/sci/ - Science & Math

>>15023351
What's an EASY application of spectral theory in functional analysis?

>>15023351
>pic
Is this satirising an actual person or has OP just created a bizarre fictional subculture to dislike

>>15023468
jodan desu

>>15023468
The second one

Series splitters

>>15023463
modeling economies that create new sectors using Leontief input-output model with infinitely many dimensions

>>15023468

anyone else notice they have a far better time working through math texts written by just one author?

it's like you can feel a coherent, logical train of thought vs. the disjointed paragraphs of a multi author text

>>15023351
Yiu kids

Stochastic terrorism for subhuman niggers

>>15023601
>he doesn't use Dummit and Foote to control Saturn
>he doesn't use Hoffman and Kunze to control Jupiter

>>15023468

It's a joke/meme image highlighting traits that most people carry to some degree, beckoning us to reflect on how these potentially negative traits have an affect on our psychology

pay attention in gen ed dude

>>15023757
>pay attention in gen ed dude
I'm not American; I don't have to waste >25% of my degree on applied Malian gender theory.
>caption: Y2KYS

I'm looking at past tests for review
I do not understand the plugging in part at all. How are the middle two terms equal to the last term?

>>15024551
The left factor is just the definition of f'(a).
The right factor is just substituting x with a.

>>15023565
He said application.

>>15024555
>The left factor is just the definition of f'(a).
Yes, I understood that bit
>substituting x with a
How?
I feel like I need a detailed elaboration on it because I'm retarded. How is f'(a) at the numerator in the end anyway? What about the x-a?

>>15024565
>How?
Because of the continuity of division, addition, sqrt, and f.
>How is f'(a) at the numerator
Where else would it be?

Excuse the handwriting.
You need to sleep, dude.

>>15024581
oh my god
yes I do

>>15023480

>>15024583
Good luck on your exam.

I'm trying to find a group operation on the set of Left-invariant orders on a group [math] G [/math]. Suppose I was able to generate new left-orders using automorphisms that don't preserve the original order. If I were to establish a bijection between some subgroup of the automorphisms and my original set, I should be able to define an operation on it, right? And would that be a meaningful group structure or just, like, arbitrary?

Have any type theories resulted in useful applications?

Can someone take me step-by-step through this question so I understand the process of finding x? I'm having trouble interpreting the question, and identifying which step to use where. I just wanna learn the process so I can get through my exam on Friday.

(27^x)+(3^(3x+1))=450

I'm hurt that I have to ask strangers smarter than me to interpret this because it's passing the workload. I apologize for bothering you guys because my math level is ≈ college algebra. Everywhere else I've gone only dives into the entry level knowledge on the subject of logarithms, but fall short of sufficient explanation.

>>15024613
27 can be written as 3^3, so replace that to get
27^x = (3^3)^x = 3^(3x), last equality is by using (a^b)^c = a^(bc)

If you have a^(b+c), then that's (a^b)*(a^c)
We use that with the second term
3^(3x+1) = 3^(3x)*3

Now our equation is
3^(3x) + 3*(3^(3x)) = 450
We can combine the terms to get
4*(3^(3x)) = 450
Divide by 4 to get
3^(3x) = 225/2

Take log base 3 to get
3x = log(225/2)/log(3)

Divide by 3 to get x
x = log(225/2)/(3log(3))

>>15024625
I think I understand better now. The step in the center is where I was stuck. I feel like a fool for not recognizing this, like someone who plays "Baba is You" and then looks up an answer.

I will ensure I remember what you have taught me, anon. I sincerely thank you.

>>15024644
You have a mistake in what you wrote.
When you took logs, you took log on one side (which is base e), and log base 3 on the other.
You should take the same on both sides. Whichever one you choose will lead to the same answer, but you need to be consistent.

>>15024653
The little things hurt my grade the most

I saw a troll thread about 0!=1 being bullshit with a rebuttal that [math]n!= \frac{(n+1)!} {n+1}[/math] is a good definition and works for n=0.
It's an okay rebuttal, but gamma(0+1) is 1 so it seems like a better rebuttal could be built from the gamma function.
I switched from math to eeng, so forgive me if these seem like dumb questions as a result:
>Is the gamma function a unique consistent extension of factorials or at least part of a unique class of consistent extensions?
>If so, can this be used backwards to prove that 0! has to be 1?
>Is there a good analysis text that thoroughly explores the gamma function and explains every part and consequence of it?

>>15024762
>prove 0! = 1
It's a definition.
We chose this as a definition because it's convenient.
There's no "proving" to be done.

How do you know what analysis is, but don't know what definitions are?

>>15024772
I always thought there was some way that the factorial of zero could be proved from some other properties of the factorial.

>>15024762
If you try to make a smooth function from the set 1!, 2!, 3!, ... without including 0! you wind up with infinitely many options to choose from. Gamma is the only extension that also satisfies 0!=1.

>>15024798
No it isn't.
You could literally add any multiple of sin(2k*pi) to your chosen extension and get a smooth extension of the factorial.
You need log-convexity.

Read up:
https://en.wikipedia.org/wiki/Bohr%E2%80%93Mollerup_theorem

>All elephants in this room are pink
>This statement is (vacuously) true because there are no elephants in this room
Are mathematicians for real?

>>15024808
Congrats, you got filtered early, tard.

>>15023575
kek

>>15023480
HAHAHAHHAHAAHAHAHAHAHA

what does a basic elementary ring theory or abstract algebra proof look like
example? or where to find one?

>>15024875
>what does a basic elementary ring theory or abstract algebra proof look like
"Define this map, show it's well-defined, prove it's a homomorphism, consider its kernel. use Zorn's lemma and get a maximal element, take this chain of ideals, etc."
>example? or where to find one?
Abstract algebra books.

>>15023351
does anyone have the solutionary to "functions of several variables" by wendell fleming? Thx

>>15023468
I'm the opposite of OP's meme personality. I would spend excessive amounts of time in supermarkets because I'm spending all the time deciding what I want to buy. The overly analytical type of person.

Logically quantified field

>>15024560
>avoids betting $billions against Russia
You can do the calculations in finitely many dimensions, for example simulation support for economies that supplements mathematical modeling. However, with finitely many dimensions, there must be some industries that are relegated to "novelty" status. With infinitely many dimensions, new industries can be created, and that can be expressed mathematically and formally, and it is from that theory that a prediction as to the accuracy of the simulated finite dimensional model is made.
The fact that you deny it is evidence that the practice is held closely, and so its status as an application of the theory is not well-known.

>>15024875
Dummit and Foote - Abstract Algebra
Artin - Algebra
Hoffman and Kunze - Linear Algebra

>>15023463
First, memorize the same results in linear algebra and learn to use them.

Two, you WILL not learn Stochastic Analysis. I will say that Functional Analysis is just for the fun of it and gatekeep my area of research by sending clueless math students into Algebraic Geometry because it's `le beautiful'

>>15023601
Hmm, you're right. You can baby yourself to the style more easily. Multi-author books end up being like encyclopedias without the benefit of an exposition like Rudin or Serge Lang

>>15024875
try Judson friend.
my plan is tackling Judson then Lang for the clear exposition.

