/lit/ - Literature

>adding letters together
kek is this really what mathematicians are up to these days?

>>20292901
Math is pretty much a scam.

>>20292887
I got filtered by Algebra in high school and still haven't been able to recover

>>20292901
You gotta do what you gotta do when you run out of numbers

>>20292887
Wait until you get to Abstract Algebra in your forties

>>20292919
I'm a math post grad student, I can confirm we're playing you for absolute fools

>>20293379
>mathfags brag about making up math with no practical applications
>they start judging each other by this standard
>think they're pulling one over on their funders
>mathfags fail to make math with no practical applications most of the time
>engineers turn their math into massive profits AND mathfags seethe seeing their lifework put to productive use
>everyone laughs at the mathfags
Enjoy your 300k starting. We WILL monetize your theories and you cannot stop us.

>>20292919
Mathematics is the most autistic science field no doubt

>>20293366
>Wait until you get to Abstract Algebra in your forties
what? what the fuck does that even mean. why do people in this board always write these cryptic could-be-insults that only make sense in their heads

>>20293453
post body

>>20293453
>why do people in this board always write these cryptic could-be-insults that only make sense in their heads
I don't know, why don't you tell us

>>20292887
You fell for the Gelfand meme, its a shite 90 page introduction if thats what you're needing get an AOPS textbook

>>20293453
kys nigger

>>20292887
No shame in doing some khan academy first bro. I was a high school dropout and khan literally saved my life with his site.
t. cs/math double major (in some shithole but still)

*grinning* that’s a really cool cover

>>20293844
go to bed tao

>>20293453
If you can't characterize the automorphisms of simple rings by the time you're in your forties you're ngmi

>>20293453
lol that's not a cryptic insult, it's a pretty straightforward joke anon

>>20293400
Based double digits of truth.
As a engineering student, I relate to opening a book and reading what some maths-fag would spend hours writing out.

>>20293847
shut up jad

Modern math is bullshit and I will explain why

>>20296196
Modern math is full of paradoxes and contradictions. Why? Set theory and its retarded axioms. Sets can not have multiple elements, for example A = {1, 1} is not accepted, however, for some reason, they can look like this: A = {1, {1}}. Which makes no sense. You either have 1 or you don’t. So sets are not well defined in modern mathematics. Sets should never contain sets, especially not sets of themselves! This eliminates things like the power set, which allows you to take a set and multiply its size greatly by forming all permutations on that set, which is literally magic. For this reason we have absurd conclusions like Cantor’s theorem which shows that some infinities are bigger than other infinities. Yeah, that’s bullshit.

Infinite sets and power sets are both AXIOMS in modern mathematics. If you look at the axioms, some of them only exist to avoid problems caused by other axioms! And yet we still have paradoxes and contradictions, like Hilbert’s hotel. Can an infinite hotel with all its rooms full accept another guest? YES, says modern math. Just move each guest to the next room! And the problem stops there. But wait, what if the hotel manager wants to simply rearrange the guests? He should be able to do that since there is one guest for each room. So he simply tells all the original guests to go back to their original rooms, and the new guest to find the empty room. But there is no empty room! How can he gain/lose a room just because of the arrangement of guests? We can represent this problem with pure math:

A = {1, 2, 3…}
B = {0, 1, 2, …}

The mapping x~x-1 (1~0, 2~1, etc.) maps each element in A to an element in B. However the mapping x~x maps all elements but 0. According to the modern math, these sets have the same cardinality (size). Even though there is a case in which their size obviously seems different, we simply IGNORE this and focus on the case in which they’re the same! Isn’t math lovely?

>>20296253
Don’t even get me started on IRRATIONAL “numbers.” What is an irrational number? Can you tell me?
>a number that isn’t rational
Okay, but how do you actually CONSTRUCT an irrational number? A rational number is easy, just take two natural numbers and arrange them as a fraction. But how do we define something sqrt(2)? The Dedekind cut method just says that sqrt(2) is the set of all rational numbers to the left and right of sqrt(2). In other words, x^2 < 2, and x^2 > 2. But how is this meaningful? This doesn’t allow us to construct the number itself, in decimal form. Not only that, but a collection of irrational numbers (and rational numbers, as they are also real numbers) would just be collections of collections of rational numbers. How does that make any sense? There are probably DOZENS of way to construct the real numbers. Why? Because there is no correct way, because they’re all flawed. Most textbooks don’t even attempt to construct them! You just assume the existence of the “continuum” and that real numbers simply exist. Nevermind the fact that 0.15192629…… isn’t a legitimate representation or definition of this number (how do you define it? Try it).

