QTDDTOT—Questions that don't deserve their own thread

i have no idea about chemistry, but i summed the amounts of letters in your picture and googled it
https://en.wikipedia.org/wiki/Capsaicin

>>8161859
basically it says "hot." don't wear it around your in-laws.

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I couldn't get into Spivak Calculus, and Apostol's introduction to proving Archimedes just left me confused and I have no idea of what these guys are doing.

So I am obviously too dumb for these two. Is there some other book that kind of gives me the type of thinking required for this type of math? Induction, proving, etc.

How much do you study each week?

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Whats the extent of things I can do with designer babies ?
Can I have my baby with 4 arms ? Can I have it fused with squid DNA ? Can I have my babies eye color red ? Can I have my baby to have a square shaped skull ? Can I have these things ?

>>8161878

I dedicate an hour a day to math, but I could dedicate some more time.

Problem is, with the trouble I am having to understand these guys, I just feel that my approach is not the correct one, and I am going nowhere.

>>8161867
Keep at it. You'll get it.
Other books:
Abbott - Understanding Analysis
Bartle - The Elements of Real Analysis
Carothers - Real Analysis
Krantz - Real Analysis and Foundations
Landau - Foundations of Analysis
The last book, Landau, really helped me get use to proofs. It basically constructs the real and complex numbers from the Peano axioms of Natural numbers.
Doing every little proof gets you use to it.
I also did a lot of googling to get through proofs that I couldn't get.
Proof wiki is a great reference.

>>8161879
none of things you mentioned except red eye color, you don't need genetic manipulation for it though - one can wear contacts or get them colored permanently

>>8161891
I forgot Pugh and Rudin somehow. Both analysis texts.

>>8161891
DO you have something good for Number theory + Abstract Algebra + Linear Algebra?

>>8161896
I think Landau's Foundations of Analysis is considered a number theory book.

For linear algebra and abstract algebra I can only recommend the standard texts.
Axler - Linear Algebra Done Right
Artin - Algebra

>>8161896
Asking for a number theory text is a little broad. Are you looking for basic elementary number theory? As for the others, I would recommend Axler and then Artin. Artin has a couple of chapters that form a good intro to algebraic number theory.

>>8161901
Thanks!

>>8161905
>>8161905
>Are you looking for basic elementary number theory?

Yep. Soemthing which introduces me into the cryptography and the concepts of number theory on a beginner level.

Thanks as well

>>8161884
My advice may be shitty at its best, but just keep going at it and support yourseld with all the resources you can (books, videos on youtube, local math students or teachers, internet forums for learners, etc.) and don't give up.

If it's your first time reading into "formal" mathematics then understand that what you are going through is 100% natural. Once you wrap your head around the logical language you're ready to start (I've still hit many brick walls since Calc, but it's always the same thing; some stuff is gonna be new, some old, some tough, but you just keep going at it).

Also, Spivak is an incredible book for redreshing your memory and flexing your math muscles with excercises, but it is definetely not recommended for beginners (I personally believe it's the worst place to start, but it should be a goal to go through chapters you've already read elsewhere and go through as many excercises as possible; you will notice how you have matured if you confront that book once in a while).

The Apostol is a great book for starters IMO, but another anon recommended other good ones. I'd also recommend Mathematical Analysis by Hasser. Godspeed, anon

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Is it true that if you were hypothetically able to manipulate the structure of atoms you could create anything from anything?

>>8161947
Sure. If you could do it fast enough.

>>8161928
Ah. So I'm no expert in cryptography, but you'll probably just want a light exposure to group theory and then find some dedicated cryptography resources. Basic cryptography shouldn't need any number theory beyond modular arithmetic and some facts like Fermat's little theorem, which are all facts about groups.

>>8161968
You will laugh or be pity me but I've never worked with a book outside of school. All my classes so far in University I passed with the lecture + homework/exercises.

So I don't know if it's the better jump to start off with Groups or Number Theory

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Ok I know this is probably a very stupid question but whatever.
>I'm not trying to get an exact fucking thing here, I'm just looking for a very general idea of what happens to sate my curiosity.

Say Red and Blue are two electromagnetic waves, either radio or microwave, traveling down wave guides.

What exactly comes out? (green)

Do the waves outright combine somehow?
Do they overlap each other, retaining their own wave lengths, power, wavelengths and frequencies?
Do they just basically ignore each other like two flashlights crossing beams?

If they do just overlap, what is the measured effect of the "green" coming out?
Is it a combination of the energy of both waves but at two different frequencies?

Just trying to get a general idea of how electromagnetic waves interact.

>>8161891
Different guy here. I know this is going to sound dumb and lazy but I've been through a lot of real analysis material (started with lazily going through a youtube lecture series) and all of the concepts I've seen are intuitive to me, yet when faced with a homework question I feel clueless. Haven't done proofs since a discrete math course for CS. I bought a book I hoped would help me (Foundations of Mathematics by Stewart & Tall) and I'm being bored out of my skull going over decimal expansions and construction of reals again while not feeling much more prepared for the work, which is seriously killing my motivation to go through it. Do your suggestions change at all given that? Otherwise, I'll check out Landau since you suggested it helped you. Really want to get to complex analysis, suppose I need to work on my impatience.

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>>8161749
I've been self teaching maths for a while since I didn't pay attention in school, and I'm still confused about one thing, which I wasn't until now, but I guess a brain fart had to happen sooner or later. Pic related

>>8162235

Correct your definition: a/b = c/d iff ad = bc.

>>8162235
[math]a/b=ab^{-1}[/math]
[math]\frac{2a}{2b}=2a(2b)^{-1}=2a2^{-1}b^{-1}=a22^{-1}b^{-1}=a1b^{-1}=ab^{-1}[/math]

>>8162235
Okay so a fraction is the ratio (result of division) r of two numbers a,b. So we have [math]r= \frac{a}{b} [/math]. Here r,a,b are variables they can be any number but b!=0. e.g. a=10, b =5 then r = 2. Two fractions are equal if their r is the same i.e. the numerand diveded by the denominator. So knowing how division works we know [math] r \cdot b = a [/math]. Now if we multiply both sides by a number c ( = 3) we get [math] r \cdot (cb) = ca [/math]. Which means [math] \frac{ca}{cb} = \frac{a}{b} [/math]. In the example, we have [math] 2*5 = 10 [\math] and [math] 2*5*3 = 10 * 3 [/math], so [math] 2*15 =30 [\math] and finally we have [math] \frac{10}{5} = \frac{30}{15} [\math]. Hope you see why multiplying works and other things don't such as adding the same number, exponentiating to the third power etc.

>>8162267
Okay so a fraction is the ratio (result of division) r of two numbers a,b. So we have r=ab. Here r,a,b are variables they can be any number but b!=0. e.g. a=10, b =5 then r = 2. Two fractions are equal if their r is the same i.e. the numerand diveded by the denominator. So knowing how division works we know r⋅b=a. Now if we multiply both sides by a number c ( = 3) we get r⋅(cb)=ca. Which means cacb=ab. In the example, we have [math]2\cdot5=10[\math]and[math]2\cdot 5\cdot3=10\cdot3[/math], so [math] 2\cdot15 =30 [\math] and finally we have [math] \frac{10}{5} = \frac{30}{15} [\math]. Hope you see why multiplying works and other things don't such as adding the same number, exponentiating to the third power etc.

>>8162189
Landau is a long book full of extremely boring proofs. Especially if you've finished constructing reals (You talk about decimal expansions, are those the real number construction you're talking about?)
I was completely fresh to proofs, so it was helpful to me, but I didn't even finish the book.

For real analysis:
Rudin has great proofs, Pugh has amazing explanations for the most part
Put them together, they have a great construction of the reals via Dedekind cuts.

I forgot to mention Terrence Tao's analysis book as well. He actually works toward both real and complex analysis at the same time. Great book, a little wordy for me, so I've been skipping around.

If you haven't covered things like mean value theorem or proved the fundamental theorem of calculus, I'd suggest continuing with real analysis.

If you're moving into complex analysis, the books I'm probably gonna go into is Bak, Tao, and daddy Rudin.

Also > all of the concepts I've seen are intuitive to me, yet when faced with a homework question I feel clueless.
do proofs man. Get a notebook and just start proving shit.
ProofWiki is an amazing place to go when you get stuck.

>>8162267
Easiest to understand, thanks.

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Can anyone help me out with this?
How's solid state (or any single-phase state) fixed with just 2 of these properties? For example, if I pick a point in the Solid region, by increasing specific volume, eventually I'll be over the solid - vapor region.
In fact, what happen if I pick a point that's over the solid - vapor region, but not touching that area?

