Ask your stupid questions here.
Here's mine: Let A be some finite set and 1_A be a mapping from set A to set A. I want to show 1_A (the identity mapping on A) is an isomorphism.
An isomorphism is defined as: gof=1_A and fog=1_B for f:A->B, g:B->A.
I need to find the inverse of 1_A which I know is 1_A but not sure how to formally prove it.
I was thinking of saying f:A->A: then I_A o f = I_A and f o I_A = I_A but I don't know if this is right. Can someone help?
well at least the question belongs in the thread
1_A o 1_A = 1_A
I don't know what more you need really
>>8117456
Yeah, it is so trivial I wasn't sure what to show. Thanks.
How do I integrate this from -1 to 1?
Who's the god in the pic
>>8117462
He contains all mathematical knowledge and wizardry. His other form is seen in the 'advance' version of this thread.
>>8117463
What's his name?
>>8117461
You integrate 0 from -1 to 0, then integrate 1 from 0 to 1
>>8117461
go back to the definition of riemann integrals
>>8117470
"magic the gathering guy" a.k.a "math genius guy" on /sci/
>>8117461
For every [math] \varepsilon>0 [/math] consider the function
[math]f_\varepsilon[/math] which is equal to [math] 1 [/math] for [math] x \in [1- \varepsilon, 1][/math] and [math]0 [/math] else. Then
[math] 0 \leq \int_{-1}^1 f(x) dx \leq \int_{-1}^1 f_\varepsilon(x) dx = \min(\varepsilon,2) \leq \varepsilon [/math]
Since this is true for every [math] \varepsilon>0 [/math] we must have
[eqn] \int_{-1}^1 f(x) dx = 0 [/eqn]
>>8117451
Do humans really affect climate change?
>>8117510
https://www.youtube.com/watch?v=ztninkgZ0ws
he explains a lot about what influences climate
>>8117516
>is an ice age coming
we're still in one
what university should you check if you're interested into body implants/nanomachines and all that kind of stuff?
>>8117614
he means in 12000 years
>>8117621
>body implants/nanomachines
no one is interested in a micropenis transplant, trust me.
How do you go from step 1 to 2? I don't see how you get that right side of the numerator to reduce down the way it does. I keep getting something different.
Is there an intuitive explanation for why the sum of all pos numbers is -1/12? I saw the numerphile's proof of it, but it is counter to all intuition.
s goes into a how many times?
>>8117887
it sure is. I didn't understand the numberphile explanation either.
>>8117887
It's not in the traditional sense. We have a thread on this every day. Try lurking or reading one of the hundreds of internet articles on this.
>>8117895
It makes no sense to me. The one I watched they showed what a few sums converge to and then used those facts to manipulate the fact that infinite summation of the positive numbers converges to -1/12. It's almost as if they just did a proof by using trickery, picking certain sums that add to things they needed to show the fact they wanted to present. It's like a magic trick and you're left wondering what the trick was.
>>8117897
Care to point me to a few? I don't see these threads everyday and tried googling it but keep getting the numberphile's explanation.
>>8117902
https://4gravitons.wordpress.com/2014/01/24/how-not-to-sum-the-natural-numbers-zeta-function-regularization/
We should just sticky a post about this.
>>8117886
they factored out (1+x^2)^(1/2)
>>8117905
sorry, they factored out (1+x^2)^(-1/2)
>>8117904
>https://4gravitons.wordpress.com/2014/01/24/how-not-to-sum-the-natural-numbers-zeta-function-regularization/
Thanks.
>>8117886
hope this helps senpai. they factored out [math] (1 + x^2)^{-\frac{1}{2}} [/math] in the numerator.
>>8117917
Thanks based anon
>>8117900
That's exactly how I felt when I saw it. LIke it was some smoke and mirrors bullshit.
M
what are the steps involved simplifying this:
(1/15((2x+1)^5/2)) - (1/15((2x+1)^3/2)) + c
into this
1/15((2x+1)^3/2)(3x-1) + c
how the fuck do I do this?
don't I need to know the force applied?
I certainly need to know how fast it goes
wtf
I am taking a community college professor who had a PhD. Does this mean this guy is an asshole who doesn't know how to teach?
>>8117461
Mumble something about Riemann integral doesn't care about single points and write 2
>>8117462
math meme man himself
>>8118167
(mg)(y)
>>8118237
it's horizontal
How do I solve using these formulas? No L'hopital's
>>8118431
Taylor expand, you fucknut.
>>8118167
Ezpz
>find the area between the curves x^2+y^2=R^2 and x+y=R
>when trying to find the intercept keep getting results like x=R and y=R which of course doesn't make sense
>for some reason I can't find an example of this question no matter where I search
why
How do I force myself to study?
Drugs, punishment, rewards, etc. What works best?
>>8118568
lighting your computer on fire.
>>8118563
The intercepts are (x,y)=(R,0) and (x,y)=(0,R). The area is just pi/4 R^2 - 1/2 R^2
>>8118631
That doesn't make sense though, shouldn't it be 0.707R?
hey guys my Real Analysis exam is worth 70% and insemester work 30%(I gotted 12.74/30=42%). I need to get 41/70 (58%) to pass. Will I make it :/?
My exam is in 3 days; will i pass? I've finished two practices exams and redone four problem sets and 7 more to go >.<.
the exam allows one sided cheat sheet, but my course doesnt have metric spaces. What should i put on my cheat sheet?