So math is FULL of these counter-intuitive and useless axioms and theorems and paradoxes and contradictions, but it’s all accepted! And you’re just supposed to go along with it as if everything’s fine. Wittgenstein knew all of this was laughable, so did Kronecker and others when this stuff was being introduced. But people like to believe in things they don’t understand.

>>20296253
>Sets can not have multiple elements
>Sets should never contain sets
according to who?

>filtered by muh INFinity
Okay?

>>20296302
>just go along with it don’t worry about the paradoxes keep wasting your time over useless problems
it doesn’t have to be like this bros WHYYYYYYYYYYYY???? IM GOING INSANE AAAAAAAAAAHHHHHHHHHH

>>20292901
You can weed out the smart autists from the retarded ones by watching how they react when you say "number A."

>>20296313
>wasting time
Very subjective fren. Normoids will dismiss literature because
>Its just like, all dead Wypipo!
Do you see the similarities?

>>20296253
Take your meds, John

>>20292887
Throw that shit in the garbage and get Euler's Elements Of Algebra.

>>20296253
Lmfao, I will never cease to derive pleasure from you autists who can't handle infinity and sets. Never any rigor, just schizo assertions like
>{1,1} is not accepted, but {1,{1}} is, this is nonsensical
Like you're so stupid that you don't even realize that you're raising an aesthetic objection to a formal system.

>A = {1, 2, 3…}
>B = {0, 1, 2, …}

Oh no, its you again isn't it? Can you simply not accept that CARDINALITY and SIZE are different concepts, and that CARDINALITY = SIZE only for finite sets? They are different concepts, YOUR MERE PERSONAL AESTHETIC INTUITIONS ABOUT WHAT YOU FEEL ABOUT THE SETS {1, 2, 3…} AND {0, 1, 2, …} HAS UTTERLY ZERO RELEVANCE TO THE VALUE OF SET THEORY.

>>20296325
>a + a = 2a
wow nice "science" you got there

>>20296486
>two sets have the same cardinality if and only if there exists a bijection between them
>two sets have the same cardinality if and only if every injective mapping between them is a bijection
Why should we use the first definition but not the second? Please explain why, without saying “it’s just the definition!.” Both of these definitions apply to finite sets, so why do we only apply one of them for infinite sets??
>aesthetic objection to a formal system
NO. I’m simply pointing to a superior formal system. The set {1} and the set {1,2} are distinct, but the moment you collect them together in any way, you should have {1,2}. You can use a CLASS if you want to be able to group them together without combining them. But SETS do not contain duplicate elements.

Can you tell me WHY we should accept the traditional model of sets, as opposed to mine?

>>20296489
You outed yourself as a retard mate.

>>20292887
fuckin get over yourself OP
>>20292901
Yes.

>>20296527
>Why should we use the first definition but not the second? Please explain why, without saying “it’s just the definition!.” Both of these definitions apply to finite sets, so why do we only apply one of them for infinite sets??
>Can you tell me WHY we should accept the traditional model of sets, as opposed to mine?

Because that's the definition that's being used. You can use your own definitions if you want but you're no longer talking about modern math.

>>20296253
I think I should stop browsing 4chan. Full of pesud freshmen like you. Why don't you ask this at math stack exchange, let's see what responses you get from educated people and not NEETs on 4chan.

>>20296527
>Why should we use the first definition but not the second?
Because the second definition presupposes that we only work with finite sets. If you want to make the second part necessary, we can talk about only finite sets and simply use the word size, but cardinality is a broader concept than size. Size and cardinality happen to coincide when we're talking about finite sets, but reveal subtleties when talking about infinite ones. I think its completely natural to be disturbed by notions like "{1,2,3,...} and {0,1,2,...} have equal cardinality," clearly one of these sets is a subset of the other, shouldn't it be "smaller" then? And in the sense that the first set is indeed a subset of the latter, the first set is, in some sense, "smaller," but this doesn't change what the cardinality of a set is measuring. You might not like cardinality but there is no inconsistency in its definition, I think you just don't agree that cardinality is capturing a notion of "size" properly. And that's a perfectly fine opinion to have, there's tons of cool finitist, constructive stuff, etc, what I don't understand is the insistence that somehow reasoning about infinity is contradictory. Like, you agree that there exists a one-to-one and onto function from {1,2,3,...} to {0,1,2,...} right? You aren't disputing that, correct? F(n) = n-1 is clearly one-to-one and onto here. I don't think you disagree about that, it seems like you're saying the mere existence of a bijection is not encoding the size of infinite sets as reliably as finite ones.