Let H be a set of horses.

Theorem: if H contains at least one white horse, then all horses in H are white.
Observation: there is at least one white horse.
Corollary: all horses are white.

Proof of theorem: we proceed by induction on n, the cardinality of H. Base case: if n=0 or n=1, the proposition is clearly true. Induction: suppose the statement is true for n; suppose H has cardinality n+1; and suppose H contains at least one white horse W. Pick another horse X that is not W in H. Then H without X is a set with n horses that contain at least one white horse (it contains W). By the induction hypothesis, we conclude that all horses in H except possibly X are white. But now we do the same thing with H minus W, which contains X and only white horses. By the induction hypothesis applied again, we deduce that X is white. Therefore all horses in H are white. QED.

I'm back from some well-deserved sleep
Can you really write proofs like this? This is an answer from a past test.
When I write proofs, I always get stuck on notation and never actually use sentences or words to indicate what I'm trying to point out.
Can you just spell it out without the mumbo jumbo? I'm taking proofs for the first time and I got the impression that there are some hard nomenclature rules that you NEED to follow

>>15025215
Is it true that being differentiable on (x,y) implies continuous on [x,y]? Genuine question.

>>15025220
>being differentiable on (x,y) implies continuous on [x,y]?
If the function is defined on [x,y], then yes.
Continuous functions however are not always Differentiable.

>>15023757
Does it affect our psychology or our anthropology?

>>15025226
Let's say I define f on [0,1] by f(0)=f(1)=1 and f(x)=0 for all other points. Clearly f is differentiable on (0,1) but not continuous on [0,1]. What am I missing?

>>15025212
>now we do the same thing with H minus W, which contains X and only white horses
What if H minus W doesn't have any elements other than X?

>>15025195
you have to go back

>>15025205
go to /b/

>>15025212
You're just posting moronic garbage on the internet because you're desperate for attention.
Like, wtf, man.
these aren't even lies

>>15025238
no no no
Anon made a typo
If f is differentiable on (a,b) and continuous on [a,b] then f is differentiable on [a,b]

>>15025212
>behold a pale horse
I suppose we have to tell you to go to /x/ now
I love the government
Support the CIA stations in your foreign country!
>Anon wonders why he must suffer burger claiming he lives in a "foreign country"

>>15025215
>can you really write proofs like this
No you cannot. Authors write it like that because they think it's more elegant or whatever delusional nonsense excuse they use to avoid the effort of rigour. The whole point of propositional logic is to avoid using a language which can be misinterpreted easily.

Still stuck on combined rates and mixtures after a week. I decided to make a template for solving these problems so I just have to plug the right numbers in and get a quick solution. It's this or I kill myself.

what the fuck?
can someone explain?

>>15025349
A professor wrote that though, as an example for a "true" answer
is it just for explaining, or do you think that would hold in a test?

>>15025364
If all you care about is le hecking test and marks, oh le gpa goodies, then yes, writing like that is enough. Apologies for assuming you are not a midwit.

>>15025359
Brother...
1 / f(x) - 1 /f(a) = f(a) / f(x)f(a) - f(x) / f(x)f(a) = ...

>>15025359
you are given the definition g = 1/f on the first line. once you have g' it's just substitute and rearrange.

>>15025377
>>15025384
nevermind, I'm just stupid
what about the second line? why factor out the -1/f(a)?

>>15025400
because it's just a constant independent of the limit and so you're left with f'(x) / f(x)

>>15025400
You factor out f(a) because it's a constant and -1 from
f(a) - f(x) = (-1) * (f(x) - f(a))
so you can get the exact definition of the derivative of f(a) with respect to a

math chads whats a good introductory universal algebra text? my profs ""notes"" are half-finished and not very helpful

>>15025438
>Bergman

>>15025215
What ARE you trying to communicate? I think you still don't quite get what proofs are. Proofs are literally equivalent to the colloquial definition of "proving something", or "having/presenting an argument". Proofs are not notation. Proofs are not formalism. Notation is formalism.

Now let's investigate your "faulty notation" case: well, what DID you wrongly notate?
That e.g. a < 0, but you actually meant to write a >= 0? Then that's simply faulty logic, a non-functional argument.
But what if you write "For all x in the real numbers, it becomes apparent that [blah blah] must imply that [blah]" instead of "∀x∈ R : [blah blah] [blah]"? Or even something like "f is revealed to be a function that paints a graph quite like a dromedary -- it has three zero roots" instead of [imagine the formal sentence here].

Well, can you tell me why the first example would *not* be acceptable? What would be your reasoning?

Proofs have to just hold logically, via their reasoning. That the symbols and so-called "non-symbols" you use for that are interchangeable is actually quite the fundamental math fact.

ESL.

>>15025508
>"∀x∈ R : [blah blah] --> [blah]"?

>>15023351
Help me QFT chads, i'm being filtered hard :(

>>15025508
Don't argue with me, I was just asking if it was acceptable.
Argue with this guy >>15025349

>>15025614
I asked YOU on purpose. I know you were asking in "favor" of my side. I addressed directly you because I was interested what arguments you could come up with, so that if you can only can come up with stupid/non-sequitur/pointless arguments, you kinda create a "proof by contradiction" in the course of posting here.
I tried to use this math/logic technique as part of the discussion (not because this is a math thread -- I'd have done the same in an entirely non-math related topic, e.g. I'd have asked some vaxxie what he perceives/reasons to be the pro and contra arguments of both sides would be for getting the clotshot in 2022, etc.).

The notationsfag can of course also chime in.

Hello kind people of /mg/. I come with another problem. I'm too tired to attempt it right now but tomorrow I have a lot of free time at school so I'll try my best at it. But no matter what, I'll try to check the answer of anyone who finds a solution to this problem. Thank you very much if you decide to attempt this problem but if you instead choose not to, I understand. I suspect for many people here this problem isn't that interesting so wouldn't be worth their time. Farewell and good luck. I'll reply to the answers as soon as I can but that will most likely take some time so I apologize in advance.

>>15023351
Hope this is the right place to ask this:

Anybody have any good books for learning how to create a numerical simulation?

>>15025776
assuming balanced coin, same as Pr(exactly 5 heads out of 10 total), just flip the name of heads to tails and vice versa in the second half
So (10 choose 5)/2^10 = something
this idea can be used to prove vandermonde's identity in general

I have a stupid question for some linear algebraist.

If you have a 3D vector space like our universe, and we would allow for imaginary numbers to exist in such a way more dimensional axis's would form, would we then have a 6D vector space or a 4D vector space?

Would the square root of any negative axis coordinate value fall to its own imaginary axis or would they all fall to the same?

Sorry I'm a comp sci retard. I need this answer for a call of cthulhu roleplaying campaign I am planning.