>>8118569
what if i theoretically need a computer to code even though i don't ever code
for those who do not hypothetically code, this is good advice, water damage also works
What do Software engineers use calculus for?
>>8118649
> 50% is passing
Nigga, what kind of grade inflation bullshit is this? Where do you go to school? We had 10 point systems (60 is passing, 70 is C- (or C), 80 is B- (or B), 90 is A- (or A)) which seemed generous, but what is this? Also, do they curve? I had a class where I got ~40/100 points and got a B-, lol.
>>8117451
Suppose a single particle is broken into an infinite number of equally sized, infinitely small pieces. If a particle equally massive to the original particle and the infinite number of particle fragments are propelled at equally sized objects in the same exact manner, would there be any difference in how much the targets are displaced? Or does having an infinite supply of infinitely small fragments result in an infinitely high output?
>>8118692
They rarely use it for anything.
What is your answer to the Fermi paradox?
>>8118708
Fucking Monash. All the math units/subjects weighted percentages are 70% exam and 30% assignments/tests.
Normally, students that get 20+/30 have a better chance of passing...
But honestly do you think a three hour exam thats worth 70% of your grade, sucks? I mean they can pull any cuntish questions in the exam. *sigh* everyone; please just call me a brainlet.
Why is it that for quarks the mass eigenstates are identical to the qcd eigenstates?
>>8118649
Just draw a big breasted woman
>>8118738
In the real world this isn't possible.
In the abstract mathematical world, you should take a look at banach-tarski. But, yeah - it would be infinite.
Having trouble solving this problem. According to the solution, the acceleration of aA=.5aB. But wouldn't they have opposite signs since they are accelerating in opposite directions? i.e: aA= -.5aB?
[eqn] (x2-2x+3)^1/2 - (x2-2x+3)^3/2 [/eqn]
What are the steps in simplifying the above
into this:
[eqn] (-2x+2x-x2)(x2-2x+3)^1/2 [/eqn]
Is psychology considered a science?
Random question that popped up while studying classical fields.
When you define the field equations to be isotropic, does that induce a spherical symmetry on the equations? It would explain where the factor 4\pi comes from.
If not, where does the spherical symmetry then come from? Is the factor 4\pi only for 3D?
>>8118649
Probably not. My Real Analysis final was murderous.
>>8119212
Are they accelerating in opposite directions?
I'm just kidding, that's one of those teacher questions people use when they don't know.
You're right.
What are some good prereqs with regard to math that would be useful when self studying classical mechs and electromagnetism?
Kind of a game theoretic / stochastic question
Imagine 2 players shooting at each other in an alternating way (player 1 shoots first, then player 2, then player 1 again and so on) until someone dies.
They don't have perfect aim, so they will only hit with a probability of p_1 and p_2.
How do I calculate the probability of for example player 1 surviving?
I already did it numerically, but it would be nice to have a closed form solution.
How am I meant to remember all of these for my exam.
They take forever to derive from fp and are only a small part of the exam, but any of them could come up
hardest / most complex fields of math?
>>8119955
Use Markov chains to represent the state vector for (p1hp, p2hp) and the changes as a transition matrix. Then just keep applying such a matrix.
>>8119987
never worked with markov chains so far.
would you be so kind to tell me what the transition matrix should look like?
I should be able to do the repeated application with eigenvalues/vectors
>>8119985
how much do you know
I'm having trouble getting an intuitive feel for the motivation behind constructing a normal subgroup from a group.
Also, does being cyclic have anything to do with normal subgroups? The process of constructing residue classes eerily seems like it is. I understand that given a group G and h in G we can make a subgroup H = <h> = {h^n : n an integer}. We then make the left (or right) cosets by multiplying everything H by x. If x is in H then we get H since of course H is closed to be a group. If x is not in H (not in the cycle <h>) we get the coset Hx.
Is the fact that that xH may be different from Hx lead us to the importance of normal groups? Sorry if this isnt a very well formed question.
>>8119985
high level algebraic geometry / arithmetic geometry
i would include IUTT but i've never done any IUTT so i don't know how hard it is
>>8119955
>>8119997
I got the solution now for anyone interested.
The transition matrix is
[math]
A =
\begin{pmatrix}
(1-p_1)(1-p_2) & p_2(1-p_1) & p_1\\
0&1 &0 \\
0&0 & 1
\end{pmatrix}
[/math]
where the first column contains the probabilities that
-nobody dies
-player 1 dies
-player 2 dies
in one round.
the second and third column just describe, that once a player is dead, they stay dead.
With some eigenvalue trickery, we get
[math]
\lim _{n\to \infty} A^n =
\begin{pmatrix}
0 & \frac{ p_2(1-p_1)}{p_1+p_2-p_1p_2} & \frac{p_1}{p_1+p_2-p_1p_2}\\
0&1 &0 \\
0&0 & 1
\end{pmatrix}
[/math]
which leads us to a probability of [math] \frac{ p_2(1-p_1)}{p_1+p_2-p_1p_2} [/math],that player 1 dies
>>8117887
if numberphile gives me 1$ + 2$ +..... then i will give them -1/11$s just to be nice
anyone think the proof of fermats last theorem is not legitimate in the sense of fermat not being involved with that branch of maths?
>>8120319
that would make a lot of proofs illegitimate and is pretty arbitrary.
Would you think the proof would be more legit, if wiles was the first one making the conjecture?
>>8120334
i guess so yea.
I can't for the life of me remembers how a certain type of diagram is called.
