathbb{R^{n}}[/math]', as a more general statement.

>>10040110
is there an original question this comes from? what are you actually supposed to be doing with this? Better yet, take a picture of the original question.

>>10040120
Yeah here it is

>>10040129
Gonna be honest with you, your penmanship is utter shite.
Also, the problem is in ONE variable, not two.
Therefore
[math]e^{x+5} = 7\cdot 2^{x} \implies x+5 = \ln(7\cdot 2^{x}) \implies x+5 = \ln(7) + x\ln(2)[/math]. You can take it from here now, yes?

>>10039971
Thanks senpai

>>10040140
Sorry but this is where i'm having trouble. What rule or what do i do to get the xln(2) to suddely have a 1 in front of them. In other words i don't really get how there are two x at the start but at the end you end up with one x that equals the rest of the numbers. How do i have the x in front of xln(2) become 1? Thank you again for your help

>>10040158
You factor out the [math]x[/math] from [math]x[/math] and [math]x\ln(2)[/math].
[math]x-x\ln(2) = x\cdot (1-\ln(2))[/math].

>>10040174
I see, thank you a lot for your kindness.

>>10040185
No problem. You really should practice these things a lot more. The process of solving for/isolating a variable is extremely important. You can't learn higher maths if your foundation is going to be crumbling apart all the time.

How do I show that this:
>For all [math]\epsilon >0 [/math] there exists a finite union of open intervals, [math]U[/math] so that [math]m^{*}(U\Delta A) < \epsilon [/math]
Implies this:
>[math]A[/math] is measurable.
I know that [math]U[/math] defines an open set, but I need it to cover [math]A[/math] somehow to fit the definition as laid out here >>10040042

Why is styrofoam so staticy? Why does it stick to everything when it breaks into smaller componenets?

>>10040292
[math]m^{*}(U \Delta A) = m^{*}((U\setminus A) \bigcup (A\setminus U)) [/math] has zero measure.
But
[math](U\setminus A)\subset ((U\setminus A) \bigcup (A\setminus U))[/math] and [math](A\setminus U)\subset ((U\setminus A) \bigcup (A\setminus U))[/math]
Therefore
[math]m^{*}(U \setminus A)[/math] and [math]m^{*}(A \setminus U)[/math] both have zero measure (and are therefore measurable).
The gist of the proof (at least the simplest one I can think of) is just proving that A can be given as the result of operations between measurable sets (difference, intersections, unions, etc). So far you know that [math]U[/math] is measurable (because it is the finite union of open intervals), as well as [math](U\setminus A)[/math] and [math](A\setminus U)[/math]. As a hint, remember that for any 2 sets [math]X,Y[/math], you have [math]X \bigcap Y = X \setminus (X \setminus Y)[/math].

>>10033203
I'm presenting two number series in libre calc and wish to have a chart showing the mean and standard deviation of each series.

What's the chart type that does this?

So why do people on here care about going to other planets as much as they do currently?

The Universe as a whole isn't made for us to explore it. The distances between stars let alone galaxy are nigh infinite compared to us

The planets and stars around us withing 50 light years are mostly all exist in conditions where humans can't survive or all dead like pluto

it just feel arrogant honestly.

>>10039969
Consider the sum of the first n terms:
S(n) = a+a*r+a*r^2+...+a*r^(n-2)+a*r^(n-1)
Multiplying by r "shifts" the sequence one place to the left:
r*S(n) = a*r+a*r^2+a*r^3+...+a*r^(n-1)+a*r^n
= S(n)-a+a*r^n
=> r*S(n) - S(n) = a*r^n-a
=> (r-1)*S(n) = a*(r^n-1)
=> S(n) = a*(r^n-1)/(r-1) = a*(1-r^n)/(1-r)
If r<1, then as n->∞, r^n->0 => 1-r^n->1 => S(n)->a/(1-r)

Or more directly:
S = a+a*r+a*r^2+...
r*S = a*r+a*r^2+a*r^3+...
= S-a
=> (r-1)*S = -a
=> S = a/(1-r)

>>10040395
nvm, figured it out.

Does substances become slower to react the colder it gets because of the Electron's taking more to connect 'to the opposite charge'?

Sorry just starting to learn chemistry.