>>20296489
not my problem u can't understand how useful logic is

>>20296596
>I’m sick of listening to Socrates, do you think the sophists would say this?
>I’m going to ask Protagoras and get some REAL answers!
Sunk-cost autists; gaming for government money. AKA academics.
None of this matters.

>>20296624
nice bro thanks for the good reply, not the guy youre replying to but that was rly good. makin the board better bro:)

>>20296583
The NPC response that I was expecting. Why should we choose the path of paradoxes when it can be avoided? Just because we can generate more and more theorems doesn’t mean the system is consistent or correct. What noticeable effect has this type of math had on society? Why are our brightest minds wasting time on these surrogate activities? Useless puzzles? If it’s not computable or constructable or applicable to the real world, then why is it so prevalent? Why is it being taught in universities? There are CONSEQUENCES to creating bad mathematical systems. It completely changes the trajectory of the species. Why the FUCK are going along with this? Bomb the universities!

>>20296640
You haven't shown any inconsistencies instead you've just said you don't like the definitions. If you can show an inconsistency in the accepted definitions and axioms that will be notable and people will listen. But just complaining that you don't like them will get you no where.

>>20296640
write a paper bro im serious, ill read it. best of luck.

>>20296627
>I have a diamond in my house
>John vists my house
>I realize that the diamond is missing
>Therefore John must've stolen my diamond
that's logic. let's see how useful your 2X = 350Z bullshit is

>>20296650
hello jew, go do your pilpul somewhere else, we're enjoying this discussion. evidently youre not. so leave

>>20296656
go try to program a computer bud

>>20296640
>The NPC response that I was expecting.
why did you ignore >>20296624

>>20296664
>durr learn to code
typical bugman libtard response

>>20296713
You were the one to bring up how useful something is. Math is extremely useful for technology

>>20296713
logic is literally how computers work at a molecular level, you need to build those properties in when making the chips.

>>20296650
The PROBLEM is that you can ASSUME all type of things like the existence of an infinite set of sets of sets, but this loses sight of the PURPOSE of mathematics, which should be to solve problems in the REAL WORLD. I cannot point to a contradiction in the axiom of infinity, I simply don’t think it is useful to include it, and it is not justified because it is not intuitive. What does it even mean for an infinite set to “exist” ? How can we model this on a computer when we do actual WORK? Do you think we can take a ball and duplicate it by cutting it into pieces and rearranging it? That is what modern math says. How can anyone look at this and not realize that SOMETHING is wrong?? What is the POINT of all of this?
>>20296624
Yes, there exists a bijection (but even this requires assumptions). So what? Why is this useful? I don’t believe in uncountable sets because they aren’t proper sets. If I assumed the existence of infinite sets then I would believe that they all have bijections. But again, none of this is practical because infinity doesn’t exist in the real world. I can make a graph on a computer by creating bounds for my x and y values, I don’t have to ASSUME that for every x value, there is a y value.

>>20296731
Or, I don’t have to create bounds, but the computer will never stop graphing the function. At any point in time the mapping is still finite. Infinite sets do not “exist” in any meaningful sense.

>>20296737
>>20296731
im unironically curious about whether infinity is actually useful. I know that in some physics problems we like to set the bounds at infinity to make the problem solving easier, but im not nearly educated enough to say either way. could you explain further why infinity is useless, or someone please add something on why is is useful.

>>20296731
>The PROBLEM is that you can ASSUME all type of things like the existence of an infinite set of sets of sets, but this loses sight of the PURPOSE of mathematics, which should be to solve problems in the REAL WORLD
Math doesn't care about the real world. It's still funded though because of a weird propensity for pure mathematics to find application in the future. And a /lit/ poster shouldn't be talking about applications to the real world anyway. Beam in your own eye and all that.

>>20296744
I know Cantor didn't just come up with cardinality out of nowhere he had been working on trigonometric series when it arose. As to whether that work on series has some application I don't know.

>>20296747
youre having a personal argument rather than adding any evidence for or against the proposition being argued, you must really be a jew

>>20296744
Please, PLEASE do not take anything that schizo says seriously. There is a vanishingly tiny minority of mathematicians that take issue with the idea of infinite sets and the like. If you'd like to learn about it read on the philosophy of mathematics, particularly about finitism, ultrafinitism, constructivism, intuitionism.

>>20296762
interesting thanks

>>20292887
(a-1)(a+1)=a2-1

>>20296763
What proposition? That the purpose of mathematics is to solve problems in the real world?
That is not the purpose of mathematics the proposition is wrong.