It's something in electronics when you're talking about basic transistors and NP juncties etc. They draw like valleys and hills with electrons on wone side and wholes on the other site. I think. It has something do with visualizing the voltages as gravity or something.
I don't know. I just took a sleepingpill, so I'm feeling pretty stoned.
>>8120539
I didn't know those diagrams had a name.
>>8120547
"energy band diagram" is apparently how they're called, but aster 3 years of seeing them everywhere, I still don't have the slightest idea what they mean
>>8120556
they just represent the potential energy of particles with a certain charge as a function of position.
This allows you to easily visualize it and you can superimpose the density of said particles to see how a certain potential shape results in a certain distribution of particles
>>8117510
>Do humans really affect climate change?
Everything effects climate change.
Even the dim starlight in the night sky effects climate change.
Your question is too vague to have an answer of any significance.
Solar cycles play the primary part in earth climate, as would be expected, as the primary energy input in this non closed thermodynamic system.
>>8117621
>what university should you check if you're interested into body implants/nanomachines and all that kind of stuff?
Hardware backdoor exploits.
>>8118738
>Suppose a single particle is broken into an infinite number of equally sized, infinitely small pieces.
It wouldn't matter as their mass would be infinitesimal.
>>8118751
>What is your answer to the Fermi paradox?
Optical cable.
>>8120714
What is this continuously divisible to infinity bullshit? The answer is "fuck you, it doesn't work that way, there are fundamental particles". Math is dope as shit but not all is equivalent to the real world.
Prove that if f: A->B and k: B->C are isomorphisms, k o f: A->C is also an isomorphism.
Definition I am using: A maps f: A->B is called an isomorphism, or invertible map, if there is a map g:B->A for which g o f = 1_A and f o g = 1_B. A map g related f by satisfying these equations is called an inverse for f. Two objects A and B are isomorphic if there is at least one isomorphism f:A->B.
My attempted Proof:
Let f: A->B be an isomorphism with inverse g: B->A. This means g o f = 1_A and f o g = 1_B. Let k: B->C be an isomorphism with an inverse h: C->B, this means h o k = 1_B and k o h = 1_C.
Then g o h o (k o f) = 1_A and (k o f) o g o h = 1_C thus we see that k o f: A->C is isomorphic.
Is this correct?
>>8119490
>>8120167
The intuition is that you have to require a subgroup to be normal for quotienting to give a well defined group.
>>8120759
sorry bout that, couldn't posttextitfor sum reason.
>>8120732
That's not what isomorphism means though. Just show bijectivity and multiplicativity, which is very easy.
>>8120766
It is what isomorphism means in Set.
>>8120766
he clearly means set isomorphism, which is bijectivity
>>8120774
there are many kinds of isomorphisms. "set isomorphisms" are bijections and are what you're looking for
>>8120781
Yes, set isomorphisms are bijections.
Is my proof correct?
If not, how would you prove it using set isomorphisms?
>>8120781
Fucking category theorists
>>8120766
What if the objects are topological spaces? Even loosely interpreting multiplicative as continuous, your post still won't prove isomorphism.
>>8120787
your proof is perfectly correct, as it's easy to see from your every step
>>8120789
Isomorphisms are canonically defined for groups you dumbass. Faggot category theorists decided to use the word "isomorphism" for "structure preserving bijections" for every category out there, which means that in Top isomorphisms are homeomorphisms, which has nothing to do with groups.
>>8120788
What the fuck do you expect?
Do you just want us to use the same definition for everything?
Isomorphism of Sets = Isomorphism of Groups = Isomorphism of Modules = Isomorphism of Manifolds = Isomorphism of Schemes = etc.
How would that make sense?
>>8120793
Ok great, thanks man!
>>8120796
I want you to use different words to describe different shit you fucks.
>>8120795
I must have missed where the OP was taking about groups when he uses words like "objects" you fucking mong.
>>8120802
People talk about isomorphisms are usually talking about groups or vector spaces you fucking cunt. Not everyone is a gay ass category theorist
>>8120805
Well when OP uses terms and definitions from category theory, it's pretty reasonable to assume the guy is thinking about categories.
>>8120789
The objects in this category are defined as sets and the arrows are defined as functions.
Isomorphisms are defined as he described them.
Read the sentence starting with...
"Isomorphisms are formalized using category theory..."
https://en.wikipedia.org/wiki/Isomorphism
&
https://ncatlab.org/nlab/show/isomorphism
>>8120811
>what is reading comprehension
>>8120809
I'm not sure what you're trying to say here. When was it stated that we were using the category of sets?
>>8120816
you said
>People talk about isomorphisms are usually talking about groups or vector spaces you fucking cunt
and it's blatantly false. all you mean is you've only seen group morphisms.
>>8120817
OP gave the definition for set isomorphisms. suddenly someone asked for "multiplicativity" like it mattered.
>>8120818
>an anecdotal statement is blatantly false
You're a special kind of retard aren't you?
>>8120817
It follows from the definition,
>'A maps f: A->B is called an isomorphism, or invertible map, if there is a map g:B->A for which g o f = 1_A and f o g = 1_B. A map g related f by satisfying these equations is called an inverse for f. Two objects A and B are isomorphic if there is at least one isomorphism f:A->B.'
>>8120795
you say
>isomorphisms are canonically defined for groups
but you really mean
>I only took algebra 1 thus far and that's all I've ever used it for
>>8120821
if you mean
>people [in my algebra 1 class] are usually talking about groups or vector spaces you fucking cunt
then say so, underage faggot
>>8120826
Or that I'm not a category theorist you stupid idiot.