>>15025776
>>15025855
Let's get the obvious brute-force method out of the way, but not before noting that it provides a slick combinatorial proof of the identity [eqn]\sum_{k=0}^n \binom{n}{k}^2 = \binom{2n}{n}[/eqn]
(every path from the cell [0,0] to the cell [n,k] reflects about the nth row to a path from [n,k] to [2n,n])

>>15025935
I would think 6D. If you replace vectors of three real numbers (R, R, R) with vectors of three complex numbers (C, C, C) you will have 6 variables. You could try and use a fourth real number to mark the imaginary part (R, R, R, Ri), but then what is (0, 0, 0, i)*(0, 0, 0, i) ? It should give -1 in some way, but where would that -1 go ? How do you make it a vector ?

Tldr; [math]\mathbb{R}^3 \to \mathbb{C}^3[/math] goes from 3D to 6D.

>>15026036
Yea I see your point. I think for my game I will use your point to make the rotation to the imaginary plane be more permanent as the information from where the point was rotated has been lost, so returning to the real plane would be impossible.

Thank you.

>>15025935
>>15026036
If you require that the coordinates of the vector space be real numbers, then it has to be 6D. But you can also interpret it as a 3D space with complex number coordinates, i.e. a "vector space over [math]\mathbb{C}[/math]".

This has practical applications to Internet arguments, for example when estimating the height of an anime girl from a screenshot, by counting pixels and comparing against a reference object.
The mathematical invariant that underlies this is called the "cross-ratio", and it is computed from 4 points as shown in pic related (stolen from https://en.wikipedia.org/wiki/Cross-ratio).). Unfortunately, this cross-ratio is only well-defined when the 4 points are collinear, which severely limits its validity.

This is where the "complex interpretation" comes in: by re-interpreting the screenshot from a 2D image to a 1D image with complex coordinates, all points in the image trivially become collinear, and we can use complex-number division to compute cross-ratios and win autistic fights without having to worry about the collinearity restriction.

Is it a good a idea to go from Fleming's Functions of Several Variables to Do Carmo's Differential Geometry?

>>15025935
>Le complex numbers are so Lovecraftian
Kill yourself.

>>15026245
I don't know about that. My favourite Lovecraft novel, dreams in the witch house, is about a student who has to live in a really shitty apartment in which a witch allegedly lived in earlier. As his studies come along he starts getting an intuitive understanding of hyper dimensional spaces while simultaneously falling into severe illness. The witch is actually a servant of Nyarlethotep or something and is corrupting his mind.

Lovecraft also had the idea of a dream world, a different realm some can enter when dreaming. I'm mixing those two ideas and having the dream world actually be a physical place but it's a rotation along a 4th imaginary (get it, imaginary -> dream) axis.

If you want to gatekeep math I'd suggest you choose some other concept than complex numbers as even retards understand what they are.

>>15025648
Why are you wasting your time on that midwit? He clearly doesn't care about anything other what will fetch him le hecking marks! The fact that he will be allowed a degree is just sad.
That said, using notation is important, because not only is it more accessible to ESLs, much faster to read, takes a lot less space, but also it prevents you from using faulty logic like >>15025212. English can also often be hard to interpret, especially if the author doesn't use punctuation, or does not follow the convention of predicate calculus; I have read authors writing quantifiers in English at the end, and it's fucking annoying.

>>15026262
>OH LE IT's THE IMAGINARY AXIS I AM GOING INSANE

>>15026086
That sounds like a fun idea. In your case, different real points connect to one imaginary point, so the roleplaying interpretation is that the "move to imaginary" action can bring things from different parts of the universe to the same imaginary space. Like you said, there is loss of information so going back might be impossible. But in the right situation you can do some crazy Lovecraftian thing where going from imaginary to real will give you all of the possible real options at the same time, bringing and multiplying chaos all over the real world...

>>15026091
Very interesting, that is a subtle distinction, thank you for the helpful example.

>>15026267
i breathed air out of my nose

>>15026267
t. >>15024180

Is there a good way to dea with angles in R^2 with power series and no mention of trigonometric functions?

Why does it seem like 90% of the questions posted here are abstract algebra?

>>15026784
you should examine the permutation group of shitty math posts

Is J.K. Rowling stupid? Logically this doesn't make sense. The contrapositive is:
Peeves says nothing => Filch says please
So saying please is not sufficient for saying nothing. So Peeves can say whatever, but he acts like Filch made him say nothing. I think what she meant to write is:
"Shan't say nothing only if you don't say please."
>>15026715
What do you want to do? You can just define angles by position of two normal vectors.
>>15026784
All math is Abstract Algebra

>>15026784
It seems finals are coming up and getting help
here is...ideal...

>>15025935
>>15026262
Not any of the previous anons, but I think the quaternions here are your best friend: they are 4D over the real numbers, they have nice properties, have a cool-sounding name, and have just enough room for one extra oh so mysterious dimension.
The only catch is that the usual notation for them is: w+ix+jy+kz, so the three coordinates "in our world" would have an "imaginary" notation, and the extra dimension would have a "real" notation. Another way is to describe a quaternion as a scalar part + a vector part (fun fact, this is actually where the terminology scalar, vector comes from)

Idk how much you would need them in your campaign, but a neat thing is how the product of two vectors v, w is the vector product v×w as its vector part, and minus the scalar product -v•w as their scalar part, so in a roleplaying context you could partially enter in contact with this otherworldly dimension by performing something like a product (which could be a ritual where you fuse two things together idk)

Other anons will laugh at me for going along with your idea but who cares, cringe is fun

>>15026838
>OH LE IT's THE QUATERNIONS I AM GOING INSANE SAVE ME EULERMAN

>>15024551
Is this analysis or calc level?

>>15026870
calc

>>15026873
Show me something from Analysis then cuh

Retard here. Need some help with the mathematical side of a programming project.
I have limited space on a graph (say, 300 pixels, but the unit is arbitrary). I need to draw a gantt chart (meaning I fill the space on a chart within a certain range between two numbers, then blank space until the start of the next set of numbers, then again for the next set of numbers, and so on). However, my data set goes far beyond 300.
Examples:
Start at 500 units, end at 1000 units.
(blank space)
Start at 1200 units, end at 3520 units.
And so on.

How do I equally scale down all the numbers I might have so that the last number in the [pair/range/whatever], which will by definition be the highest value in all the numbers; equal to 300, while still preserving each range's... aspect ratio? Thanks.

Also, bonus round: What's the nomenclature for all of this? I feel like it has something to do with "sets" and "tuples" and "limits" or something, but I'm just a code monkey.
And no, this isn't homework.