Having trouble finishing this (taken from IMO 2005):
In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2/5 of the contestants. Moreover, no contestant solved all the 6 problems. Show that there are at least 2 contestants who solved exactly 5 problems each.

I'm sorry for such a basic request, but I thought you folks would be more likely to have acces than /wsr/.

If anyone could share the texts of these articles I would be most appreciative. i don't have WoS access currently.

Ratnam KV. Effect of sexual practices on T cell subsets and delayed hypersensitivity in transsexuals and female sex workers. Int J STD AIDS 1994;5:257–61.

Richards JM, Bedford JM, Witkin SS. Rectal insemination modifies immune responses in rabbits. Science 1984;224:390–2.

Thanks for your time.

>>8162438
http://sci-hub.bz/
just plug in the website hosting the article

>>8162475
Thank you, that worked just fine. Hadn't heard of this.

>>8162166
> Just trying to get a general idea of how electromagnetic waves interact.
They don't interact.

Is a graduate degree in chemical engineering worthwhile? I don't want to sit around in a factory in the middle of nowhere staring at excel sheets all day.

>>8162385
> every two
In English?

>>8162500
Not sure about chemical engineering, but for most engineering a masters or mba is nice.
A PhD in engineering is for people who want to go into academia.

>>8162385
there's solutions to all of these online

so unless you have a partial solution you actually need help finishing there's not much point in asking here

>>8162499
>They don't
not other person, but then how do different colors of lights add to create new colors? Are they actually undergoing a change or am I just perceiving a change that has not actually occurred?

My little sister's going to Chemistry soon -- it's been a while since I've had it, so I don't really remember what I did to prepare for it. What do you guys recommend she read up and study on during her summer? I need to occupy her with something or I'll go crazy.

Hey guys, questions on Titor from years ago. The more i follow the news the more i realize the events are coming to pass that Titor spoke of years ago. The divergence seems like a very possible explanation as to why these events are happening now as apposed to Titor's original dates.

Anyone out there feel the same?

Our current technology is far more advanced than it was a decade or so ago. So i wonder whether time travel is an actual thing that could happen now?

>>8162551
was reading about Titor again lately as current events occur. I feel like his coming here and the people's hysterics pushed the events from the original dates to the future (now). I don't have anything to add but I do feel the same. time travel is always interesting.

Nice to know someone else feels the same, just wanted to let people know this stuff is very plausible. And to read up on what could happen.

>>8162512
> how do different colors of lights add to create new colors?
They don't. It's essentially an optical illusion.

> am I just perceiving a change that has not actually occurred?
Colour perception is fundamentally a property of the retina. This contains three types of sensory neurons ("cones") each of which is sensitive to a different portion of the spectrum (centred roughly on red, green and blue).

Pure yellow light (~580 nm wavelength) stimulates the red and green cones to roughly the same extent. Consequently, a mixture of pure red and pure green light is visually indistinguishable from pure yellow light to the human eye.

However, various physical processes can distinguish them. E.g. passing red+green light through a prism will split it into red and green, while yellow light will go in yellow and come out yellow. Shining yellow light on a dye which only reflects yellow or through a filter which only admits yellow will have a significantly different result than doing the same with a red+green mixture.

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>>8161749
66 years from the Wright brothers to footprints on the moon. Has aerospace progress really slowed?
ISS and Pluto flyby is cool but shouldn't we doing better? Thoughts?

Why does my body signal I'm not thirsty/hungry immediately after I've drank water/eaten food even though I haven't digested it yet?
Is my brain lying to me?
Is it just to quickly inform me that "food in throat when stomach hurt = good" as if I didn't know that already?

>>8162588
count the number of years since prints on the moon to incredibly hd (like 8k by 8k) photos of the furthest totally-a-planet, I think so

>>8162588
> shouldn't we doing better?
Such as? Sending stuff into space is fairly expensive and, aside from satellites, doesn't have much commercial potential in the near or medium term.

>>8162685
especially compared to airflight which is super profitable.
Hey, why don't we have supersonic air travel yet? wtf happened?

>>8161749
Is there any reason to believe hell exists?

>>8162687
> Hey, why don't we have supersonic air travel yet? wtf happened?
We had it. It was never profitable overall, and only marginally profitable (i.e. ignoring sunk costs) for the very top end (less than 0.1%) of the market.

Ultimately that segment turned out to be too small to sustain the fixed overheads of the maintenance operation. Air France decided to terminate their Concorde operations which effectively forced BA to do likewise (otherwise they'd have had to pay the entire cost of the maintenance program rather than just half).

Since then, fuel hasn't gotten significantly cheaper, noise regulations haven't been weakened, demand for really fast long-haul flights hasn't increased (short-haul being dominated by getting to, from and through the airport), and the laws of physics haven't changed. So there's no reason to believe that another attempt would fare any better.

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What happens to the body during exercise that is so good for people?
What are the exact processes and results of those processes, and/or what longer-term growth or changes does it stimulate?

It's so difficult to find good non-popsci resources on this even in an nih search. Most things are pretty non-specific and just say lower blood pressure and even helps fight cancer without any specifics.

>>8162710
isn't this pasta? i swear i've seen this before

>>8162710
A totally pop-sci explanation is that in rips and then repairs muscle with thicker and stronger materials (much like the body does for bone and blood)

I think it matters if you're talking about aerobic and aerobic exercise?

>>8162724

I should have been more specific, I meant aerobic in general and cardio specifically, I'm somewhat familiar with anaerobic exercise for muscle development.

>>8162719
No, just so incredulously ignorant that my question probably looks something like pasta.

>>8161947
Like nuclear transmutation?

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>>8161947

>really, it's just a question of [re]assembling the components in the correct sequence...

>>8161749
just call it SQT you big unstoppable autismo

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How do I work through a math book effectively? How many times should I revise to not forget the knowledge? Is every exercise / prolem setr ecommended to solve?

I have a ketone. Through a 2 step mechanism involving 1)LDA and 2) molecular oxygen and Triethyl phosphite it becomes an aldol.

I assume that the first step generates an enolate, but what happens next?

>>8163225
Enol reacting with molecular oxygen could lead to carboxylate or peroxic acid. And there is always the possibility for aldol condensation.

>>8163240
I excluded the aldol condesation because that wouldn't need the oxygen, would it? but I understand jackshit about organic chemistry.

Thanks

How long do you need to work through a book? Like in average?

Is it possible that in the far off future, we will have mapped the brain. And with this we will be able to create a virus that will create zombies based on this map?

What's a curriculum that I could take to create the zombie virus?

>>8163256
No it wouldn't but aldol condensation would still be the side reaction in the first step. It's not the answer this question is looking for but it's always good to list all possible outcomes.

>>8163336
molecular biology
biochemistry

>>8161878
If you're a full time student, you should study at least 40 hours a week which includes the time you spend in class.

>>8163385
That's not his question though. Don't be such an autist anon.

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What if the universe is expanding because black holes are tugging on space time? Similarly objects pulled into black holes aren't destroyed because the black hole isn't pulling on objects, instead on the fabric on which these objects rest. We cannot perceive the flexing of space time because we are within it, like how looking through a distorted lens or mirror doesn't change the objects, flex in space time is similar.

Idk random thoughts.

How are you learning a subject in a real fast way?

>>8162347
Phase is dependant on two things, pressure and temperature. I'm not sure what you are asking exactly but if you decrease the volume the pressure will increase between the molecules inside. Increasing the volume of the solid will eventually decrease its density and intermolecular forces to where it will become a liquid or gas.

This isn't very intuitive with solids.

Does p have to be an integer in a rational number?

>>8163430
A rational number is a ratio of integers, i.e. both the numerator and the denominator are integers.

>>8163432
Thank you

>>8161749
>drawing non-acidc hydrogens

Thats capsaicin. Its chilli peppers

Question for code monkeys:

Just picked up programming (JavaScript), what's the difference between console.log and print?

>>8161878
A lot,and its not worth it since i have no way to apply it and I quickly lose interest and forget it.

>>8162655
basically its just a function of few enzymes,you can read up on here and take it from there.
>https://en.wikipedia.org/wiki/Gastric_inhibitory_polypeptide

Is the brain a muscle?
Why are they calling it "brain muscles"?

is the brain like a muscle?

>>8163401
Have personality tendencies toward obsession and have heavy interest in a subject.
The combination will get you through anything no mater how complicated it is,but only if YOU and only you want it and it is not a task given by someone else or is a job you have to do.

>>8162499
So basically green would just be red and blue overlapping each other then?

Assuming a perfect waveguide that would line them up perfectly, the measured power of green would be red+blue?


I assume this is how multi LED flashlights work right? Just more sources all channeled together?
>>8162583
Neat.