>>8120829
No.
>'A maps f: A->B is called an isomorphism, or invertible map, if there is a map g:B->A for which g o f = 1_A and f o g = 1_B. A map g related f by satisfying these equations is called an inverse for f. Two objects A and B are isomorphic if there is at least one isomorphism f:A->B.'
all isomorphisms need to be invertible, but all of them (except ONLY set isomorphisms) need more conditions
>>8120832
>wahhh I'm an idiot
ring morphisms, module morphisms, algebra morphisms, monoid morphisms, order morphisms, ...
>>8120834
If by "map" you're trying to say "set function," then yes, but you're using that word wrong.
>>8120836
Are you fucking retarded? Are you implying non category theorists would use the name "x-morphisms" for object specific invertible maps?
>>8120845
Every single thing he listed gets said. Are graph isomorphisms far enough from category theory for you?
>>8120845
no, invertible maps are usually qualified as injective X morphisms, or X-monomorphisms
what I am stating is that anyone who took a couple of algebra classes at least refers to structure preserving functions as morphisms
saying something as ridiculous as
>isomorphisms are canonically defined for groups
shows you only took a single algebra class, and only saw groups in it
>>8120848
>I don't know what canonically means
>>8120850
show in what way you claim it is canonical or shut the fuck up, you underage imbecile
>>8120850
I'm starting to think you don't, and that's what the confusion is.
>>8120856
>I was only pretending to be retarded
> arguing about terminology
>>8120858
>still this autistic
These two are piss easy double integral and triple integral problems. I don't understand this notation though. Anyone has any idea of what does it mean?
>>8120879
Lmao what the fuck am I looking at? Just integrate in order
>>8120879
someone fucked up latex
So I've been wondering... If the outer edge of the universe (surface area) expanded at a constant rate, would that make the volume of it expand at an accelerating rate? Meaning that the universe isn't really expanding faster due to dark energy, but due to a constant expansion of the universe's "surface"
>>8120886
That's what I thought, but I'm 100% sure that after I turn it in they're gonna say that the snake symbol was x/y and fail me. Also the second problem is lacking a dx/y. I was just hoping this was some advanced notation but I guess it's not. Thanks.
>>8120898
you sound like you're trying to make up shit about a field you don't understand. taking out all of the nonsense, if a region's surface measure increases at a constant rate, its internal measure increases at a linear rate
>>8120902
The "snake symbol" is i dumbass. It's the root of -1.
>>8120913
It's an inverted question mark you fucking tech-illiterate child, how long have you been on the internet?
>>8120916
Jesus you're a retard. Of course I know what it is dumbass. What I meant is that it's common to use that symbol as a stylized i to represent the root of -1, while you use the normal i to represent a variable that has nothing to do with negative roots.
>>8120926
Says the retard who thinks double and triple integral of i with respect to nothing is what is intended.
>>8120933
That's exactly what I'm saying, because the root of -1 is a constant, so you can integrate the other stuff and add that later on. You don't even know how to integrate and you're talking shit.
>>8120936
I'm not. In advanced mathematics sometimes you have so many variables that you run out of letters to represent them, and when that happens you try to represent constants with symbols that are not letters, so you can keep enough free letters for actual variables. In that context ¿ is used as an stylized i and it's reserved to the root of -1. You guys should know this stuff.
>>8120969
Pray tell what combination of variables of integration the triple integral implies, brainlet.
>>8120984
Obviously those should be at the very beggining, integrating the xy+yyy. Either you're autistic or in full damage control.
>>8121011
>integrating the xy+yyy
For the third time, with respect to what, mouthbreather? dx^3, dx^2dy, dxdy^2, dy^3
>>8121014
It says it right there too. I get it, you're in full damage control. Stay mad queer.
>>8121021
>i'm too stupid to look at the image i'm explaining
Thanks for the enlightening conversation. Dunno if you're staring at dxdy like a child misunderstanding the question or just throwing shit at the wall.
>>8121023
Of course I'm staring at dxdy fag. I'd ask you to enlighten me so I can laugh at the retarded shit you would say, but to be honest I don't want you to make an ass out of yourself further.
>>8121027
>triple integral
>two differentials
Go back to high school.
>>8121030
DING DING DING!
After you integrated the first two and evaluated the 3S0 only one variable is left, of course you're gonna be integrating that variable the third time, because the other one doesn't exist anymore. You're a retard if you did not realize this sooner, and I tried to defuse your autistic rage so you wouldn't expose yourself as the retard you are, but you just had to say it didn't you. You're a basket case kid.
>>8121035
This is the best /sci/ rekt i've seen in a while i almost want to believe what you said about the snake thing.
>>8121035
>the other one doesn't exist anymore.
Are you confusing integration with differentiation? I feel bad for you now. I'm almost sorry for calling you a brainlet, brainlet.
>>8121055
Damage control harder faggot. You do realize that definite integrals result in plain numbers and a variable is eliminated in that process right? I'm feeling bad for you right now.
>>8121060
Are you telling me that braindead notation implies three definite integrals with the same bounds on different variables? Who the fuck writes that? I concede, you are fluent in retard.
My computer room is always a lot hotter than every other room of the house even when the air conditioner is running. Is it possible that I'm generating so much heat from my computer and my own body that this hot air is clogging the vent from bringing in cool air?