>>15026889
>cuh
I hope you're being ironic, zoom zoom

>>15026894
>zoom zoom
hehe

>>15026890
Can you show like a small example of what the numbers would look like

>>15026898
Since the project is in TypeScript I'll just write it in JavaScript syntax.

let values = [
[ 1423451, 2574993 ], [ 4544792, 6390322 ], [ 7903100, 9250264 ]
]

Or, as objects if that makes more sense:
let values = [
{ start: 1423451, end: 2574993 },
{ start: 4544792, end: 6390322 },
{ start: 7903100, end: 9250264 },
]

My goal is to basically draw a rectangle of arbitrary height from (1423451, 1) to (2574993, 1), then have blank space from (2574993, 1) to (4544792, 1), then draw another rectangle from (4544792, 1) to (6390322, 1). For all intents and purposes, these can just be considered line segments. However, I am limited to a maximum width (X) of 300 (this could change depending on the size of the device's screen this is being used on), so it's not as easy as just plotting the raw values since they would be off the edge of the screen.

In reality, I am plotting dates when a project was started to the time a project has ended, so users can see how long they took and what dates the project was being worked on. The dates are UNIX timestamps, which is how most dates are measured by computers: they count the seconds since January 1st, 1970. So my values are actually much larger (in the millions). But that's irrelevant.

>>15026929
>>15026898
>>15026890
Also also, the API I'm using does have the option to simply scale the shapes; as demonstrated in https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API/Tutorial/Transformations#a_scale_example

>>15026832
No...it seems to be correct. As a if-then statement,
the line:
>Shan't say "nothing" if you don't say please.
becomes
>If (Filch) don't say please, then (Peeves) shan't say "nothing".
or the equivalent
>Peeves shan't say "nothing" only if Filch don't say please
(quote marks for my emphasis)

Filch not saying please is sufficient for Peeves to
not say "nothing" (as Peeves deems it sufficient).
Filch figures Peeves might say something
(because of nothing with no quote marks), but
Peeves hides the fact that upon Filch saying
please, he makes the conditional statement be
true by simply dropping the "not" of his deal.

The contrapositive is logically equivalent, but that
switches around what's necessary and what's sufficient.
What do you think?

>>15026939
>>If (Filch) don't say please, then (Peeves) shan't say "nothing".
>or the equivalent
>>Peeves shan't say "nothing" only if Filch don't say please
>(quote marks for my emphasis)
The equivalent of if P then Q, is P only if Q, not Q only if P

I saw this is a geometry book 4 years ago and forgot the name of the conjecture, book and author, does anybody recognise it:
Take any pair of different natural numbers a,b except for the pair 0,1.
Conjecture: the angle between the lines y=ax and y=bx is always a transcendental amount of radians and a transcendental amount of degrees.

>>15026929
let values = [
{ start: 14..., end: 25..., percentStart: start / maxVal, percentEnd: end / maxVal, yStart: percentStart * yMax, yEnd: percentEnd * yMax },
{ start: 45..., end: 63..., percentStart: start / maxVal, percentEnd: end / maxVal, yStart: percentStart * yMax, yEnd: percentEnd * yMax},
{ start: 79..., end: 92..., percentStart: start / maxVal, percentEnd: end / maxVal, yStart: percentStart * yMax, yEnd: percentEnd * yMax}
]

Here's an idea

>>15026978
Let me give that a try, I'll map over the values and do that.

>>15026978
No good. Wouldn't the number of total pairs (in your example, 3) also factor into this?

>>15026950
>>15026939
Yes..."if P then Q" is the same as "P only if Q". I had
to double check. Thus:
>Filch doesn't say please only if Peeves shan't say "nothing".

The rest of it should be fine, I hope. Been a while since
attending a proof course.

>>15026960
But [math]acos( \frac {1} {\sqrt{m^{2}+1}} )[/math] is not always transcendental for integral m>1, so the conjecture is retarded

>>15027136
Acos of an algebraic number between 0 and 1 is never algebraic.

>>15027136
>>15027138
Just because the angle between [math]0x[/math] and [math]mx[/math] is always transcendental for [math]m \in Z, m>1[/math] doesn't mean the angle between [math]mx,nx[/math] is always transcendental for [math]m,n \in Z, m,n>1, m \neq n.[/math]
A general algorithm for querying a pair m,n seems like something that would be independent of ZFC though.

Will be going back home tomorrow. Can't wait to start reading math again.

>>15023468
I quit my job because I rolled a dice

Why can't you just use a computer to algebraically solve all unsolved math problems? What happens? What goes wrong?

I just shat all over my real analysis exam. it's over

>>15027397
Many problems cannot be represented algebraically.

>>15027406
What about calculating all possible number theory theorems?

>>15027411
Can't be done. Enumerate the theorems, you can do a diagonalization.

>>15027397
Try to computer quark dimensions with 2d circuit board.... projection

rings > fields > vectorspaces > modules >>>> gr**ps

>>15027397
So this tells me that you're at most an undergrad, around freshman year.
If you've done any proof-based math (and not the neutered one you did in high school), you'd know that proofs require creativity.
The reason there are unsolved math problems isn't a lack of effort (why you'd use a computer), but a lack of inspiration.
There is no obvious way to approach any given problem; give a problem to 10 different people and you'll get 10 different ways of approaching it, each most likely having heavy roadblocks.
What you've learned so far up to high school was all computational, with no creativity required. We already have tools online to do those kinds of problems.
There's a video by 3Blue1Brown about a hard math Olympiad problem about points and a rotating line, and at the end of the video, he says that sure, the problem may seem obvious in hindsight, but there were dozens of ways one could've approached it.
Give a problem like that to a computer and you have two questions that you should answer:
1) How would it even know to come up with these approaches?
2) How would it know which approach is viable?

>>15027489
you can just go through all possible permutions of symbols and check if they constitute a proof of what you want
just takes a heckin long time

>>15027495
Two issues:
1) What do you mean by "go through all possible permutions of symbols"? Proofs aren't just symbols you throw around. Proofs have words, and words have meaning. You have to actually implement a way for a computer to understand meanings.
2) You already said this: It would take too long. Even just using 26 letters in English, going through every possible 9 letter "word" would take possibly half a day. You wouldn't have even reached "homomorphism". So what's the point?

See, even here as we are talking, you're struggling to approach this problem of having computers solve our problems. It's not clear what to do. And computers don't really do anything on their own; we're the ones who are supposed to tell them what to do. How are we supposed to implement "inspiration" and "creativity"?

>>15027397
You can, that's how unsolved math problems are solved, by checking solutions, and that's a formal, algebraic process that everyone learns and internalizes, but the details are transmitted to math students; they aren't spelled out in a book anywhere
This is no different from Chan transmission.
Separation of algebraic reading from understanding didn't happen until Knuth published his seminal paper on the LR parser in 1965.
The Buddhists have been spilling the beans for 2500 years, but it took hundreds of years between 1114 and the birth of Newton for the differential calculus to travel from India to England.
So, I'd say the formal, mathematical understanding is about the last thing that people care about, and they solve the stress problems in their life using this sort of understanding.

>>15027526
Also the set of all permutations of a finite set of symbols with repeats allowed is uncountable

>>15027546
He said "permutations", but what he really wants is the set of "strings".
Either way, these are each finite in length (a proof is a string that is finite in length), so they're countable.