>>20296766
ok thanks for the recommendations. I am curious about the matter

>>20296747
There are so many other useful areas of research. Genetic engineering alone could be the catalyst to solving lots of our problems. If we could create super-intelligent individuals then they could tell us if all the pure math is nonsense or not much faster then just continuing to research this stuff for hundreds of years. Do we really believe that we’ll find a solution? Zeno’s paradox is apparently “solved” but it isn’t. That was 2000 years ago and we still don’t know if space is continuous or discrete. This problem will exist whether or not we continue to advance in math. We should be advancing in physics, biology, chemistry, neuroscience, etc.

>>20296731
i didn't know wildberger was a /lit/ poster

>>20296773
theres not one purpose to math. my question is whether infinity is useful or not, and if this guys objections about sets have merits. leaving for a dentists apt, interested to so yalls responses if its a discussion you care to have

>>20296777
avoiding the issue

>>20296777
I mean if we followed this line of thinking we could keep the math department and still get money for the sciences just by axing all of the humanities as useless. Philosophy would be the first on the chopping block since it doesn't even have the practical successes of math and suffers all the same problems of application to the real world.

>>20296253

Mathematicians just ACCEPT that their systems can’t be consistent and complete. So they stopped CARING completely. Why??? Because of Gödel. His incompleteness theorems shattered the dreams of the mathematician. But are his theorems even true? NO!!! He RELIES on the liar “paradox.” Is this a “paradox” ? No. There are no paradoxes, only contradictions and meaningless sentences.
>I am lying
about WHAT?
>I am a liar
So you lie “a lot” ? Yeah, that can be true while also not being a contradiction.
>I always lie
Does this mean you’ve never told the truth? You can tell the truth now and it wouldn’t be a contradiction.
>I am incapable of telling the truth
Such a being would NEVER utter this statement. It would ALWAYS say “I CAN TELL THE TRUTH” or “I CAN ONLY TELL LIES.” To just ASSUME that it could say otherwise is the reason for the contradiction! “What if it just contradicted itself for no reason haha then what? omg :3”
>this sentence is false
This makes NO sense. It can also be shown that it is a pure contradiction as every sentence has an implicit assumption that it is true, so that it is saying it is true and false at the same time. But how can it be true or false at all?? Not every sentence has a truth value.

You’re telling me that we used a PARADOX to prove something in math? If we see a paradox it means we should go in the REVERSE direction and change our assumptions or fix our definitions. That is all!

>>20296856
>If we see a paradox it means we should go in the REVERSE direction and change our assumptions or fix our definitions
This is a basic type of proof taught in high school geometry. You assume the negation of what you want to prove and show that it leads to a contradiction.

>>20296866
Yeah, so we can’t create statements such as “G: G is unprovable.” That’s all it means. It doesn’t mean that there exist statements that are true that can’t be proven. It means those statements never exist in the first place. This is the clever trick that modern math pulls. It creates a contradiction then blames the contradiction on something else rather than the problematic assumption.
>>20296779
I would like to be wildberger but I’m not. Picrel is me lamenting the state of modern math

>>20296873
>This is the clever trick that modern math pulls. It creates a contradiction then blames the contradiction on something else rather than the problematic assumption.
That's not how proof by contradiction works. You're hoping that the rest of math besides your assumption is consistent so that when you get to your contradiction it must the assumption that was incorrect. Godel's work is highly technical and he gives a painfully precise statement that G is unprovable. Arguing about it informally is pretty pointless

>>20292887
The next one is:

1 6 15 20 15 6 1

Right?

>>20296880
What math notation allows us to represent a statement as being “provable” ? Does every system allow us to construct such a statement? NO. If your system allows you to state “G: G is unprovable” then your system is flawed in the first place. In a consistent system we could never take such a statement seriously. It couldn’t be formed from the definitions, axioms, and notation.

>>20293400
>Enjoy your 300k starting
Am I supposed to feel bad if I were in this position?

>>20293833
>t. cs/math double major (in some shithole but still)
Post country.

>>20296873
watching some wildy now

>>20296895
>What math notation allows us to represent a statement as being “provable” ?
This is the whole idea behind Godel's proof. For a bad idea how it works consider that every well-formed statement in formal first order logic can be represented by a number using Godel numbering. Godel numbering works by assigning every symbol from formal logic to a specific number then using that number as an exponent to a prime number in increasing order. So if the variable A and B are 2 and 3 and the logic operation AND is 4 (A AND B) would be 2^2*3^4*5^3. Then with some handwaving and trust assume Godel has come up with a way to represent natural deduction using arithmetical operations on those Godel numbers. After that you can codify questions mathematical logic as arithmetical operations and whether they are possible

>>20296737
the, uh, set of integers is infinite

yes you can set limits on the size of an infinite plane, that's when calc exists

>>20296946
JUST TRUST THE GODEL ALRIGHT?

hello i am zeno
i will read half of your post, then a further quarter, another eighth
man idk if ill finish it...