>>8121075
>they clearly botched the problem when they typed it
>"are you telling me that the problem was typed wrong? i'm just realizing, you must be retarded"
AUTISTIC
U
T
I
S
T
I
C
>>8121079
>the problem is formatted completely wrong in every way but i know EXACTLY what it means
definition of autism
>>8121082
There's exactly one way it could be that it would make it solvable, I can tell you that. Not like I hope a retard like you to catch on that kind of stuff anyway.
>>8121083
Why don't you browse wiki with your encoding forced to shift-jis and tell me what other miracles you discover, rainman.
>>8121088
>I can meme my way out of all the stupid shit I said that was wrong and people forget how retarded I looked
You should stop defending your position already, you will be ashamed in the morning. Just close the window and don't ever come back to this thread, pretend that it didn't happen, and once the thread dies no one will remember it. If you keep acting retarded your only risking yourself to being screencaped and then you will relive the shame every time you see it posted. This is pretty solid advise that you don't even deserve DESU.
>>8121077
>Is it possible that I'm generating so much heat from my computer and my own body that this hot air is clogging the vent from bringing in cool air?
No. I hope you were trying to be funny and this isn't an actual question.
>>8121091
I'm too sleepy for this, but I find it incredibly amusing that you are so adamant on an interpretation of completely broken disorganized notation. You are making more assumptions than you admit. You have to re-order the lines first before squeezing them together, add an implicit differential, and interpret the single bounds as intended on all three integration steps. Oh, and the inverted question mark used for i clearly means we should put it in parens after the second term. And the second inverted question mark i after the double and triple integrals, let's just ignore that one I guess.
It's more than a little bit of shitty formatting, yet you are standing by the one true interpretation like autismo supremum.
Night night anon, the thought of being wrong on the internet will haunt me just as much as I'm sure it haunts you. Tenks 4 advise.
>>8121101
>I'm too sleepy for this
Me too. To be honest I'm the dude who posted the problems originally, I just wanted something to do while I do my homework and I made everything up. Thanks for the keyboard battle. Sleep tight.
I'll be starting Physics I on Monday. The syllabus says that I need Calculus I. What do I need to brush up with Calculus I to do well in Physics I?
>>8121106
Hey man, respect, someone's gotta keep this place trashy.
>>8121107
You need to be able to derivate and integrate simple functions. That's because acceleration is the derivative of speed (or the other way around) and you can get one formula from the other using calculus; stuff like that. It isn't really necessary but it helps if you can do basic stuff.
>>8121112
>being this passive aggressive over the Internet
You sure are mad. Cry me a river queer.
>>8121114
>passive aggressive
That comment was 100% honest, but I recognize that tone does not carry through text. Sorry for making you feel sad. If I was that easily butthurt I wouldn't be here.
>>8121118
>If I was that easily butthurt I wouldn't be here.
>>8119981
Actually use them to solve problems, so, find some problems that you need to use them in, and then do a lot of those problems. DO NOT just memorize them.
>>8119985
1. do your own research. different fields of math are more or less difficult for different people
2. there is not such thing as a "hard" or "easy" field of math, only ignorant and knowledgeable mathematicians
3. discrepancy theory
4. don't listen to the people saying algebraic geometry.
5. everyone says algebraic geometry.
>>8119985
This question makes no sense. There are easy problems and there are difficult problems. Any famously unsolved problem is likely to be very difficult because many competent people have tried and failed. All "branches" of math have such famously unsolved problems.
If a scalar field is a field where every point in space has a value defined, and a vector field has a value and direction at every point in space, can you have a field where there is a vector field at every point in space. And what properties could it have
>>8121378
Yes, a general tensor field.
An example would be a quadrupole field (eg. Two anti-symmetric electric dipoles). There's not really anything more exciting about them as opposed to vector fields and scalar fields. In fact - scalars are 0-tensors and vectors are 1-tensors.
>>8121385
cool. What about the same situation but every point on field has another field at every point which also has another field at every point, and eventually somehow comes full circle until after some n number of iterations you get the initial field you started with, all governed by some kind of continuous albeit arbitrarily complex function of some description.
>>8121395
No, you're drunk. You can keep going up in dimension of the tensor field though. Eg.
For a dimension rank n you have the number of components in tensors:
Scalars, 0-tensors - n^0=1 components
Vectors, 1-tensors - n^1=n components
2-Tensors - n^2 components
And for a general tensor of rank m in a dimension of rank n you have n^m components.
>>8121408
no you're a towel
Can a tick transmit rabies?
[eqn]\beta = S e^ {i \phi} \hspace{1cm}
-1 \leqslant S \leqslant 1 \hspace{1cm}
0 \leqslant \phi \leqslant 2 \pi \hspace{1cm}
\beta \in \mathbb{C}[/eqn]
How do I write an equation such that [math]\phi = f(S, \beta)[/math]? This seems like it should be retardedly simply, but I keep getting an equation that can give complex numbers, and obviously [math]\phi[/math] has to be a real number.
>>8121606
IT DOESNT WORK BECAUSE THE MAPPING ISNT INJECTIVE FAGGOT
>>8121606
if -1<s<1, the complex exponential is never going to give you a value as big as 2pi
what is the area of a circle with radius i?
When looking at a probability equation like pic related,
What does the P(n|M) represent, or more importantly, the (n|M) portion?
I see it all the time in my field of study and I can't figure it out.
>>8121744
probability of n happening given that M happened
>>8121744
Conditional probability. P(n|M) is read "the probability of n given M". If you've had calculus and discrete math, you should check bout an intro to mathematical statistics text.
I was thinking about the possibility of a quantic universe.