>>15027553
>All proofs are non-infinite
doubt

>>15027616
Can you write an infinite proof?

>>15027526
>1) What do you mean by "go through all possible permutions of symbols"? Proofs aren't just symbols you throw around. Proofs have words, and words have meaning. You have to actually implement a way for a computer to understand meanings.
coq, lean or similiar

>2) You already said this: It would take too long. Even just using 26 letters in English, going through every possible 9 letter "word" would take possibly half a day. You wouldn't have even reached "homomorphism". So what's the point?
are we engineers or what? the point is that its possible not that its practical

>>15027645
>weeb shitting up a discussion
What else is new

>>15027649
good post pal
you have truly enriched this thread
but whatever im going back to mjrm, which isnt filled with retarded undergrads

>he's looking for (You)'s

>>15023351
Who decided that decimals only went up to 9 before they went to the left? Seems arbitrary.

>>15027714
Humans have 10 digits on their hands.
So we got 10 digits, 0 to 9.

>>15027544
https://eyecave.bandcamp.com/album/oh-its-just-some-sorcerer
https://www.youtube.com/watch?v=al697st1oeU

>>15027733
Math objects are related to axiomatic fantasies.
The content of proofs is related to the real fact.
The possibility that a math object could attain to a real fact is as remote as the possibility that a hallucination could be real nutritional substitute for ordinary food.
Why do people pay money for real food when a hallucination would fill the belly?
There is a scene from pic related on this topic.

>>15027641
Yes. Not the proof itself, of course, but an algorithm that constructs the infinite proof. Here's a brief sketch of how it works:
Take some property [math]p[/math] that holds for [math]\omega[/math]. For some n, use induction from [math]\omega[/math] to some [math]\omega n[/math] to show that [math]p[/math] holds for the infinitely many terms between [math]\omega[/math] and [math]\omega n[/math]. You have then produced an infinitely long proof.

>>15027786
How long does it take to check an infinite proof?
>An infinite amount of time.
So how are we going to get the result of checking the proof?
>We're going to wait an infinite amount of time.
Uh, okay, WHO exactly is going to wait an infinite amount of time?
>Whoever wants to learn the outcome of the process used to check that the proof is correct.
Great. That isn't me, but I still want the answer.
>Tough, you'll have to wait an infinite amount of time.
To parse what, exactly?
>The proof.
Why don't you just tell me how you generated it?
>I did.
Ugh...

>>15027796
Wait until you hear about [math]\Omega[/math]-logic.

>>15027702
>mjrm
What's that?

>>15027786
This is not true; you're trying to catch a frisbee thrown into a lake. What you've presented is a theorem schema. It's part of 2nd order logic. You're suggesting that the arbitrary substitution of a formula parameter is equivalent to infinity, and the point is that this isn't true because infinity is a symbol defined in the fantasy world, and substitutions take place in the real world; in each case, the substitution of a formula parameter does not produce an infinitely long proof.
Here is another way of looking at it: an ordinary induction proof on the natural numbers does not produce an infinitely long proof when any particular natural numbers substituted and the base case plus n "parameterized proof modules" are lined up to establish an inductive condition
You could say that induction provides you the facility to produce a proof of arbitrary length, so that if you give me a number of lines, I can produce an induction proof of some ordinary fact with a number of lines exceeding that bound, when each P(n) -> P(n+1) step is written out with n substituted with a specific value, increasing from 1 to the limit.
You're taking the possibility of writing a correct proof with length greater than any given number of lines (taught in algebra to high school students who learn induction on the natural numbers) and confusing it with "infinitely long proofs" but what's really going on is the production of infinitely many proofs, each with length greater than the last, and each individual proof is finite.

>>15027803
>I have an infinitely long proof, but I refuse to present it; instead, I will change the topic to your hearing.
Sounds like /mu/ is leaking.
Hearing is for /mu/ and if you have an infinitely long proof, then why don't you present it to us so we can check it...after you wait an infinite amount of time, of course.

>>15028225

>there is single variable, two variable, three variable, etc calculus
>there is still no fractional variable calculus

Why isn't there? Can we not represent partial axis physically the same way we can't represent n>5 dimensional axis physically? We can still show that symbolically, so where can I learn about something like 6.08742 variable functions?

>>15028405
There is fractional calculus, but not in the way you
think. Check the Wikipedia article on it or,
for a start, look at pic related. There's also a
PDF or two floating around.

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

Okay so frankly the problem was disappointing in a sense. I didn't realize it was this simple but perhaps I should have seen that before solving it.I just looked at the probability of both having 1,2,...,5 heads and the answer popped up right away.
>>15025855
That is indeed correct mister. Good job and thank you for taking the time to solve and reply to this problem I shared. And while I just said that I was dissapointed a bit about the problem, what you say regarding vandermonde changes that. I'll look into that and let me say I appreciate you telling me about it.
>>15026012
That is poggers, sir.Very kind of you to tell me about this. Thank you.

>>15028498
and the probability of having 0

Could someone give me a hint on how to prove that (x^i, y^j) is primary in Z[x, y]?

>>15028498
I too do not know how combinatorics or the choose thing works.

Hey /mg/. Some anon told me that the notion of a set is not rigorous and not even defined. Apparently mathematicians just list a bunch of properties that they wish their supposed sets to have without actually constructing these objects. He also said that if there is one structure satisfying these properties,then there are many very different structures with no correct one. Is that true? If so, how is that rigorous?

>>15028966
>Apparently mathematicians just list a bunch of properties that they wish their supposed sets to have without actually constructing these objects.
That's exactly what constitutes the definition of a set.
To borrow the lingo of software engineering, what the foundation of mathematics provides for its mathematical objects is a formal specification, as opposed to an implementation. This is not to say that implementations (or "models", as they're usually called) are undesirable, just that they're not necessary.

The justification for this cavalier attitude (whether you agree with it or not) can be traced back to Godel's completeness theorem, which roughly states that any valid proof of a mathematical theorem (under the rules of classical first-order logic) can be mechanically translated into a model. The problem is that this so-called "term model" is a highly artificial construct that rarely yields any insight on the original theorem, and the mechanical transformation depends on many arbitrary choices (a loose analogy can be drawn with the compilation of a software program into machine code: the final result depends on the processor it is intended to run on, and is seldom useful to share around).
It's a rigorous procedure that solves the "model implementation problem", but no one's going to spell out the implementation details in full, and even the people who write automated theorem provers would rather work on something else, like type universes or higher-order logic, before translating set theory into their preferred foundations.

But if you're still game for it, look up https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem and shop around for a proof that meets your standard of rigor. (Though I should warn you in advance: if you happen to be one of those dumbasses who likes to screech that "everything is invalid", then be prepared to search for a long, long time...)

>>15023351
Gonna be using AI to explain math to me now. Math professors have been replaced.

Were you not good at math in school?