>>8163491
What are you even studying for then? Find something to research

>>8163518
no, the brain is not a muscle
if anyone calls it a "brain muscle," punch them
It does act kind of like a muscle, in that when parts of it aren't used, they are removed. search myelination for more on that.

>>8163580
>Find something to research
I cant due to limitations surrounding me.
Ive made coupe of threads about my situation and noone seems to know how to approach it,which is fine but it got me really depressed.

>>8163610
>couple*

>>8163610
>I cant due to limitations surrounding me.
?

try something else then
theres no point in studying something if all you plan to do is forget it

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Is there a way to remove edges of a petersen graph to create a new graph that is connected and contains a Euler cycle?

I know the goal is to remove edges so each vertex has a degree of two, but I can't find a way to do this without the graph being disconnected. Is this possible?

>>8164370
pretty certain this is impossible. Anyway I could explain why this is the case or how to rationalize this?

Specific enthalpy [kj/kg] and specific work refer to the same thing is that correct anons?

>>8164370
oh jesus christ, you're a cringy fucklord from /x/.
abandon all that shit and you're welcome back here any time.

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>>8161749
>Think geek

Top tier cringe shit, pic related is one of their shirts

who /didn't_do_shit_the_whole_semester_so_theyre_learning_everything_in_one_day/ here?
Going over constraint satisfaction problems, description logics, default logics, answer set programming, and nonmonotic reasoning makes my head go ouchie

>>8165137
>didn't_do_shit_the_whole_semester_so_theyre_learning_everything_in_one_day/
What did you do all year? shitpost?

>>8165145
yes

>>8165168
Then you should fail

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so i'm trying to simulate 2D fraunhofer diffraction in MATLAB but i'm stuck on working with changing coordinates.

For example i start at point xi,eta then end at x,y.

My function is a combination of components but I don't know how to define two separate coordinates in the same function while keeping the matrix dimensions agreeable.

So the quotient ring R[x]/(x^2+1) is isomorphic to the complex field.
This is an algebraically closed field constructed from a ring.
I have a few questions regarding this:
Can every algebraically closed field be constructed from a ring or similar structure? If not, what fields have that property?
The spectrum of the above ring is equal to the whole ring (i think)
If an algebraically closed field can be realized as a quotient ring, is the above statement about the spectrum true in general?

Hey /sci/,

I'm currently a student in the Southeast studying Mech Eng with a minor in sustainability. I'm interning at a nuclear station this summer and am looking at interning in the PNW next summer to try to get connections out that way so that I can get a job and move there after I graduate. Any recommendations of companies to look at? I know Boeing, I interviewed with them this summer, but unfortunately they really preferred me working at the Charleston plant rather than heading across the country

>>8165281
Blow it up fag

>>8165272
Any algebraically closed field K will contain a proper subfield F. You can then construct K by taking a quotient of the polynomial ring in some absurdly large number of variables by an ideal containing all monic irreducible polynomials over F. You can probably Google around for this.

>The spectrum of the above ring is equal to the whole ring (i think)
I'm not sure what you're trying to say here. I don't know a meaning of "ring spectrum" other than the set of prime ideals. Since R[x]/(x^2+1) is a field, there is only a single prime ideal, namely 0.

>>8165272
>Can every algebraically closed field be constructed from a ring or similar structure? If not, what fields have that property?
It's a bit of a strange question to look for subrings inside of an algebraically closed field but at the very least there's the 'prime subfield' generated by 1, which is either Q or Z/pZ depending on the characteristic of your field.


>The spectrum of the above ring is equal to the whole ring (i think)
Are you referring to R[x] or R[x]/(x^2+1)? Spectrums of fields are trivial

>>8165340
>>8165338
You're right, i had the definition of spectrum confused with something else
Thanks

How do I prove that
[math]{ (x,sinx) : x \in \mathbb{R} [/math]
is a closed set?
I really have no idea how to start with this.

>>8165516
fuck I'm an idiot
I meant
{(x,sinx): x belongs to R}

>>8165516
>>8165517
With things like this involving the topology of Euclidean space, it's easy to get bogged down in the specifics of the problem. I think it can be helpful to think about a more general formulation, because there are less moving parts to consider. This is true most generally by considering a continuous function [math]f: X \to Y[/math] where Y is Hausdorff (this just means that any two distinct points have disjoint neighborhoods). Then you can show that [math]\{ \left( x,f(x)\right) : x \in X \}[/math] is closed in [math]X \times Y[/math]. The best way is probably just to show the set is closed directly using the definition.

>>8165544
So what I did was
[math] Xn \to x and Yn \to Y makes Yn = sinXn[/math]
Since Xn and Yn both have their limit at (x, y) then it means that
y = sin x which is a continuous function and thus the whole set is closed.

>>8165572
hey bby remember to use \text{text in here}

>>8165575
sorry i'm new to Tex, it's my first year of college.

>>8165583
If someone could help I would be really glad, I'm really bad at googling

Can someone explain to me how to do tensor analysis? I understand that tensors can express scalars, vectors, matrices, etc., but how does the notation work?

this is a real silly question, why is the punctured disk [math]0 < |z| \leq 1, z \in \mathbb{C}[/math] neither open nor closed?

I think know that for a set to be not open, there exists a boundary point contained in that set (this is true because [math]|z| \leq 1[/math]), but for a set to be not closed, there needs to be a boundary point that is not in the set

what boundary point isn't in the set? I'm misunderstanding something here

>>8166352
the origin, z=0 is not in the set since |z| > 0, but you can get arbitrarily close to it

>>8166352
> what boundary point isn't in the set?
[math] z = 0 [/math] , lol

>>8166350
look up the concepts of covariance and contravariance then "einstein notation"

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Is an ellipse the same as a "foreshortened" circle thats been compress in one dimension?

I do a lot of old-fashioned engineering drafting, and I usually draw a foreshortened circle by calculating a shitload of points on the circle then compressing the distance normal to a reference centerline that I've drawn, but I want to find a better way. I figured I would start by educating myself on terminology. any other tips much appreciated

>>8166477
> Is an ellipse the same as a "foreshortened" circle thats been compress in one dimension?
Yes.

>>8166361
Einstein notation is gross. How does [math](T^{-1})_\nu^\mu[/math] make you feel? It shouldn't feel good.

>>8166552
Even better is when you have 8 goddamn indices and you start running out of greek letters you can write well that small.

>>8167649
I'm a little unclear on what the video is supposed to show, seemingly he "squeezes all the guts out" of the rabbit.

This is not possible because everything in the rabbit is connected. There is no blood in this gif, but the veins and arteries in the rabbit are connected to the organs, so if the organs came out there would be a lot of blood.

If the entire vascular system came out, there would still be large arteries severed going to the head, as well as ones that go around/between bones. These would create a lot of blood.

Is what's shown in the gif possible at all? Probably not, I'm willing to bet that the rabbits hide is strong enough to crush most of those organs that he delicately handles afterword.
Even if not, the pressure he's putting is supposedly pushing the organs out, but the organs don't form an airtight seal in the body.
Doing this would, at best, rupture the rabbits anus and cause blood to squirt out. Much more likely, the rabbit would just squish and nothing would escape.

For exactly the same reasons this could not be done to a human, and the gif is fake. Just some slight of hand with a prop, maybe some organs he bought at the asian market.

What's a small, quick, concise book on most math to upto a point suitable for 3d graphics/programming/general cs? I need something to get me back into the swing of things and fill in any holes in information that were left from my garbage school.

>>8167723
Calm down autism

>>8167792
>>>could this be done to a human
>>no and probably not to a rabbit either, here are some reasons since you asked
>calm down autism
Never change, /sci/.

>>8167796
>be retarded
>doesn't understand that the rabbit was bled out first
>doesn't understand a rabbits tissue is extremely weak

You can do this to a rabbit. You might be able to to this to a person too.

What's the generalization of Riemann or Darboux integrals for complex functions for proving the existence of a primative?

>>8167838
Given all of this, you'd still need to make a nice circular incision around the rabbit's anus first. Unless you REALLY can't into anatomy.

A person's bones are a much bigger problem than a rabbit's.

I have a couple
1. Is it a bad idea to retake a course that I failed last year if it's not essential to my degree? I dont know what my major should be but I failed a modern physics course last year and I felt bad about it. It's in the upcoming semester and I have the option to take it again

2. Is earth science (geology) a joke major? I had trouble with physics major and now I have to pick something else, but nothing really appeals to me.