Given a 3d space with dimensions x,y,z and the existence of n of particle 1,m of particle 2,o of particle 3, p of particle 4.
How would i go to calculate how many possible states there are in this system?
>>8121847
There are infinite states unless you introduce some kind of quantisation, in which case the density of states will become finite.
Does Dalton's law work for mixes of different quantities(in moles) of gases?
>>8121854
>I was thinking about the possibility of a quantic universe
Yeah, exactly my point.
particles are 1x1x1 cubes and the space is divided in 1x1x1 spaces.
How would i go to calculate that, given that all particles must be used?
>>8121859
Do you mean that each 13 space can contain maximum of one of each particle, or only one from the choice of 4?
>>8121874
>occupying 1x1x1 spaces with multiple 1x1x1 objects.
A single cubicle can contain a single particle m8
>>8121879
>That's exactly how our space-time works...
@8121897
>baiting this hard
Won't even give you the satisfaction of replying to you.
By the time you spent shitposting i actually took the time to write it down myself.
>>8121723
-pi
How do I prove that [math]\gamma:[0,\pi/2] \to \mathbb{R}^2, \gamma(t) = (2x,cos(2t)^T[/math] has arc length of
[math]2\sqrt2 \int_0^{\frac{1}{2}\pi} \sqrt{1-\frac{1}{2} \sin^2(t)}dt[/math]?
I am trying to show that it's equal to [math]2\int_0^{\frac{1}{2}\pi}\sqrt{1+\sin^2(2t)}dt [/math], but I am not sure if this is the right way to go about it, considering that I don't know how to actually integrate either of those.
I would really appreciate a nudge in the right direction.
So if NaCl dissociates into Na+ and Cl- in aqueous solution, what prevents the now-independent sodium atoms from reacting violently to the water, like pure sodium does?
Hello, I am really sorry to be a bother, but would you mind correcting my work? (and showing me how to solve the third one?) Thanks.
A line l intersects the parabola y=x^2 at two points, (a, a^2) and (b, b^2) b>a.
1. Calculate the area bordered by the line and the curve:
2. If l is perpendicular to the tangent line to the curve at (a, a^2) Express a in terms of b.
3. When (2.) holds true, find the minimum area m of S in terms of b. For what value of b, the area is minimized?
Say there's an object A traveling with a force F1. At the tip of A there's a second object growing in the same direction, extending with a force F2 relative to its base.
From an external point of reference, is the force exerted at the tip of B equal to F1 + F2?
>>8122190
the key here is that they are ions and that it's not Na in the water. Because the ions take a lot more energy to lose an electron, the reaction between the Na+ and H2O is no longer exothermic and probably isn't favorable thermodynamically.
>>8122336
we will not do your homework
>>8121606
phi=arg(beta/S)
>>8122383
Thanks!
>>8122374
>traveling with a force F1
maybe try and look up some of the terms in the question you want to ask, this phrasing doesn't make much sense
You know how a person running on a suspended log will cause the log to spin?
If one was to do repeat this process in space, using a some force to keep the person on the log, would it to an observer from a neutral frame of reference:
A) The person remains still while the log spins underfoot
B) The log remains still while the person circles the log
C) Some combination of both?
>>8122415
Depends on the motion of the observer. They can either be motionless relative to the runner or to the log- they can't be "objectively" still.
>>8122414
It's moved by a constant force of magnitude F1 at a speed that's not relevant to the problem. Is that really not clear enough?
>>8122415
heheh but seriously, that;s not the way to do it.
first you tell her you have candy, then comes the chloroform
>>8119212
>But wouldn't they have opposite signs since they are accelerating in opposite directions?
lmao
>pic related
>>8122415
> using a some force to keep the person on the log
The answer depends upon the nature of that force.
If it pulls the person toward the axle, the person will rotate around the log. As the force has no moment (torque), net angular momentum will be conserved, so (assuming that both the person and the log are initially stationary) the person will have angular momentum equal and opposite to that of the log.
If the force has a fixed "down" direction, then you're simulation the earthbound situation. The log will rotate, the person won't. The person will place their centre of gravity so that it's slightly "behind" the axle (in terms of running direction), so the torque arising from the downward force will counteract the torque from running (in effect, the running motion will be simply be transferring this torque to the log).
Ohm's law says that V=IR. Let's say that I have a 9V battery and then I add a resistor of X magnitude. Will that resistor affect the voltage or the current or both? Am I right to assume that the voltage anywhere in the circuit is always 9V and that what changes is the current?
>>8122485
V/R=I
>>8122501
I know that, but that's not what I don't understand. Let's say that V/R=I takes the values 500/100=5, and then I change the 100 to a 50. The result can either be:
500/50=10 (affecting the current) or 250/50=5 (affecting the voltage) or any x/50=y (affecting both). How do I even know what happens?
I'm thinking that since voltage is related to the amount of electrons and the electrons are flowing from the - of the battery to the +, then the V across the circuit is constant because electrons can't escape anywhere. I could add as much resistors as I wanted of any magnitude and V would still be 12V, but the I would change because the resistors make the electrons travel slower. Is that so?
>>8122511
As I understand it, voltage does change throughout the circuit. But I'm only just learning this stuff too.
This might help:
https://www.youtube.com/watch?v=paDs-Hnmklo
>>8122485
A battery behaves like a voltage source (with some built-in resistance).
So the voltage will be 9V and the current will be 9/X amps.
For small values of X, the built in resistance R will matter, so the current will actually be 9/(X+R) and the external voltage will be X*9/(X+R) (i.e. X times the current).