>>15029184
Yeah I was terrible through mainly apathy and an underfunded deep south school district.
I recently worked through most of Sheldon's Axler Precalculus and was surprised how engaged I could get from a math text.

>>15029174
Yeah, but I have a degree from Anon University, and you don't.

>>15029174
>inverse image of every open set is open
dumb AI

This year I have read and completed:
> Set Theory, Jech
> Real and Complex Analysis, Rudin
> Abstract Algebra, Dummit and Foote
> General Topology, Kelley
I can't decide what to read next. I'm vaguely interested in transfinite numbers and graphs but haven't found a topic that really interests me.
My uncle suggested loaning any one of these three that he already owns to me:
> Graph Theory, Diestel
> The Higher Infinite, Kanamori
> A Tour Through Mathematical Logic, Wolfe

I want /mg/ to vote on this. Whichever one has the most votes when this thread is archived is the one that I will ask him for.

>>15029587
very

>>15029685

>the openness of the inverse

>cunt-IN-you-US fuck-shuns

>>15029688
I have to stop using.
I'm reading Neuromancer now.
My head hurts.

>>15024919
needs more soilent abstraction, that will for sure show them pseuds

>>15029706

soundtrack: https://www.youtube.com/watch?v=BObRAdGbSF8

>>15028405
Sure you can, why not.
You just need a good definition of wtf a fraction of a variable even means... Good luck with that.

>>15029723
The empty set has no boundary points. Since there aren't any boundary points, therefore it doesn't contain any of its boundary points, so it's open. Since there aren't any boundary points, it is vacuously true that it does contain all its boundary points, so it's closed.

Anything else?

>>15029672
From those three The Higher Infinite is the best. But maybe you would want to read about multivariable calculus.

>>15029802
the context is the open chatbot that just opened, chat.openai.com
it's very stupid, and these assholes will just piss and shit everywhere about how fucking brilliant their cute baby AI is
bunch of morons

>>15029587
>>15029685
>>15029688
>they don't know the topological definition of continuity
If you're underaged, just shut the fuck up.

Bumping >>15023463

Wtf kind of arrow is this

>>15030710
>returns to [math]\mathcal{H}[/math] instead of going to [math]\mathbb{R}[/math]
Hikikomori arrow

>>15030727
>"math" joke
>has little to do with math, but just a coincidence of what something is named (in english, at that)

>>15030727
>>15030759
True, but anon's joke made me chuckle, so what is the problem? The fact that it interprets mathematical notation in an absurd, unrelated way is what makes it funny and even clever.

>>15023351
How can you tell if an operation is associative without testing every possible combination of (x*y)*z = x*(y*z)? I know the operation is commutative in that set because it only has 4 elements, so it's easy to check all combinations, maybe it helps?

>>15030775
well never mind i figured it out. But now I'm curious about how to figure out if the operation is commutative in relation to the set without testing all combinations to find a countereaxmple. The same would apply to finding and identity and the inverse. Is there a deductive way?

>>15030773
get real

>>15030780
Assume any arbitrary element from the set, and prove.

>>15023351
niggers

>>15023351
what the fuck, i have an actual maths problem, it is not homework. i keep getting blocked from posting it. but i can post the word niggers.
fuck it, fuck /sci/ i am just going to guess.

>>15023480
oh you

>>15030907
Screenshot the image and FUCK JANNIES

>>15030934
thanks

Is literally everyone here still an undergrad?

>>15030964
i do not know what your ameriwords mean, i am here from /diy/ the maths i usually use is very simple. I have been to college, i won college.

>>15030710
>is an unitary representation
It's really weird notation for unitary representations and that's a weird way of stating Stone's theorem on one-parameter groups of unitary transformations.

>>15030951
What the fuck are you talking abot?

>>15030808
easier said than done though, how the hell do i prove x*y = y*X without looking for counterexamples?

>>15030987
Counterexamples is used to disprove things not prove them.

>>15030982
P must equal one for the equaltion
p=a-c
values a and c are products of B. oh maybe i didn't state, this is a formula i will have to run in succession, b is a cumulative value, i.e. each time this formula is run, b is added to a tally. that is cumulative b.
anyways i figured it out sort of;
B = 0.5 x (cumulative b for previous run) + 0.33

>>15030999
sorry, +0.5, not 0.33, to keep P closer to 1.
hey sci, figure this one out too.

>>15029174
What AI is that?

>>15030971
Do you find it fun to learn this math that also has an application to physics and the real world?

>>15030964
I'm a grad student

>>15030995
>>15030995
What's the difference? You can just affirm the opposite and use a counterexample to prove the original claim

>>15029814
oh, its a chatbot.

>>15030964
Master's
But yes, everyone else is a retard

>>15031056
The proposition you are trying to prove is
[math] \forall x, y P(x,y) [/math]
To disprove this, you only need to have one counterexample because the negation is
[math] \exists x,y \neg P(x,y) [/math]
However to disprove the negation you need to show that [math] \forall x,y P(x,y)[/math] i.e, the original statement, so having only one counterexample will not work.

>>15030999
I have no idea what you are talking about, what is the actual problem you are solving?

>>15023351
Any recommendation for a combinatorics book? Preferably something with lots of exercises and a wide range of difficulty. Thanks in advance,

- anon

>>15030951
1=3B-(B+?)
1=2B-?
2B-1=?
2B=?+1
B=(?+1)/2
B = ((cumulative B) +1)/2
did you fail Algebra 1 or something?
or are you failing it now because you're asking strangers on the internet for help solving easy problems?
you should just solve the problem instead of asking for help
like, really
just solve the problem, dude
like, why are you asking for help
are you a fag or something
are you autistic

>>15031172
>are you autistic
yes. i figured it out though eventually. see >>15030999
>did you fail Algebra 1 or something?
no but it has been 18 years or so since i really did anything like that.

What is the best book on teichmuller theory?

>>15023351
I wish I had the habit of letting rng decide things for me. Because God is the True RNG and He is bound to make better choices than myself.

Is reading Euclid a meme if I want to relearn Geometry?

>>15031373
Depends. If you've had further mathematical training after high school, it's a great choice.
Otherwise it's probably a bad idea.

I'm stuck on conditional expectations, it's over boys, how do you even condition a variable by a sigma-algebra bruh fuck that I'm going to the army

>>15029672
None of the above. Instead read De Carmo - Differential Geometry of Curves and Surfaces.

>>15031746
This is one of those times where a little undergrad category theory is actually a helpful simplification, at least once you understand what the pushforward measure is doing:
https://ncatlab.org/nlab/show/conditional+expectation#conditional_expectation_relative_to_a_subalgebra

>>15031924
Thanks anon, it does put things into perspective, I was being facetious, but it is still kind of a hard to grasp notion for me, especially with my professors rushing the lessons so much, I'll add that link to my study folder

Hello everybody!

