The qaratic was deemed impossible to solve until the 16th century and this jewish galois chud allegedly says this image right here is not possible to solve.
>not possible to solvein closed form
>>16866872elaborate
>>16866873there is no general equation that, given the coefficients of a quintic, gives you the zeros of the quinticcontrast to e.g. a quadratic polynomial whose zeros are given by the two equations of the quadratic formula
>>16866871Solvability of roots of polynomials is equivalent to the solubility of a certain group of permutations of the roots. Since the permutation group of 5 symbols contains an insoluble subgroup, viz. the subgroup of all even permutations, the result follows fairly easily by just finding an example.
i'll add that one can always numerically find the solutions of polynomials, but algorithms aren't closed form solutions that can be evaluated for any coefficients given, instead you have to iterate the algorithm to get an approximate solution
>>16866878>there is no general equation that, given the coefficients of a quadratic, gives you the zeros of the quadratict. everyone before the 1500show do you actually know for certain
>>16866883Read the thread.
They are perfectly solvable in terms of series solutions. I don't know why retarded algebrists think that solutions involving roots are any better than solutions involving infinite series when in both cases you need computer to approximate them.
>>16867008t.analystroots reflect symmetry groups, which are at the heart of literally everything in algebra, while infinite series are a meme with no place in the field
>>16866871Is it EnergeticTopomorphical?
>>16867008>>16867009>in both cases you need computer to approximate them.What are the asymptotic complexities of time and space in terms of numerical precision? I'll be coding my solution in C, btw.
Not sure if this is closed form https://math.stackexchange.com/questions/540964/how-to-solve-fifth-degree-equations-by-elliptic-functions
>>16867116Ok, it actually isn't. AI said it was, I had to read into that post more carefully.
>>16866871It's a defect of math axioms. They don't like to admit this though.
>>16867128Defect of math axiom how?
>>16866873>elaborateLook it up. AIs were invented to spoonfeed toddlers like yourself.
>>16866871The dimensionality of the solution space increases exponentially in the number of roots (2^N, N = # of roots = degree of polynomial). Three starts the strain the ability of algebra to express itself, five is pure overload. Hyper-logarithm and hypo-exponentials did not offer a way out.So, here we are.
>>16866871take it with the dueling kid
>>16866871You're using Euclidean space for a solution space.>>16867222Just say you don't understand enough to elaborate or don't bother posting, newfag.>>16867222>Dimensionality of the solution spaceThis guy gets it. The abstraction only gains meaning in the context of the space it is injected into.The video game industry broke peoples minds by pretending 3d euclidean space was the same as 4d projected space and it isn't and never will be... going beyond 4 melts most people's brains because their comprehension of 3d is a commercial definition, not an actual definition at all.
>>16867009>while infinite series are a meme with no place in the fieldHow do you think e is computed
>>16868518Why do I need to do any of that? A polynomial of N degree is arbitrary. I could add color as a dimension to my sphere and now I have 5.
>>16868536>A polynomial of N degree is arbitraryyour mom is arbitrary, what's that got to do with projective space?
>>16868612>Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spacesYou brought up like some constraint you retard
>>16868534Instantaneous interest on my infinite wealth account?
>>16868518I got a highly non-Euclidean context embedding project to mine the 4chins for the glowies in Minecraft.You interested?
>>16866883>there is no triangle anyone has drawn with internal angles totaling more or less than 180 degreest. everyone before the 300s BChow do you actually know for certain? oh wait you can actually decisively prove certain things can't be true if they're incompatible with the logical rules of mathematics.
>>16868536Oh, I'm sorry. The answer is, "What is a non-sequitur, Ken?".We also would have accepted, "PeNgUiN oF D00M!".
>>16868637Because that’s the definition of a triangle. The definition of Quintic is purely its a polynomial of degree 5. That’s states nothing about its solvability.t. Everyone who isn’t an undergraduate moron like you
>>16868638>non sequitur That’s ironic, since I btfo you here >>16868630Not sure why you brought your little sphere to the party since it has nothing to do with OPs question
>>16868641>Because that’s the definition of a triangle.You poor abused child. You were tutored by mental rapists.
>>16868518>going beyond 4 melts most people's brains because their comprehension of 3d is a commercial definition, not an actual definition at all.do some golfinghttps://www.youtube.com/watch?v=y53UNskR-zU
>>16867164>Muh heckin axioms are free from fault!!Axioms of choice and infinity are both faulty. Going through the axioms of ZFC, they seem to all be bullshit.
>>16868953>Axioms of choice and infinity are both faulty>faultyThis is pretty much a meaningless statement. Any internally coherent set of axioms has implications that reflect something of the logical structure of reality.
>>16868954>internally coherent set of axiomsThey're not tho. Even mathematicians acknowledge this by publishing proofs both with and without AC
>>16868961>They're notProve it.
>>16868964Why do mathematicians publish proofs both with and without AC if it's all internally consistent? They love rigor. Surely one proof with AC should suffice. :^)
>>16868961>publishing proofs both with and without ACThey do that because it's interesting and stylish, you dumb fuck.
>>16868967I wrote a legitimate response and then decided you're a mouth-breathing, mentally ill mongoloid and don't deserve one. :^)Closing this retarded thread now. Notice how your mental illness forces you to reply again.
>>16868970The inbred retard is effectively just asking "why do mathematicians use different systems of axioms" a minute after I answered this question.
>>16868953>Going through the axioms of ZFC, they seem to all be bullshit.Aargh, le bullshit Successor(n) function!!!
>>16868972Mimicry is a high form of flattery. Thank you.
>>16868967>Surely one proof with AC should suffice. :^)as for without, they are constructivist or intuitionists, that's all, AC ain't either of those things
>>16869057>There are two categories of mathematicians >Those who include AC and those who don't in proofs>AC has nothing to do with either of these categoriesRetard lol
>>16869059Dude, you're stupid as fuck. Just leave this site and learn how to read.
>>16869063I accept your concession.