>>10040637
"Taking more time to connect"*

>>10040637
Cold means lower kinetic energy, meaning fewer atoms/molecules interact with each other per unit time. In case of self sustaining exothermic reactions, if the threshold energy isn't reached, the reaction will die out.

>>10040637
>taking more to connect
https://www.youtube.com/watch?v=ckc6XSSh52w

i've been going through these algebraic proofs in my textbook, but i can never seem to come up with the solutions myself, i always resort to looking it up, and there is some method which i understand, but i could never have come up with myself. is there a way to resolve this or am i doomed to looking up proofs forever?

>>10033203
Ethene, C2H4(g), reacts with aqueous potassium permanganate solution, KMnO4(aq), dilute acid, H2O/H+, and hydrogen bromide, HBr. Compare and contrast the reactions of ethene gas with each of these three reagents.

What kind of question is this called, when it asks for reagents? Does anyone know any videos on it? (I checked Khan Academy and such)

>>10039966
The big bang describes the early expansion of the universe, and thus space.

>>10040411
The alternative is extinction. No one who's serious about the prospect believes it is something that'll happen in their lifetimes, but the sooner one makes steps towards it, the less likely humanity, along with the history of the struggles of all life on Earth, will be wiped out and made all for naught by a wandering cosmic golf ball, or any of the other 50,000 events that can kill all the eggs while they are all in one basket (many with no warning).

There's also the fundamental issue of freedom to consider. There's no longer a frontier on Earth where one can establish a sizable society, truly independent from the existing ones, so the only hope to continue a true democracy of social ideals requires distant colonies. The risk is, meanwhile, global culture will continue to homogenize until nearly all humans have the same point of view, and become increasingly unable to see outside of that box.

Granted, sometime between now and then, there'll likely be fundamental changes to human nature, both psychological and physiological, which will hopefully make the effort more feasible in the far off and distant future.

Otherwise, we will eventually collectively fail in the one clear imperative nature has given us: survival.

>>10040039
outer measure = inner measure

>>10040952
>No one who's serious about the prospect believes it is something that'll happen in their lifetimes

Except Muskrat and the idiots who follow him.

>>10040671
give some example of what you couldn't do

>>10033203
I've read and done this example a million times and I still have no fucking clue why this is so in GAP. Please help

is the inf of this set -sin1 and the sup sin2/2 ?

New ML research engineer job lads. One week (and a day) in already. Feel like I want to kill myself. I'm shy and awkward around my teammates, there's lots of reading and, well, researching going on and I just want to program. I feel like a brainlet reading papers, every single time my eyes drop and I feel like falling asleep. I've told 2 friends I got hired and they've ran their mouth to literally everyone about my new job and whatnot, I feel like the only way I'm getting out of this now is by suicide or skipping town.
What would you do? I wouldn't feel bad about it if the pay wouldn't be so good, it just feels like stealing and I fear being fired.

Should I change my major from comp sci to comp engineering if I am bad at coding?

what the fuck is spirituality and/or 'faith' and why does every normie think it's important?

>>10042304
what does "bad at coding" mean?
computer engineering is all the same shit except you don't get abstractions to hold your hand for you.

>>10042343
I can't do any of this Java stuff for shit no matter how much I try or even see my professor or get tutors, even when I took AP CS in high school I didnt get this shit and I am slow as fuck and don't understand it

>>10042349
all I'm hearing is bitching and moaning, what don't you understand?

If you can't coherently express your concerns in words, how do you expect to be able to solve any kind of problem at all?
At least if you could do that, you could ask questions that lead to useful answers, whether you ask it to Google or a professor or even on here.

what's the difference between see and see plus plus

>>10042356
I don't understand anything. What the hell a constructor does or is or why it is used where it is, methods, variables, fields, everything

>>10042358
well with see plus plus, you can see a little better, incrementally so.
but you would probably save time with just see sharp

>>10042358
C is older and procedural oriented, while C++ is the "new and improved" object oriented version.

>>10042366
D-

>>10042364
Your problem is that you are trying to boil the ocean when everyone around you just wants you to take a sip. You want to learn physics while everyone else is learning how to play dodgeball.
Just accept that "these are the rules of the jungle," and don't think about it too hard.