I need help solving an Integral Equation that my professor put on our HW without teaching to us. I've tried emulating the textbooks example but I still can't crack it.

\begin{equation*}
f(t) = cos\, t + 4e^{-2t} - \int{sin\, (t-\tau)f(\tau)\, dt)}
\end{equation*}

My work so far on the problem:
\begin{equation*}
f(t) = cos\, t + 4e^{-2t} - \int{sin\, (t-\tau)f(\tau)\, dt)}
\end{equation*}

\begin{equation*}
\mathcal{L}\{f(t)\} = \mathcal{L}\{cos\, t\} + \mathcal{L}\{4e^{-2t}\} - \mathcal{L}\{\int{sin\, (t-\tau)f(\tau)\, dt)}\}
\end{equation*}

\begin{equation*}
F(s) = \frac{s}{s^2 + 1} + \frac{4}{s+2} - F(s)\frac{1}{s^2 + 1}
\end{equation*}
\begin{equation}
F(s) = \frac{s}{(s^2+2)} + \frac{4s^2+1}{(s+2)(s^2+2)}
\end{equation}

I know that from here I'm supposed to take the inverse Laplace Transform to find f(t) but everything I've tried on the second term (Partial fractions, expanding it out) either fails me or gives me a super ugly equation that I'm sure is false

Any and all help is appreciated.

>>15030964
i am and professor

>>15032419
[eqn] f(t)= \cos(t) + 4 \exp(-2t)- \int{\sin(t-\tau)f(\tau) d\tau} [/eqn]

>>15024808
Depends on the axiomatic system

Who was in the wrong here?

If this new AI can do my comp sci homework for me, how long until it can do my linear algebra homework for me?

>>15032722
Make the AI write a program that can solve any linear algebra problem.

>>15032722
kek

did grothendieck's works help or impact physics

I just found a neat site called ncatlab with physics topics.

Solve it.

>>15033311
It's those elements of [math]S_6[/math] that consist of either one 6-cycle or two 3-cycles.
Of the former there are [math]5!=120[/math] and of the latter there are [math]2^2 {6 \choose 3} = 80[/math] so in total there are [math]200[/math].

>>15033321
Correction there are [math]2^2 {5 \choose 2} = 40[/math] elements with two 3-cycles.

>>15033321
NO
>>15033330
YES

>>15033110
Without Grothendieck there would be no schemes and the fields of algebraic geometry and algebraic topology would be much less developed. Those two fields are the bedrock of most recent developments in QM, GR, condensed matter physics, material science and, weirdly, genetics. Never mind physics, there are entire journals dedicated to teaching biologists modern algebraic geometry.

Is differential topology more based than functional analysis or less based?

>>15031007
google openai chat gpt

>posted a math meme in the math Discord
>everyone got pissy because it "insulted" groups of people

>>15033892
>the math discord
That doesn't tell us literally anything. discord.com/math?

>>15033926
would make sense, they reeeee at any remotely edgy / "toxic" content

>>15033926
>>15033931
yes, i posted picrel and a mod removed it because it "insulted groups of people"

>>15033949
lol thank you for sharing

>>15026832
>a woman

>>15033949
>naive lie theory
KEK

subitize easier with silvera

>>15026832
peeves is a shitposter, he doesn't care about being logically precise

>>15033949
lmao saved
aluffi's algebra, sheaf theory, naive lie theory, and homology were some personal favorites

Can someone recommend a measure theoretic probability book which doesn't solely focus on theoretical problems?

>Numerical Methods that Work (Acton)
From the interlude, it looks like an entertaining read if nothing else. But is the material still worth careful studying in $CURRENT_YEAR, or has it become outdated?

Why does this serve as proof of the incompleteness of the hilbert system in question? https://math.stackexchange.com/a/4417183/990227
They've shown that there exists an interpretation of the symbols under which all of the axioms are true, but under which something that is a tautology in the standard semantics isn't a 0-tautology under the new interpretation. How does the incompleteness follow from this? I feel like there is something I am terribly misunderstanding. Please help.

How do you get over slumps and burnout when you're studying? I'm an engineer by trade and trying to learn real analysis by myself, but I've hit a wall and I'm tempted to call it quits.

if you know something but the other person doesn't believe your proof, did you prove it?

>>15035405
Doesn't matters, you don't ask illiterates in the first place

>>15035409
if they don't believe your proof, you didn't prove it to them

>>15035223
Anon, the answer considers a different (from the usual) semantics that is still sound for the proposed Hilbert system.
Now if the axiom system was complete w.r.t. the usual classical semantics, then any classical tautology must be a theorem of that proof system. But as we proved the system sound w.r.t. the new semantics, any theorem must be a tautology of the new semantics (what they called a 0-tautology).
Summing up, any classical tautology must be a 0-tautology, but the answer pointed out one particular formula for which this fails.

It's worth mentioning that this entire "coming up with a different sound semantics" was mostly to help us find our counterexample (in the form of that classical tautology). If someone were to tell you to consider that formula from the start, you could simply show that it is a classical tautology but not entailed by the proof system (this part would require induction as our proof system is inductively defined)

My calculus classes are pretty slow and easy. My school won't allow me to take on extra classes until April and I want to speedrun learning about transfinite ordinals with my spare time, what's a good way to do this?

>>15035409
If they can't refute my proof with their own proof then they're retarded and I will continue my claim that my proof is correct

>>15031187
>it has been 18 years or so since i really did anything like that.
This is Zoomerspeak for "I'm 14 years old and trying to learn math on my own". I've seen other people use the same lie on other threads before.

bumpo

>>15037177
What does the downward arrow mean in (c)?
>inb4 le zoomer doesn't know how to screenshot
It's from an iPad Air1 and it would be slow as shit to upload from there.

>>15037195
https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols
Is it on this page?

Does anybody here know anything about finite automata theory? My school allows you to take a masters level course as an elective in the last year of undergrad and this is one of the available options for the next semester. My question is basically: what are some main results, what are some applications and should I take some more classical masters course instead (say, for example, on Riemann surfaces).

>>15037206
For fuck's sake anon, it's a one-sided limit (that is: a limiting process where h approaches 0 from the right), the context makes it clear that it's part of the definition of right-continuity.

>>15037195
As h approaches 0 from the right; i.e. as h limits downwards to 0

>>15037233
Thanks.

>>15037215
That's it's equivalent to regular expressions. That it can be normalized hence equality is easy to compute. And also the pumping lemma.
https://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages

>>15030964
people further than that know that asking their questions here won't get them any results, so I'd guess they're mostly lurking or answering other anon's questions. Like I'm doing equivariant stable homotopy theory, whats the chances people here know about that?

>>15033445
more

>>15035287
don't overdo it, take frequent breaks. Ideally discuss the material with someone

Just wanted to thank whoever it was from several threads ago that suggested Pinter's book on algebra. Been reading and doing exercises in it for a week now. I honestly really like his approach. It's like a slightly different approach compared to Hungerford/Jacobson/Lang, and I've found it easier to digest. I also appreciate Pinter's increased focus on extensive drills and proving exercises at the end of each chapter; it honestly has helped convince me to try my hand more at proving results. His book may not be as encyclopedic nor as comprehensive as other contemporary & oft-recommended textbooks, but it is good.