3. Is going to college for a fixed period of time a day (say, 4-6 hours) even when you dont have lectures to occupy that time a bad idea? I was thinking that its a good way to stay on topic with minimal distractions, but I havent really tried it before

>>8168448
>Is it a bad idea to retake a course that I failed last year if it's not essential to my degree?
Generally yes. I suppose it depends on your scholarships, but courses definitely aren't free and it may be a distraction from courses that are important if you've already had trouble with it before. If you still have the textbook, consider studying it on your own time, if it's not going to get you hired you don't need a transcript saying how good you were at it.

>I dont know what my major should be
If you're already in your second year, I'd really focus on going through some career advising and figuring out what you want to do before you've put too much time and money into this.

>Is earth science (geology) a joke major?
This is a bad question, especially around here where undergrads are running around shitting on any major that isn't theirs. It's employable, and that's what matters. I personally don't know much about it, but it seems perfectly valid to me.

>Is going to college for a fixed period of time a day (say, 4-6 hours) even when you dont have lectures to occupy that time a bad idea?
It really depends on your course schedule, and the environments available to you. I went to a shitty community college and the fancy study areas were pretty small and a bit too loud for me. Dunno if this is common, but the library had a metal detector and I couldn't bring a laptop. I would suggest you work on setting up a distraction-free environment at home, but considering how many students seem to need computer labs to do computer work at all, there certainly do seem to be people who do it that way.

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>>8165518

>>8168448
From my (ample) experience re-taking classes I failed, there is two ways to look at it.

1. You have the stuff fresh in your head and are ready to re-do it with a new start and really nail it this time.

2. You just did that fucking class and repeating it immediately will make you burn out and hate that shit even more, and you will just drop the fuck out halfway through and take an 'I' after an 'F'.

Sometimes a little time off will give you more of a drive to go back and nail it. Also relevant if there was any prerequisite courses that the class builds on, in that case more time going by can be a bad thing.

When doing a (discrete) Fourier transform of a real signal, the result will be complex. How do I get the frequency spectrum out of that? I suppose I would take the absolute values to get the amplitudes, but how do I find the frequencies?

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Which design do you guys think is better for a dome? Hollow but thick or thin but held by a strong structure?

>>8169470
with a structure, unless you're trying to prevent bullets or something.

Why does [math]\sum_{n = 0}^{\infty}ne^{-n}[/math] equal [math]\frac{e^{-1}}{(1 - e^{-1})^2}[/math] ?

I can't figure it out. Someone please help or tell me what obvious trick I'm missing. Thank you.

>>8169478
looks like you could use the snake oil method there

>>8169500
Sorry I don't know what you mean. Could you explain a little more?

>>8169478
[eqn]\sum_{n \ge 0} ne^{-n} = \sum_{n \ge 0} \sum_{k=1}^n e^{-n} \underset{Fubini}{=} \sum_{k \ge 1} \sum_{n \ge k} e^{-n} = \sum_{k \ge 1} \frac{e^{-k}}{1-e^{-1}} = \frac{e^{-1}}{(1-e^{-1})^2}[/eqn]

>>8169506
big pdf: https://www.math.upenn.edu/~wilf/gfology2.pdf

it's on page 118 but on second glance i'm not as sure it would work, i haven't used it in a while.

you basically take [math]\sum_{k\geq 0} \text{your sum here} x^k[/math] and then swap the order of summations and simplify using known formulas for generating functions.

I think you would have to let one of the n's in your sum be a free parameter and then specialize at the end, but I could be misremembering the trick.

>>8169513
ooh that's nice

>>8169513
Thank you.

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help me with this integral.. wolfram doesn't have a step-by-step solution

does anyone here have experience with ROOT?

>>8161980
Do you have any familiarity with introductory proofs? If not check out any generic introduction to mathematics books for an undergraduate understanding of proving

Then maybe you look into Chapter 0 by Aluffi after you have a strong introduction to proving

>>8169378
> How do I get the frequency spectrum out of that? I suppose I would take the absolute values to get the amplitudes
Correct. Similarly, the argument is the phase angle (a phase of 0 is a cosine wave).

> but how do I find the frequencies?
A DFT gives you an array of amplitudes, one for each frequency. a[n] is the amplitude of the Nth harmonic, i.e. with frequency 2*pi*f*n/N, where f is the sample rate and N is the number of samples.

>>8169614
[eqn]\int \frac{vdv}{\sqrt{Ev^2 + 2Av - 1}} = \int \frac{v - 2A/E}{\sqrt{Ev^2 + 2Av - 1}} dv + \frac{2A}{E}\int \frac{dv}{\sqrt{Ev^2 + 2Av - 1}}[/eqn]
The first term is of the form u'/2sqrt(u), which integrates nicely and the second one you can probably integrate with a trig substitution (either circular or hyperbolic depending on the sign of [math]A^2 + E[/math])

>>8169666
ah okay, thanks

>>8169668
you're welcome (although it was actually A/E instead of 2A/E, I can't differentiate..)

>>8169657
Cool, thanks!

>>8169614
Reminds me of the mechanics book by Landau.

>>8169701
yeah I'm working from Kotkin & Serbo "Collection of problems in Classical Mechanics" which corresponds to the material in Landau according to the introduction

>>8169707
Really liked the book by Landau, but I have to admit it was too hard for me.
Hope you have more luck with your book!

>>8169478
You could try this trick...
[math] F(t) = -\sum_{n=0}^\infty \exp(- n t)[/math]
[math] F'(t) = \sum_{n=0}^\infty n \exp(- n t)[/math]
Get an expression for F(t), take derivative, plug in t=1.

[Seinfeld pic]
What's the deal with carbon? Carbon matter, carbon gases, carbon nanotubes, carbon footprints, what's so important about carbon?

I never took a chemistry class so someone please explain like I'm a retard

>>8169755
> What's the deal with carbon?
Catenation. The ability to form long chains of C-C bonds, leaving two spare bonds at each site which can be used to attach radicals, or for additional C-C bonds (allowing the formation of loops and trees).

Catenation is possible with other elements but the bonds are less stable.

>>8169808
What's catenation and what are the implications of it

>>8170138
> What's catenation
The ability to form long chains of a single element.

> and what are the implications of it
Practically unlimited complexity. E.g. some proteins can have ~170,000 carbon atoms (~500,000 atoms total); a DNA molecule can have 250 million base pairs = ~5 billion atoms.

Inorganic compounds (or rather, compounds which don't involve catenation, which isn't entirely limited to carbon) rarely get larger than a couple of dozen atoms. In turn, that limits the number of distinct combinations.

Whereas organic molecules often use a single name for an entire family of compounds of which there are almost limitless permutations (consider how many distinct permutations exist of the compound known as "DNA").

>>8170224
what's the difference between catenation and a grain-sized crystal?

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What did he do here when he said ''...finding the modulus...''

I am not quite sure how he got that result I highlighted.

>>8170266
n/(n+1)-1
= n/(n+1)-(n+1)/(n+1)
= (n-(n+1))/(n+1)
= (n-n-1)/(n+1)
= -1/(n+1)
Assuming that n is positive:
|-1/(n+1)] = 1/(n+1)

>>8163460
>writing out the carbons

>>8170279

Got most of it now.

But I am kind of embarrassed to admit that I dont quite get why you replaced the -1 by (n+1) / (n+1)

>>8170309
to make a common denominator?

how are you planning on doing what looks like an analysis text if you don't even know how to give fractions a common denominator?

>>8170309
To subtract fractions, you'll want a common denominator. And (n+1)/(n+1) is 1.

>>8170224
thank you for your explanation

>>8170328

Of course, makes sense now.

>>8170323

With hard work and determination :^)

>>8167792
>Calm down autism

That was an informative and interesting response. Fuck off to some other board.

>>>/whatever/

This is my stupid question. How come there are hundreds of tv channels, radio stations, cellphone signals, wifi, etc, all travelling through thin air, yet when it comes to cables there seems to be a severe limitation in the amount of data they can deliver (in relation to the previously mentioned radio waves). Shouldn't you get a much better signal on a conductive medium?

>>8170478
Light/'radio waves' has the added dimension of wavelength. Also it travels farther easier and faster so more data can be transferred given an amount of time.

>>8170497
Of course. Thank you for your patience, anon.

>>8170478
> Shouldn't you get a much better signal on a conductive medium?
Cables suffer from high attenuation once you get up to hundreds of MHz. That's why UHF (470–862 MHz) TV antenna cables are so thick (thicker cable equals lower capacitance equals lower attenuation per metre), and why satellite TV has the down-converter on the dish (at GHz frequencies, the signal attenuates 10 dB/m or worse).

For short distances, cables win at almost any frequency (otherwise data centres would use wi-fi rather than wired ethernet), due to being able to run as many cables as you like in parallel.

>>8170497
... is complete nonsense.