I could teach you from the perspective of programming language theory and implementation, or from CPU pipelines and opcodes, or even logic gates, but most people would explode from impatience so we don't do that.

Teaching a kid computer programming or computer science is a difficult thing to do because no one really knows where to start, and a lot of money is involved.

I'm going to suggest you start with pleb shit like MIT Scratch. You're going to feel like a middle schooler, and that's because that's the target audience, but you need it and you also need to chill the fuck out.
https://scratch.mit.edu/tips

>>10042380
I may just change my major then

>>10042386
>being unable to do the same thing that middle school kids can do
Anyways, changing to Computer Engineering won't help you at all. Many universities still teach the same Java and C++ shit in either major, and the concepts carry over (surprise, the same programming language theory is used to build every language)

Better do something you're more suited to, like basket weaving.

>>10042393
My school doesnt even have computer engineering

>>10042393
Also I been doing Scratch for like 6 years, why the fuck would I want to redo it? I've done countless projects on there over the years

>>10042424
if you've been doing Scratch for 6 years then why do you claim you don't understand variables?
You understand ~something~, but you evidently have garbage self esteem, making yourself a terrible judge of your own knowledge, and so you form terrible garbage questions like this >>10042364, which only tell me that you're having a panic attack, instead of exactly what you have an issue with.

Here's an example of a well formed question, just in case K-12 schooling failed you:
"I was told that a variable can be used to substitute a literal value in an operation, and can be anything I want, but why do I have to define it as "integer" or "Boolean"?

Just ask your questions.
Here.
On /g/.
To Google.

Anywhere.
Just don't have a panic attack because that helps no one but your psychiatrist.

If you want more self-guided learning geared towards grown ass adults, try this instead.
http://interactivepython.org/courselib/static/thinkcspy/index.html

You can literally run the code on your browser. You may or may not want to skip the videos.

I'm trying to synthesize WS3 to do things with later, but all I have is Na2WO4(H2O)2 for a tungsten source and then thioacetamide (C2H5NS) and Na2S for a sulfur source. I have access to any acid or base that would be necessary. Right now I'm trying to take the sodium tungstate and add 3M HCl to make it WO3 and then remove that and add Na2S and mix to substitute the sulfurs, however I'm getting some blue crystals that are also forming so I'm trying to figure out if there's a better way to do it or if I just need to make sure it is completely dry before adding Na2S?
other chemfags help would be appreciated.

>>10041943
yeah

new thread
>>10042531

>>10042531

>>10041671
well this is what i'm stuck on at the moment:
prove that [math]\frac{a}{b^2} + \frac{b}{a^2} \geq \frac{1}{a} + \frac {1}{b}[/math] for any a,b

>>10042847
a^3 + b^3 >= ab^2 + ba^2
draw a thing with cubes
i don't know

>>10042847
notice your expression is equivalent to saying

(a-b)/b^2 + (b-a)/a^2 >= 0

ie

(a-b)(1/b - 1/a)(1/b + 1/a) >= 0

Now it's just a matter of checking the million cases:

a>b>0
b>a>0
a>0>b
b>0>a

Or perhaps you can be a bit smarter, and only check when each parenthesis is bigger than 0 and what it implies..

>>10042847
>>10042847
notice your expression is equivalent to saying

(a-b)/b^2 + (b-a)/a^2 >= 0

ie

(a-b)(1/b - 1/a)(1/b + 1/a) >= 0

Now it's just a matter of checking the million cases:

a>b>0
b>a>0
a>0>b
b>0>a

Or perhaps you can be a bit smarter, and only check when each parenthesis is bigger than 0 and what it implies..

I have trouble visualizing the application of derivatives to physics problems.

Say we have the ecuation of the graph of a line, wich represents the movement of a particle:
X=t^3-6t^2-15t+40
And until this point, i understand the derivative is the 'slope of tangent of the curve', in this case, the slope of our main line.

So, we derivate (dx/dt), and we get the slope, the 'velocity';
v=3t^2-12t-15
And we derivate a second time (dx/dt) to get the acceleration.
a=6t-12

I don't quite get the process behind derivatives. If i derivate a first time i get the slope of my line, wich equals to the velocity (D/t), but why if i derivate a second time i get acceleration (d/t)?

>>10043748
A stupid question indeed, the equation represents the movement of a particle moving in a straight line.