>>15023468
I am that person, although I don't use coins or dice, I use rng and the last digit of the seconds on my watch.
Only reason I ate chicken tonight over any other option is because of rng. Same reason why im learning chinese. RNG = GOD
pic related is my history sorted by page visits.

Hello /mg/. Writing from a psych ward. Hows it going?

Has anyone used this book? The math filters me heavily, what are some prerequisites for it?

>>15039429
I have the physical book in my library. The book
is pretty good if you have taken statistics at
an advanced level since the book contains proofs
(towards the later chapters).
Each chapter is rather brief and to the point and
I've used this as a support book to another main one
that I used in class.

Algebraist's (me) prayer:
>I fucking hate Analysis
>I fucking hate Analysis
>Amen
Say it twice because 2 is a sacred number.

>copy of Wolfram Metamathematics arrived a week before release date
>First edition, first printing
Giving it a sniff for my mathmullet brother.

We have a R-Vector space V and I want to show that there exists a function in the real numbers that is additive but not homogeneous.

We are given the hint that R can be seen as the direct sum of Q⊕V.

Now I define a function such that g(q+r):=q (q+r) € Q⊕V

And for rational scalars its the identity and thus homogenous but for irrational scalars it is not.

Am I on the right track? What am I missing? Im going to sleep now, so if some one is to reply to this id appreciate it but I will only see it in 8 hours or so.

>>15040103
never open it, resell it 3 decades from now

>>15040117
I earn too much to care about value of books, and I have other books that are actually signed in person by the author (Perez-Reverte, Houellebecq, etc) that some math book is just not going to appreciate that much compared to. Whoever gets my stuff when die can sell it or keep it.

>>15023351
been struggling with a) and b) for almost 2 hours. I give up and understand that I need help

>>15040166
im so retarded I forgot the picture

>>15040169
what is phi_2?

Lim x-> ∞ Log((5x-3)/(5x-1))

Why is this 0?
I'm not sure how to solve it. The result according to the guide is 0.
I'm thinking that for the result to be zero, the equation inside log has to be one. But I'm not sure about that. I'd appreciate if anyone could show how the equation inside is solved.
Thanks beforehand

Any opinions on Kaplasnky's Fields and Rings textbook? Good or nah? Pic related.

>>15040628
you're taking the limit as x goes to infinity of (5x-3)/(5x-1). when x gets really big, the constants stop being important and you end up with 5x/5x, which goes to 1. then log(1) = 0

>>15040740
I guess it sort of makes sense.
Thanks anon.

>>15040244
the derivative over the second variable.

How hard would an undergrad number theory course be?

>>15041109
not

>>15041109
If you get a good lecturer then it's not too outrageously hard. Still failed to get an A though, in my case, lel. I think I got a B.

Why do math books put hint right below the question? I don't want to look at your stupid fucking hint.

>>15039602
What was the main text you used?

>>15041328
>>15039602
Intro. to Probability Models, 11th ed.
By Sheldon Ross

>>15041298
I'm with you, anon

Lim x->2
(√2 - √x)/(x^2-4)=0/0

I'd really appreciate if someone showed how to solve it.

>>15041365
The reason I ask, is that I think I'm missing something about conjugate method. I couldn't solve this one, and some other ones.

>>15041365
You can rewrite the denominator as [math]x^2 - 4 = (x+2)(x-2)[/math] and [math](x-2) = -\left(\sqrt{2}-\sqrt{x})(\sqrt{2}+\sqrt{x}\right)[/math] so [math]\frac{\sqrt{2}-\sqrt{x}}{x^2 - 4} = -\frac{\sqrt{2}-\sqrt{x}}{(\sqrt{2}-\sqrt{x})(\sqrt{x}+\sqrt{x})(x+2)}[/math] and then you just simplify!

>>15041400
That should be
[math]\frac{\sqrt{2}-\sqrt{x}}{x^2 - 4} = -\frac{\sqrt{2}-\sqrt{x}}{(\sqrt{2}-\sqrt{x})(\sqrt{2}+\sqrt{x})(x+2)}[/math], my mistake.

>>15041402
Or you could use L'Hôpital seeing as it's an indeterminate (0/0) form.

>>15040115
Bump, can some one Tell me whats missing

>>15040115
>We are given the hint that R can be seen as the direct sum of Q⊕V.
Why? What if V has cardinality larger than R?

How can I improve my geometry skills?

>>15041655
I think V is supposed to be the irrational numbers so that you can describe any real number as the sum of vectors from the sub spaces of the direct sum.

Thats how i understand the problem, but i havent made much progress since yesterday.

>>15041693
The real numbers aren't the direct sum of the rational numbers and the irrational numbers

>>15041735
>>15041693
Post a picture of the actual question?

>>15041736
>>15041735
Its in German. But If you want i can Post it and translate the hint to the best of my abilities.

The problem in general is about showing whether additivity of a function implies it being linear. We have to prove/disprove it for the rational, complex, real number vector spaces and the F2 field.

PLEASE somebody help me. If I have a finite group [math]G[/math], and a [math]\mathbb{Q}[G][/math] module, can I make into a [math]\mathbb{Z}[G][/math] module???

>>15041931
of course you can

>>15041931
Of course you can. It works with any injective ring homomorphism.

>>15041938
>>15041945
How? I'm sorry if it's obvious but I'm sleep deprived and just can't see it.

>>15041979
Sleep on it brother. This is so easy if you know anything about modules that it doesn't deserve to be answered outside stupid questions general.

>>15041979
Just compose the injection with the scalar multiplication. The addition can stay the same. Also, sleep is important for your health.

>>15042017
That's what I thought. So if I have [math]\mathbb{Q}G=\left\{\sum_{g\in G}\frac{p_g}{q_g}g|p_g,q_g\in\mathbb{Z}, q_g\neq 0\right\}[/math] I can choose a finite basis [math] b_1,\dots,b_n[/math] and for any [math] b_k [/math] I choose [math] c_k = \text{ product of all denominators of the fractions in the formal sum of } b_k[/math], construct [math] c=c_1\cdots c_n[/math] and then I can go from [math]\mathbb{Q}[G]\to\mathbb{Z}[G][/math] by multiplying by [math] c [/math]

Is this correct now?

>>15041983
I can't sleep deadline is coming up and the other problems drained my brainpower.

>>15041931
Yes.
Just restrict the action to Z[G].

>>15042032
Why are you mapping QG to ZG? Lose the marks on your homework for putting it off til the last minute.

>>15040663
I know we're close to a new thread, but.....
Algebra-bros, please answer. I need your guidance.

>>15042463
https://www.amazon.com/Fields-Rings-Chicago-Lectures-Mathematics/dp/0226424510

>>15042480
Thanks.
Though I am curious about that 1-star rating. Someone rated it 1-star but did not bother to write a review as to why. But judging from the other reviews it seems to be an alright book.

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