>>8161749
So, as anyone who's took a course in physics knows, the radioactivity of radioactive objects doesn't change no matter what you fucking do to them (heat them, put them under pressure, stick 'em in a stew...).

But does anything interesting happen if you irradiate them?

Okay this may be a real stupid question please don't bully me.

How were the first video drivers programmed? Obviously to program something you have to see code on a monitor. But to see code on a monitor a video driver had to be programmed so you can see it.

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>>8171332
>Obviously to program something you have to see code on a monitor.
Do you, really? Historically, instructions for computer programs were stored on punched cards, not typed in or coded using a monitor.

What contributions will I make towards society by getting a degree in Mathematics over, say, a degree in ChemE? Also, how's the pay?

>>8171332
> Obviously to program something you have to see code on a monitor.
Before monitors there were punched cards and hard-copy terminals. The market for the latter came to be dominated by Teletype to the extent that the term "Teletype" (or "tty" for short) became a generic term for a terminal regardless of manufacturer.

> But to see code on a monitor a video driver had to be programmed so you can see it.
8-bit and 16-bit microcomputers (including the original PCs) didn't have video drivers; software typically manipulated the video hardware and video memory directly.

The concept of a "driver" stems from a desire to provide a common software interface to different hardware. If the hardware is fixed, you don't need a driver.

With the PC, the first video drivers were modules for popular DOS applications (e.g. AutoCAD, 3D Studio) which allowed them to access features of SVGA video hardware which weren't part of the VGA standard. Different manufacturers' video cards provided various extensions which all worked differently, so without drivers you had to write different code for each make of video card in order to use the extensions.

What do you guys think about double majoring in both Physics and Chemistry? The main reason people tell me to not do it is that it's too much work. I'm a fairly hard worker and took all APs for both my Junior and Senior year and while I'm sure it doesn't compare do you guys think it's doable? Any other reasons to not do it?

Why the FUCK am I having such a hard time understanding math when I dedicate @ least 3 hours a day to it

>>8172641
The answer depends on the kind of math you're trying to learn. If it's baby shit it's because you're not doing enough problems. If it's big boy math it's because you've reached the limit of your intelligence.

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What's the most scientific method of killing myself?

>>8172577
okay so I'm assuming you are going into undergrad next year. This is what you are going to do, declare either physics or chemistry as your major and the other as a minor. Look at the unit costs for doing the double major and check it against how much time you have for school. If you think you can handle it fill your schedule to the brim with some harder classes at the intro level and if you handle it well then base your next semesters off of it. This is what I did and I'm doing a bio and chem double major with a minor in math so I can do more then just calculus.

>>8172680
Also get a good adviser and make friends with them, they will be your life line for a double major. They will control which classes you can get to double count and which classes you can waive. It's how I managed to get a genetics lab replaced with a grad level stem cell course.

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I'm going to sound like a complete retard, but idgaf, this is sci, and I'm here to learn. So, the more advanced math that I learn, the more I start to question my knowledge of basic math, and something has been bothering me for a while, could anyone, in simple terms, explain what multiplication and division are? I'm pretty sure that multiplication can be described as repetitive addition of the same number with itself (3x5=5+5+5), but I can't quite describe division. If we have for ex. 8/4=2, that means that we divided 8 into 4 equal parts, and that each equal part is 2?

I'm not completely retarded, just OCD, I want to be able to describe it, if I can't it tears me up from inside.

>>8172739
Division is the inverse of multiplication.

a/b=c <=> a=b*c (where b =/= 0).

Note that the integers aren't closed under division, i.e. dividing two integers doesn't necessarily yield an integer.

One way to deal with this is to approximate division with something which yields a quotient q and remainder r such that

a/b = (q,r) <=> a=b*q+r

Another is to leave the result as the sum of an integer and a fraction:

a/b = q+r/b <=> a=b*(q+r/b) = b*q+r

Then there is the concept of a finite field (aka Galois field) where division is defined everywhere. Over the integers modulo a prime number, for all a and all non-zero b, there exists a unique c such that a=b*c. The polynomials of a given degree over the integers modulo a prime also form a finite field. Finite fields are fairly important to coding theory (e.g. Reed-Solomon error correction) and cryptography (e.g. Diffie-Hellman key exchange and the AES cipher).

>>8164370
A graph where every vertex has degree 2 IS a cycle. So the problem reduces to finding a Hamiltonian path in the original graph.

>>8171846
Adding to human knowledge.
Math is not something you go into for the pay. Typical salary is probably 30-40k but it can be drastically higher if you prove some famous result.

>>8173356
And this is for academia, obviously if you become a financefag you will make bank.

>>8161749
op you're a fucking autist
just call it stupid question thread
now there's three threads like these in the catalog
and yes I know they may not be stupid, but its just tradition, deal with it

>>8173356
You are so full of shit it hurts. You know the AMS publishes salary statistics? Tenured professor make $95k on average

Apologies for shitty terminology.
Imagine there is a hollow, sealed sphere made of material that 100% perfectly reflects all kinds of radiation and everything else applicable. It is not effected by anything and it won't interact with anything other than reflection. Nothing gets in, out, into or from the sphere.

The sphere is filled completely with about room temperature, uncompressed tapwater, and shaken violently for an eternity.

Would anything happen to the water at any point in time?

>>8172739
Addition and multiplication aren't really basic operations. Counting/Repetition and labeling are better operations. Starting from the unit (labelled one), the repetition of that unit ( one and one) is two, which is one counted two times. Adding 2 and 3 by extension, is counting two repetitions of one and three repetitions of one, which is labelled 5. Multiplication is repeating counts/repetitions. Division is counting how many repetitions are in something, e.g. 6 divided by 3 is asking how many repetitions of three are in six. Neurologically speaking, division is not accessible without first handling repeated subtractions, which is fine when the first is larger than the second (or any number of subtractions). For subtractions we can't complete, we have leftovers, i.e. 4 - 5, repeatedly "uncount" ones, you're left with 0 - 1, and since we operationally always end up with 0 - something, we choose to drop the 0 and end up with negative numbers. By repeatedly breaking apart numbers in this sense, many operations can be turned into a large number of small algorithms. Simplifying a fraction turns into repeatedly breaking out primes, exponentiating turns into repeatedly multiplying, etc. Obviously decimal or fractional answers are harder to describe this way, but if you just shift the numbers into a larger space (which is what fractions and decimals do) then you can get reasonable answers.

Have you read your SICP today?

How do you solve for x in:

x^2 - a^2 * b^2 = 0

I thought it'd be:

x^2 = a^2 * b^2
sqrt(x) = sqrt(a^2*b^2)

x = +/- ab

but I don't think this is the way to go about it since it'd really be

+/- x = +/- ab

So... what is the right way to solve this?

Question on Linear Algebra:
In regular finite Linear Algebra.
I know {v1,v2,v3,v4} over determines V. From this how do you prove from this that V has a basis?

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>>8174578
>undo the +/- on the left by doing -/+
>on the right you have +/- to start
>(-/+) * (+/-) = (-/+)
>(-/+) is indistinguishable from (+/-)

>>8174583
Don't understand, what?

Did I do the problem right?

>>8174589
Order doesn't matter anon. If you says +/- x = (+/-) 1 then follow your operations:

If +/- x = +1, then x = (+/-) 1, which is +1 and -1
if +/- x = -1, then x = (-/+) 1, which is -1 and +1

They're the same answers. Order doesn't matter. Honk honk.

>>8174602
Okay great, thank you man ;-).

Means I did the problem right and not a total retard. Got confused on the (+/-) but what you described makes sense.

>>8174580
english please

i need help with the proof that universal objects are unique up to isomorphism

if X and Y are isomorphic, then there exists two morphisms f: X->Y and g: Y->X such that fg = [math] 1_Y [/math] and gf = [math] 1_X [/math]
so with two terminal objects X and Y, there's two unique morphisms f: X->Y and g: Y->X and the proof states that this is enough to prove that they are isomorphic, but i don't see how it follows
rather, i don't see how this information guarantees that fg = [math] 1_Y [/math] and gf = [math] 1_X [/math]

can somebody explain in caveman terms pls?

Can somebody recommend a good introductory textbook on functional analysis?

>>8174797
Because fg and gf will satisfy some universal property or another that the identities also satisfy. I'm tired and only half read your post, so I won't be any more specific.

>>8174797
nevermind, i forgot that composition of morphisms is guaranteed to exist

fg : Y->Y exists, but because there is only one function Y->Y, the identity, fg must equal that function

i feel stupid now :^)

>>8161749
Does measure theory hold any hope for resolving or explaining the incompatibility of space time and quantum mechanics?

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How do I obtain the result highlighted?