>>20296946
I’m not sure if I accept even this.

(a = a ^ a = a) ^ (a = a ^ a = a)

You can keep creating statements like this based on a simple true statement (a = a). Intuitively this seems wrong and similar to the problem of the power set. Anytime you have x ^ x it is reducible to simply x. So this statement is superfluous. It is equivalent to a = a. So these statements aren’t actually unique. I would have to think more about this to see all the implications but for now I’m tired. The more I analyze the more I find problems. I’m going to go crazy

>>20297051
You can look up his proof if you want it's all in there and worked out in autistic detail. Don't say I didn't warn you though.

>>20297070
uniqueness of the godel number, not the statement
i think you would benefit from familiarizing yourself with directed arguments

>>20297070
>Anytime you have x ^ x it is reducible to simply x. So this statement is superfluous. It is equivalent to a = a. So these statements aren’t actually unique.
This is just conjunctive elimination a rule from natural deduction. Godel's method of proof would say the statements are equivalent.

>>20297093
>>20297094
Do the statements have unique numbers in the numbering? If so, such a numbering isn’t even possible, because the cardinality of the set of statements is larger than that of the numbers used to create the numbering. Does he acknowledge this?

>>20297114
godelbros.....

Given the statement 5 < 7, I change it to 0 < 2, since
x < y -> x - a < y - a

Now 0 < 1 + 1
which implies 0 < 1, and this is a basic axiom.

So all statements are REDUCIBLE to axioms. Why can’t we solve the collatz conjecture? Maybe because the problem isn’t structured in a way that can be reduced to our axioms.

>>20297144
ENGLISH EINSTEIN!!!

>>20297144
Likewise, if our statement reduces to a statement that contradicts our axiom (1<0) the statement is false. Therefore every axiom has a false counterpart. A statement’s truth is decided if it aligns with the axiom or anti-axiom. Otherwise, it is not a well-formed statement in this system.

Now can anyone show me how G: G is unprovable can be reduced to an axiom in a mathematical system?

>>20296731
can you make it less obvious your entire understanding of infinity is based on vsauce videos

>>20293039
I too got filtered by groups and rings when I was in high school, it's normal.

>>20293400
how do i get 300k starting wtf

All great writers were of the past appreciated mathematics very much. Math teaches rigor, mental imagery and clarity of expression, all of which directly translate into literary talent. If you despise math your writings will be almost as bad as those of modern journalists.

>>20297114
>cardinality of the set of statements is larger than that of the numbers used to create the numbering.
This isn't true due to dictionary ordering. All statements in first order logic use a finite number of symbols.

>>20297221
That isn't funny man

>>20292901
>>20292919

>>20293379
How deep are you?

>>20297495
alright. I still think truth and probability are equivalent, like Wittgenstein. So the “proof” is just the liar’s paradox. I don’t believe in self-reference

>>20298245
I've already proven P=/=NP

>>20298266
Glad to hear RSA encryption is still safe.

>>20297228
any job you want

>>20296638
> Unironically comparing that retarded pseud to Socrates
cringe

>>20297221
> lol, did you say algebra? so you mean you where studying le groups and rings?! lol.
kys underfag pseud.

There is already a field of math that uses finite or ultrafinite axioms, it's called computer science.

>>20298245
TIL PDEs, Stoke's theorem/all of linear algebra aren't serious math, but "Euclidean Space" is
that's enough internet for today.

>>20298245
Still trying to count. Any tips?

>>20299165
Apparently americucks consider PDE "applied math" and hence less rigorous, only because there's a PDE class for engineers where they basically only learn to memorize the solution to the wave equation. Most kids on /sci/ dismissively talking about PDE have never heard of regularity theorems in Sobolev spaces, index theorems or microlocal analysis, even though those are actually extremely basic.

>>20296253
>>Modern math is full of paradoxes and contradictions. Why? Set theory and its retarded axioms. Sets can not have multiple elements,
yeah classical se theory is retarded
in constructive set theory you can have multiple same elements, but set theory in general is still mega retarded compared to cat theory

>>20298245
yang mills is not difficult

>>20299487
When counting quantities greater than 10 you don't have fingers left. Continue with your toes.

>>20298245
I'm doing theoretical physics, we do things in a very different order to that

>>20298245
Series, although I think it shouldn't be that low in the graph. Babby-level integration is as far as I go.

>>20293400
>>engineers turn their math into massive profits
...for the companies that employ them.
they see no bump in their own income, unless they are granted a bonus at the corporation's discretion, of course.