I'm having such a hard time understanding Euclid's definition of same ratio. I'm using De Morgan's illustration of the colonnades... Can anyone try to say something intuitive for me?
The algebraic (ma = nb ⇔ mc = nd) explanation makes sense to me.
Why do satellite images of hurricanes look similar to hubble images of galaxies?
>>8122511
Both of your possibilities would be true, if you used a voltage source (which has a constant voltage and variable current) or a current source (constant current and variable voltage).
Batteries are a voltage source. The difference in electrochemical potential produces a voltage, a (relatively) constant voltage, which may cause a current to flow.
In contrast, there are no such things as actual current sources. An ideal current source would have a current, and by ohm's law, must be pushing that current through some resistance. If you had open air, like 100 megohms, the voltage produced would be 1A * 100MO = 100MV, delivering 100MW of power (1A * 100MV) An ideal current source is quite literally a free energy device.
A battery can function in open air 1.5V/100MO = 15nA, with 22.5nW of power delivered.
>>8123012
>>8122511
Also, LOL, I didn't read your second question. Electrons in a circuit travel at a constant speed based on the metal through which they're going. Copper is something like 80% the speed of light, at least. It's the quantity of electrons flowing. Literally, ampere is the description of coulombs per second, coulomb being a measure of charge. As all electrons have 1 unit of negative charge (not a coloumb), and there aren't any extra large electrons or other charge carriers we can use, ampere directly translates into quantities of electrons per second.
Physics Question
Nuclear binding energy irks me, kinda like a double negative or something. When you either fission or fusion something and the products end up with a higher binding energy, how does that relate to how energy is released?
Binding energy is the amount of energy required to split a nucleus apart, yet how does combining or splitting atoms create energy when they form more stable elements?
Is it something to do with how the atoms are in a lower energy state? How does this combine with increasing energy per nucleon, wouldn't that mean it is gaining energy?
Anyone have a better perspective on this?
>>8123076
Not an expert in nuclear synthesis, but I would expect that there's an analogy to chemical reactions. You have an energy cost to start the reaction, but it may turn out that the end result is energetically favorable--and so some energy is released as heat after all's said and done. It costs a lot of energy to break down nuclear bonds, but if the products get to then react with other nuclei around the net result could be a lower energy state --> energy released.
1/0!+1/1!+1/2!...=e
1/0!+1/2!+1/4!...=(e^2+1)/(2e)
You get n=1 from the definition, n=2 by using the sum of e^x+e^-x. Wolfram has closed forms for n=3 and 4, but don't know how it got those. Is there a closed form for arbitrary n?
So if you considered the open interval [math](0,1)[/math], and then looked at it as strings of digits, for instance [math]x\in R = 0. x_{1} x_{2} x_{3}...[/math], you could map each digit [math]x_{n}[/math] to [math]p^{x_{n}}[/math], where [math]p[/math] is the [math]n^{th}[/math] prime in [math]\mathbb{Z}[/math]. Since [math]\mathbb{Z}[/math] is a unique factorization domain, this map is injective.
Does this prove that you can have an injective map from an uncountably infinite set into a countably infinite set?
>>8123546
No you idiot. Just because you don't understand Cantor's proof doesn't mean it is wrong. It is a proof motherfucker, under the same set of axioms it is literally impossible to disprove it, that's the whole point. Go read the Wikipedia page of Cantor's diagonal argument again.
>>8123546
Think of a number like 1/3=0.333333....
Then your function matches it to [math]2^{3}*3^{3}*5^{3}*7^{3}...[/math]
This is an infinite product of integers, so it's not a valid number. Thus, if you have a decimal that doesn't terminate eventually then the function doesn't work on it.
>>8123590
I mean, it is a dumb questions thread. Besides, he just wanted to clarify the concept to himself. No need to get that angry.
>>8123335
>Is there a closed form for arbitrary n?
Yes, you could use the n-th roots of unity. https://en.wikipedia.org/wiki/Root_of_unity
>>8122078
>but I am not sure if this is the right way to go about it
It is. You can get the second integral by a direct application of the arc length formula. The first integral simplifies to
[math] 2 \int_0^{\frac{1}{2}\pi} \sqrt{1+ \cos^2(t)}dt [/math]
To show that the two integrals are equivalent, you just need a suitable substitution which converts sin(2t) to cos(t).
Why are loops considered as 2 edges?
if i major in commerce, will i still have a job in 30 years time?
>>8123692
They enclose 2-cells.
Where is the distinction between isomorpic and equivalent important?
>>8124069
If you are investigating different properties.
i.e. In the Diff category, two manifolds are isomorphic if they are diffeomorphic. This is a perfectly fine equivalence from a topological perspective, but if you want to consider them equivalent geometrically then you need more. They need also be isometric.
>>8123076
During both fission and fusion the same amount of nuclei take part both before and after so the change in energy is the difference in the binding energy/nucleon of each reactant/product.
Doing this you might find and expect fusion leading to a bigger nuclei to take energy in. However similar to gravitational potential energy the binding energy is actually a negative kinda of quantity. It's defined that the potential energy due to the nuclear strong force is 0 at infinity and as two nuclei get closer they lose potential energy. The total amount of energy the ingredients to form the nucleus would lose as they fell in from infinity is called the 'Binding energy' of the nucleus, which is written as a positive quantity.