>>8175127
>incompatibility of spacetime and quantum mechanics

explain further

>>8175187
[math]\frac{n}{n+1} = \frac{n}{n+1} \cdot \frac{1/n}{1/n} = \frac{1}{1 + 1/n}[/math].

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>>8175187

Ok, I kind of get it. So he multiplied up and down by 1/n

He did the same thing on pic related, but now I don't know how he got the end result of 3/5

>>8175214
As n approaches infinity, 1/n approaches zero, so 3-1/n approaches 3, 5-6/n approaches 5, and the ratio approaches 3/5.

>>8175187
By dividing the numerator and denominator by n.

In other words, DELET THIS.

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>>8161947
I suppose so, however principles concerning Kinetics and Thermodynamics would have to be taken into account. I often ponder this concept myself.

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>>8175225
>>8175210

Alright anons, thanks so much.

>>8175230

But its a stupid questions thread anon

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>>8174902
>why is universal property unique
>because it satisfies a universal property

category theory, ladies and gentlemen

I'm a physics major entering my third year with a 3.5 at a somewhat prestigous large state school with a program ranked in the Top 20-30. I have no research experience or extracurriculars.

Is it too late for me to get into a decent graduate program? Is it time to start settling for a future in engineering?

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Can someone tell me what the fuck is meant by "multiply both sides" in step two. I don't see any multiplying other then 3/2 * 16. I was taught to simply flip a fraction like 2/3 to make it 3/2. Is that all that step is trying to explain.

>>8175520
You multiply both sides by 3/2 to cancel out the 2/3. When you multiply the left side by 3/2, it simply becomes 1x, because (3/2)*(2/3) = 1. Essentially, it's what you've been doing all along.

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>>8175531
thanks buddy.

>>8175520
When you have ax=b you divide by a on both sides. When a is a fraction this means flipping it and multiplying.

there are multiple coordinates for a given polynomial on a vector base, or are they unique? because I can make up a lot of coordinates that verify the equations

>>8175607
There are multiple possible basis. With a basis, the coordinates are unique, but they change when you change basis.

>>8162544
tell her to refresh herself on molecular orbitals and hybridization (I'm assuming she's obviously first year). Also to review organic chemistry, like basic nomenclature and stability( like resonance). Also inform her that she will get butt raped by physchem :)

Newfag here. Bout to start undergrad this fall and have only learned calc 1-3 and ODE. What should I self tech before heading to college and how?

>>8176268

You're already ahead. Read How to Prove it.

>>8176283

Help me out here

If a slot machine has 76.5% chance of winning, and you play it twice, what are your chances of winning?
This shit seems so intuitive, yet I can't figure it out after thinking about it for an hour.
Guess I'm a retard :(

>>8176373

0,765*0,765=0,585

58,5% chance of winning

>>8176373
P(winning at least once) = P(NOT(losing twice)) = 1-P(losing twice)

>>8176389
so one spin = 76.5% chance, two spins = 58.5% chance?
that's not right

>>8176393
he calculated the chance of winning twice in a row

>>8176392
>>8176396
I see
Thanks for the explanation
Wish I could have figured it out myself
I don't think I could have figured out how to calculate the probability of winning/losing twice in the first place though

>>8176393
2 success------>58,5%

To calculate 0 success: (1-0,765)*(1-0,765)=0,055

Therefore:

0 success------>5,5%

0,585+0,055+(chance of winning at least once)=1

In conclusion:
2 success------>58,5%
1 success------->36%
0 success------->5,5%

Is this correct?

>>8176418
correct up until
>0,585+0,055+(chance of winning at least once)=1
It should be
>0,585+0,055+(chance of winning ONLY ONCE)=1
and then to get the chance of winning at least once, add chance of winning only once + chance of 2 success = 94.5%

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Can these things get damaged? I mean its just a piece of metal underneath right?

I tried connecting an old as fuck Phone charger (5v) just to see if it was working with the most simple circuit I could think of (resistance, led) and didnt work.

Then I tried the same exact circuit with a 9v battery (which worked last night) and didn't work.

Tried different configurations, checked everything was connected properly but nothing worked.

What did I do wrong guys? I am fucking piss desu

>>8176500
>least
>ONLY

I didn't notice this grammatical problem. Anyway the answer is 94,5%

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>>8176505
Well, it's not just one piece of metal. The rows and columns are connected like pic related shows. I'd be pretty surprised if you damaged both +/- columns. Anyway, unless it's unusually spec'd, it should be able to handle 5v. Sure you built the circuit right?

Define an operation * as following:

1)a*b is defined for every ordered pair (a,b)

2)a*b must be uniquely defined

3) a*b must be closed

Question:

Let a * b is the root of the equation x^2 - a^2 * b^2 =0, on the set R.

This fails rule 2, but how does the notation of a*b apply to this equation?

Does it literally mean a*b = x^2 - a^2 * b^2 =0?

Because in the definition there is one binary operation, namely *, in the equation there are three binary operations: -, exponent, multiplication. This confuses me.

>>8176651
> Let a * b is the root of the equation x^2 - a^2 * b^2 =0, on the set R.
Ambiguous. Was the symbol * used for both cases in the original? Or did you change the symbol to * without realising that was already being used for multiplication?

> Does it literally mean a*b = x^2 - a^2 * b^2 =0?
No

"The root of ..." means the value of x for which that equality holds, i.e. ±sqrt(a^2*b^2).

>>8176712
* in the definition is any generic operation. I was wondering how * was applied to the equation I presented since the equation has 3 operations and not 1 as in the definition.

But from what I gather, you're saying that a*b is literally the root of the equation which is x=(+/-)ab, if that is correct then you explained it well and I now understand it.

Is that right? Because I re-read the problem and it literally says "a*b is the ROOT of..." so think you're right.

Thanks man!

How do I into Human AND animal anatomy? Was thinking about reading through greys anatomy for the human part but wouldn't know what edition to get or if this is the best way.

>>8161749
I do a lot of probability calculations. I know ANDing two things is just x*y. ORing is (x+y)-(x*y). What if I want the explicit differentiation, the XOR? This apparently isn't Googleable and returns only bitwise xor. I think I found the implicit differentiation which might be (x+y)/(x-y). In fact I just want all the good ways to logically combine two probabilities. For xor I've been doing 1 - OR which is probably just NOR.

>>8163486
Console log only writes to the console log. Print writes to the specified output, or console if none specified.

>>8162655
There are 3 basic hormonal states: Satiety (caused by leptin), no hormone, and hunger (caused by ghrelin). The body manufactures ghrelin when the stomach is empty and leptin when it begins digesting. It stops producing ghrelin when you eat almost immediately, hence feeling NOThunger but still not satiety. Later, it manufactures leptin and you should stop eating. Because leptin triggers based on a physical process, it can take 15-20 minutes to feel satisfied but ghrelin can be produced purely psychologically and stopped as fast.

>>8176736
> But from what I gather, you're saying that a*b is literally the root of the equation which is x=(+/-)ab,
Uh, sort of.

Note that the equation relies upon exponentiation using the generic * operator, i.e. x^2=x*x. More generally, x^1=x, x^(n+1) = x*(x^n).

If multiplication (*) is being treated as an abstract operation, you can't go from x^2=y^2 to x=±y. You can deduce that x=y is one solution, but the other solutions (if there are any) depend upon additional rules which may or may not apply to any given multiplication operator.

E.g. if * was matrix multiplication, a matrix can have infinitely many square roots, i.e. the equation x^2=y^2 can have infinitely many solutions x for any given y.

In fact, you can't necessarily even go from x^2=(a^2)*(b^2) to x^2=(a*b)^2 because one is a*a*b*b while the other is a*b*a*b, and they're only equal if multiplication is commutative, i.e. a*b=b*a, which is true for multiplication of real numbers, but not true for multiplication in general (e.g. it isn't true for matrix multiplication).

IOW, I think you're going to need to provide more context with these questions.

>>8176803
> I know ANDing two things is just x*y.
P(x&y) = P(x) * P(y|x) = P(y) * P(x|y)
It's only P(x)*P(y) if x and y are independent (uncorrelated).

> ORing is (x+y)-(x*y).
Again, only if x and y are independent. More generally, it's 1-P((¬x)&(¬y))) = P(x)+P(y)-P(x&y).

> What if I want the explicit differentiation, the XOR?
P(x&(¬y)) + P((¬x)&y)
This is simpler as the two cases are mutually exclusive.

If x and y are independent, then it's P(x)+P(y)-2*P(x)*P(y).

>>8177003
Mine are always independent but thanks for the clarification. I do expected values of gambits in TCGs. Hence I compare two Ps that are unrelated by doing the dependant Ps first.

So another less verbose way of stating this type of XOR is:
(x * (1-y)) + (y * (1-x))

I'm assuming this branch is called conditional probability

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so, say i have data that grows linearly, then returns to 0 after a fixed interval, then after that same interval grows linearly again at twice the rate, then returns to 0, etc.
how can i model it mathematically?

>>8177042
> So another less verbose way of stating this type of XOR is:
> (x * (1-y)) + (y * (1-x))
Yes.

> I'm assuming this branch is called conditional probability
Conditional probability is when the probability of one event is conditional on some other event having occurred or not occurred.

When events are uncorrelated, their probabilities are unconditional.

>>8177086
y=(x-floor(x))*(1+floor(x))

How do you study from a book?

(I mean this question for real).
Just reading aren't cutting it.

>>8177115
Depends on the subject.
My experience:
Engineering: do more problems
Math: prove everything
Medicine: I have a glossary of terms that I add to and review. Mnemonics help and keep reviewing those diagrams. Learning a little latin doesn't hurt

>>8176980
I think the * doesn't mean multiplication here. I think it means a generic binary operation.

The rules for something to be an operation are:

Define an operation * as following:

1)a*b is defined for every ordered pair (a,b)

2)a*b must be uniquely defined

3) a*b must be closed

and the problem from the book ask which of the rules are operations on the indicated set.

Then it gives the problem,

a*b is a root of the equation x^2-a^2b^2 on the set R.

But a*b here is literally what it says x=+/-ab, no?

But since x=a+/-ab then a*b is not an operation since a*b is not unique.

>>8174563
Thanks for the thorough answer, and nope. I just sometimes dwell upon even the most basic things even a baby should understand easily.

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How does this work? I think there's a transparent dome on top of the painted eye so I'm assuming light refracting causes it to look like the eye is moving? Does the dome need to be an exact specific shape to achieve this effect or can it just be domey?

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>>8178553
It's a legit question though

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>>8178565
>posts on chinese cartoon forum
>hates anime

?? Just answer my question lmao

>>8161867
Try Stewart's calculus. It's not autistic and doesn't jump into crazy proofs. The crazy proofs can be saved for real analysis.

>>8169614
symbolab.com

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My teacher says the two capacitors in the left circuit are in paralel why?

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I'm finding the shear force and bending moments diagram of this beam, and I'm confused when I make the first cut, there's one force, one moment, and a distributed charge, that I don't know if when I do the cut it's still a triangle or it turns into a trapezium, how would I do that part?

>>8179700
Because capacitor in series equations are like resistors in parallel?

>>8179700
>referring to "left", when picture is upside down

If you mean the diagram without the source, then probably because he meant the terminal is between node a and node b.

>>8179700
you're holding it upside down

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Ethyl alcohol is the type of alcohol that you can drink. Most industrial alcohols are just isopropyl, or 'denatured', which involves additives including acetone, isopropyl, and a few others with the express purpose of making it toxic to drink. The reasoning being that alcohol for drinking is taxed extremely heavily, and alcohol is an incredibly useful compound for all sorts of industrial purposes. So they make it toxic, bitter, and smell awful to prevent people from using it to bypass taxes, and they try not to alter the use while still leaving it cheap enough for industrial use.

My question is, are there any real uses besides drinking it where having chemically pure ethyl alcohol is important? If so, how do manufacturing companies, or whoever else, get it without paying the taxes, or is that even possible?

Been bugging me for a few days.

is x - 1 the same as 1 - x in lim x->1?
is [2-x] ^ (1/x-1)
the same as
[1+(1-x)] ^ (1/1-x) in the same limit?

>>8182035
take your pedophile cartoons back to >>>/a/

>>8182035
Seems that you can't bypass the ATF excise tax stamps in the US. Seems sort of stupid, but I guess it's less paperwork to worry about, and there's no illegalities because some dipshit decided to make margarita's with the company stock.

>>8182044
U w0t?

>>8182035
Isopropyl is not denatured alcohol and they add irritants to isopropyl because it will make you drunk then it will make you dead.
You seem to be right about denatured alcohol, even though I don't think I've seen it sold.
Personally I thought denatured alcohol referred to the process of adding benzene to get the ethanol more pure

>>8182035
Maybe ethanol fuel? Never seen a car running on it though.

>>8178551
The eye is concave under the clear convex covering.

A Banach *-algebra is symmetric if its Gelfand transform is a *-homomorphism.

Does anyone know an example of a nonsymmetric Banach *-algebra? C*-algebras and group algebras are symmetric and I don't know any other examples of *-algebras.

>>8182035
>>8182035
So some more research indicates that pure ethypl alcohol is called 'drinking grade' or just pure alcohol. Also, pure alcohol apparently doesn't necessarily mean 100% alcohol. It can be alcohol + water.

It appears that it's used for stuff involving proteins and some other specific lab uses because the varied mixtures of denatured stuff fucks with the accuracy of tests. Also used in perfumes and some weird dyes/pigments for the same reasons. Not finding anything about it being used as a cleaner, which makes sense because the additives are all residue free, and some like acetone may even enhance the cleaning power in some cases without having any impact on it's ability to sterilize.

>>8182055
>Isopropyl is not denatured alcohol and they add irritants to isopropyl because it will make you drunk then it will make you dead.

You've sort of got it backwards. Isopropyl doesn't need additives because it's already toxic by itself. Denatured alcohol is ethyl alcohol that has the additives, one of which can be isopropyl. Nondenatured (apparently that's not a double negative), is the pure ethyl stuff, and is what's considered drinking grade.

>>8178551
>>8182085
For some more examples of this effect in action, see this.

TL;DR your brain is really fucking stupid sometimes.

https://www.youtube.com/watch?v=A4QcyW-qTUg

https://www.youtube.com/watch?v=ORoTCBrCKIQ

>>8182124
> Isopropyl doesn't need additives because it's already toxic by itself.
afaik they add extra irritants/stuff that makes it taste bad so that you don't poison yourself.
> Nondenatured (apparently that's not a double negative), is the pure ethyl stuff
you cannot make 100% ethanol without adding stuff. Usually it's benzene which isn't lovely.
I believe there's a way to get it out to get the stuff like everclear.

>>8182044
kek

What is the integral of force with respect to acceleration? I get m(a^2). Help, I want to learn.

>>8161749
For medical fags:

How do I stop body tremors?

>>8182042
[math]\lim_{x \to 1} 1-x = 0 = \lim_{x \to 1} x-1 [/math].
Just graphing these, it seems [math]\lim_{x \to 1} (2-x)^{1/(x-1)}= 1/e[/math], while [math]\lim_{x \to 1} (2-x)^{1/(1-x)} = e[/math]. I'm not sure why and don't really have time to work it out now, but I'd expect there's a way to make sense of these limits in terms of the definition of e.

>>8182182
benzos

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What's the mechanism here? Cl is replaced by an OH, CN is replaced by an OH, and then there is a condensation to give the ketone?

>>8182085
>>8182127
That's a neat trick. Thanks senpai

Let's say I know next to nothing about science (physics, chemistry, and biology)

Then what books should I pick up? Is there a /lit/ starter kit?

>>8162166
I'm an undergrad EE student so I'll throw in my $0.02.

I believe that they would combine into one wave due to the principle of superposition.

Since the frequencies are different you would get some type of modulation, probably frequency I would think but honestly I'm not sure.

If you could see it it would look like this:

http://www.acs.psu.edu/drussell/Demos/superposition/beats.gif

>this is all assuming the wave guide is perfect

More reading :

http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html

>>8182272
My friend this is a lot more complicated than it seems. It's a hydrolysis reaction but Sn1 or Sn2 are improbable here. But I think because it it wants 3 steps do an Sn2 remove the Cl grab the OH proton and push the electrons to remove the CN. You will notice something is not quite right but turning a geminal diol to a ketone is 3 steps by itself.
Tell me if you want the more complicated answer.

>>8182272
the OH- forms a cyanohydrin via Sn2 by pushing out the chloride ion leaving group.

under basic conditions cyanohydrins decompose to form a carboxyl (ketone in this case) and hydrogen cyanide.

the reaction is driven by the evolution of HCN which is a volatile gas at just above room temperature

>>8182769
*carbonyl, my bad

>>8182769
Makes sense right, that's what I thought while writing my reply. But then I looked at the compound and noticed the you can't perform the Sn2 because the ring can't move to do the inversion. It's going to be an odd Sn2 if it happens.

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>>8182797
Damn, good point son
Beats me 2bh

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>>8182272
>>8182740
Here have the complicated method.
With 80% confidence and more than 3 steps.