You can maybe think of this as analogous to the GPE lost by a mass as it fell towards two planets and it picked up KE. Both planets contain the same number of atoms except one is pure iron and one is pure gold. The total amount of energy lost is higher for the planet made of gold, although this potential energy is actually negative as it is lost as it falls.
Why the nuclei change binding energy per nucleon as the number of nucleons change is quite a different reason and is kinda similar to electron energy levels in chemistry
Is it possible to quantify sadness?
Like either from observing brain activity or possible measuring the levels of some chemical like dopamine.
>>8124191
I don't think we can quantify anything that goes on in the human brain.
>>8124210
Its all chemicals, so yeah I think we could.
Also, you can use probability to measure anything that's not truly random.
>>8124069
Isomorphism is kind of blurry. It says that looking at some particular property or structure on two objects, they are indistinguishable. If we are willing to merely see the real vector space structure underlying C and R^2, we cannot tell them apart -- they are isomorphic. However, these objects are different when looked at some other way, say as rings.
>>8122910
The universe is written in complex n-dimensional numbers instead of the real line.
>>8117451
why the shit is latex broken
>>8124254
You mean on /sci/ or the markup language in general?
Undergrad currently.
If I want to do research (as a Computer Science professor) in logical systems and languages, should I start by studying the wikipedia page for Expert Systems and maybe pick up a book on ProLog?
>>8118187
I had a cc professor for linear algebra who was amazing. He taught a rigorous proof based course that made all the engineer tards tremble, all the other professors were doing braindead calculator shit the whole semester.
He worked for like 20 years at Math Works and really knew his shit.
>>8122910
Why do spirals look like spirals? Why do those objects form spirals?
>>8119612
I'm a mathematician so I'm not extremely well versed in classical field theory but I'll take a stab at it.
Isotropy and spherical symmetry are definitely different.
In your case (I don't know exactly what physicists use the work isotropy for) they could be synonymous, if not I can help shed some light.
In the mathematical literature, here's what an isotropy is:
Suppose we have a group [math] G [/math] and a group action [math] \sigma [/math] , an isotropy [math] G_x [/math] on a space [math] X [/math] corresponds to the elements of [math] G [/math] that fix [math] x [/math] .
So what's most likely going on in the mind of a physicist would be [math] G=SO(3) [/math] and then the choice of [math] x [/math] would define a group of isometries that characterizes the rotational symmetry around the axis that [math] x [/math] lies on.
[math] x=(0,1,0) [/math] would describe rotational symmetry around the y-axis.
I have to add though, physicists often use different terminology and it might just be pure [math] SO(3) [/math] symmetry that they're referring to.
39) Consider the vectorial space V = M (2,2) and the linear transformation T: V -> R3
T([...]) = ([...])
a) Show that T is linear.
b) Determine [T]ab with A and B being the canonical bases of M (2,2) and R3,
respectively.
c) Calculate v E V with T (v) = (3,-2,4)
d)Determine N (T) (nucleus of T)
I don't know how to start. Please, help.
>>8124470
>I don't know how to start
What? Just use the definition of linearity etc.
>>8124470
Read your book HUE-kun
>>8124470
This is really easy anon, start with the first one using the definition of a linear function: T(av+by)=aT(v)+bT(y)
Is 13.4 ms^-1 the right answer?
Say there's a guy with mass m falling through the air headfirst with his body vertical, like pic related. There's a second guy on the ground, standing next to the diver's landing spot. As he's about to land and without concern for his own safety, the diver whacks the second guy on the head with a perfectly downwards haymaker, swung with force F.
Is the force the standing guy is hit with just F, or F + mg? Keep in mind the falling guy is just hitting with his arm strength, as he can't put his body behind it like someone throwing a punch on the ground.
>>8118187
Why would it mean that? Why would taking a teaching only job make you think he's a bad teacher?
Combinatorics problem maybe?
A professor and his students are going to participate on the International Mathematical Olympiad.
Now he wants to choose the best students to participate in the competition from his class.
In the competition there are going to be X questions that the students have to answer, one question or more per student.
Suppose the class has N students. He can only bring Y students with him.
From the students chosen, each one of is qualified to answer more than one question. Example:
The professor chose 6 students:
- Student 1 can answer question 1 or 2
- Student 2 can answer question 1
- Student 3 can answer question 1 or 2 or 3 or 4
- Student 4 can answer question 4
- Student 5 can answer question 4
- Student 6 can't answer anything
suppose the test has 4 questions:
- question 1 can be answered by a maximum of 3 students
- question 2 can be answered by a maximum of 2 students
- question 3 can be answered by a maximum of 1 students
- question 4 can be answered by a maximum of 1 students
Question: what is the maximum number of students that the professor can bring with him to the competition, given an upper bound on the number of students that can answer a question?
-----
how can i approach this? any tips?
>>8124613
No latex because lazy.
My attempt at that problem:
m(t) = 7000 - 50 * t
m(t_f) = 6000, so t_f = 20 sec.
F(t) = B(t) - G(t) (buoyancy - gravity)
At t = 0 the forces balance. The mass at t = 0 is 7000 kg, so F(t) = 7000 * g - m(t) * g.
F = dp/dt, so p(t_f) - p(t_0) = integral of F from 0 to t. At t = 0 p(t) = 0.
p(t) = m(t) * v(t).
Therefore 7000 * g* t - 7000 * g * t + 25 * g * t^2 = (7000 - 50 * t) * v(t)
v(t) = (25 * g * t^2) / (7000 - 50 * t)
v(t_f) = 5 * g / 3 ~= 16.35 m/s