>>8161749
Just wondering if someone who knows better can give me a bit of feedback on the following:

Let [math] \tau [/math] be a topology on [math] X [/math] such that [math] \tau [/math] consists of exactly four sets, namely [math] \tau = \{ \emptyset , X , A , B \} [/math], where [math] A ~ \text { and } ~ B [/math] are non-empty distinct proper subsets of [math] X [/math]. Then [math] A ~ \text { and } ~ B [/math] must satisfy exactly one of the following: [eqn] i.) B = X / A ~~~ (ii.) A \subset B ~~~ (iii.) B \subset A [/eqn] Proof. Since [math] \tau [/math] is a topology then the union of any two sets in [math] \tau [/math] must also be in [math] \tau [/math], since both [math] A ~ \text { and } ~ B [/math] are non-empty then [math] A \cup B = X [/math]. Suppose that [math] B \neq X / A [/math], then [math] A \cup B \neq A \cup \left ( X / A \right ) = X [/math] which is clearly a contradiction.

Next suppose that [math] A \not \subset B [/math] then [math] A \cup A = A \not \subset B \cup A = X [/math] which is a contradiction. A similar argument follows for (iii).

Next we need to show that [math] A ~ \text { and } ~ B [/math] can only satisfy one condition at a time. Clearly [math] A ~ \text { and } ~ B [/math] can't satisfy both (ii) and (iii) since [math] A ~ \text { and } ~ B [/math] are distinct by hypothesis. Likewise if we assume (i) then [math] A ~ \text { and } ~ B [/math] can satisfy neither (ii) or (iii) since then some elements of [math] B [/math] would be elements of [math] A [/math] [math] \blacksquare [/math]

This seems to me to be inelegant as fuck, but other than I'm fairly sure it's correct. In the last bit I should explicitly show what I've described, but it seems pretty trivial and I can't really be bothered to go into much more detail considering that I'm just self-teaching.

Anyone here with some experience in telescopes?
I've been thinking about buying some kind of entry-level scope after watching Stargazing Live(damn you Brian Cox).
What kinds of scopes would be suitable for someone completely new? Say I want to get a decent view of Jupiter and the Galilean moons or similar shit, without having to pawn a kidney

>>8182926
>since both AandB are non-empty, their union is X
Wrong. It could also be A or B (which correspond to your cases (iii) and (ii), respectively). The rest of your proof is bad because of this.

Can someone verify my work, or point out any mistakes I've made?

I need to determine whether x*y=x+2y+4 is: commutative, associative, has an identity and inverse.

Below is my work, can someone verify it, or if I made mistakes point out where the mistakes are? This is my first time doing such a problem. Thanks!


#1. Check for commutativity:

x*y=x+2y+4

y*x= y+2x+4

if x=/=y then not commutative so fails this case.

#2. Check for associativity:

x\*(y\*z) = x\*(y+2z+4)

=x+2(y+2z+4)+4

=x+2y+4z+8+4

=x+4z+2y+12

Next check,

(x\*y)\*z=(x+2y+4)\*z

= (x+2y+4)+2z+4

= x+2z+2y+8

Thus not associative

#3 Check for identity

x\*e=x & e\*x=x

x\*e = x = x+2e+4

=

2\*e = x-x-4

2e = -4

e=-2

So plugging this into the equation I get

x\*e = x+2(-2)+4 = x

Now check e\*x=x

I get

(-2)+2x+4 = 2x+2

So, doesn't have an identity.

#4 Inverse

If it doesn't have an identity then it follows it doesn't have an inverse.

>>8183067
>It could also be A or B

So the [math] A \cup B = A ~ \text { or } A \cup B = B [/math]? But isn't that only the case when, B for example, is the empty set or [math] B = A [/math]? In which case we know it's neither since the sets are non-empty and distinct. But if [math] A \subset B [/math] then [math] A \cup B = S ~ \not \in \tau [/math] but then we know that can't be the case since then [math] \tau [/math] wouldn't be a topology, which it is by hypothesis, right? Or have I misunderstood something.

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Have a simple math question that is stumping me for some reason. maybe someone can help.


If something costs $8 dollars after a 60% discount. What was the original price?

how to calculate this?

>>8183094
>But isn't that only the case when, B for example, is the empty set or B=A?

No. Like I just told you, it's the case whenever one is contained in the other. Since [math]A \cup B[/math] is nonempty and open, it must be one of X, A, or B. If [math]A \cup B = X[/math], then [math]B = X \setminus A[/math]. This is because [math]A \cap B[/math] is open as well, and [math]A \cap B[/math] cannot be X, A, or B; thus it is empty. If [math]A \cup B = A[/math], then [math]B \subset A[/math]. If [math]A \cup B = B[/math], then [math]A \subset B[/math].

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>>8182672
neato, thanks for the links.
Now here's a really stupid question.

Say you have the two waves going down this theoretical perfect wave-guide,
If both waves have 1 microvolt of energy, the output superimposed wave combo (whatever the hell you would call it) would be 2 microvolts across the entire wave right?
>assuming no loss perfect system garbage
Like, if you somehow measured the energy of the waves right at the low point and the high point of the beat, it would always be the same, right?

>>8183112
>1 microvolt of energy
Thatd be 1 milliJoule, and that depends on the power of the two waves and also the time frame over which you are concerned.

To determine the energy of the two waves you have to find the Poynting vector(power) of each wave, then integrate the power over a span of time.

Now, I seem to recall from my electromagnetics course that the principle of superposition does not apply to the power of the two waves due to the E and H fields being vector quantities, but I might be wrong there.

>>8183108
$8=.6x
$8/.6=x
Divide the discounted amount by the amount of discount, and you get original price.

>>8161891
Tao, as well as amann/escher are also good analysis books that start from the beginning (construct everything).

>>8183154
Okay I just checked my textbook and it seems that you just add each component up then find the cross product of E and H* to get the total power of the system. Then you'd integrate to get the energy.

Also, it the energies would not be the same as two waves can be out of phase with one another. You can have two waves with matching peaks, completely opposite peaks, and then just completely different

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>>8183154
So say you had two microwaves going down those guides, and say there were perfect opposite phase.
Would the measured energy at the points where it goes to zero, like the low points of the beats, be actually zero?

>I realize this is impossible, just trying to visualize it
For visualization say you were firing the microwaves into a substance that traps the energy perfectly where it's hit by the waves, and doesn't transfer at all

Would you have a hot spot, then a cold spot, hot spot, ect...?

Like would the microwaves just seem to disappear when canceled out and then reappear in a pastern?

what is the quickest and most efficient way to refresh all my biochem and ochem shit for the MCAT? I feel like digging up old notes and textbooks is not a good use of time

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>>8183219
Yea you can get some patterns like in pic related, but the type would depend on media and wave characteristics

>>8183227
That's fucking cool as hell.

>no i'm not nearly retarded enough to try this, just curious
So does that mean under extremely controlled conditions, you could have two very powerful microwave waves that were opposite phase and cancel out right a very particular point? And you could say take your hand and put it in that very particular point and be unharmed while something directly in front and behind your hand get utterly fried?

Also, thank you for explaining this to my dumb ass.

>>8183160
So what is original price?

>>8183241
Uhhh idk enough about it to accurately answer that, sorry buddy

>>8182569
Go to the wiki in the sticked post.

>>8172674
memes

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>>8183160
WRONG!

I figured it out! You're not paying for 60% of the original price, you're paying for what remains AFTER you discount 60%.

100% - 60% = 40%

So $8 dollars is 40% of the original price.

$8=.4x
x=$20

-------------------

It checks out:

$20 - 60% = $8

---

Also

$20 x 0.6 = $12
$12 dollars is the discounted amount

$20 - $12 = $8

>>8162235
10/16 is equal to (5*2)/(8*2) which is equal to (5/8) * (2/2) which is equal to 5/8. That's why multiplication works, so long as you're multiplying by a value of 1 (2/2 is equal to 1, after all). Exponentiation does not work because you're not multiplying by 1. When you do [math](5/8)^2[/math] you're actually doing (5/8) * (5/8), which is clearly not (5/8) times 1.

>>8182740
>>8182769
>>8182872
Thanks.

>>8182769
>>8182797
Why can't it be a Sn1?

>>8182042
left sided limit doesn't equal right sided limit probably.
kinda like exp(1/x) goes to 0 if you approach x from below and to infinity if you approach x from above

>>8184569
It could. The position is tertiary and the carbocation would be resonance stabilised by the nitrile. Alternatively, Sn1 is generally run in protic solvents using weak nucleophiles.

>>8162235
because the operation of exposing (squaring etc.) doesnt follow the same rules as the multiplicative operation on fractions

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If I get a double degree in Math and Business Management, where would it lead me?

Also how does it compare to ChemE in terms of pay and contribution to the betterment of society?