/sci/ - Science & Math

Gessel-Viennot lemma.

1 = 1
it's great isn't it

>>11450798
But that's just a special case of
1>=1

>>11450804
I think 1<=1 is more general.

[math] \forall P.\ (P\lor \neg P) [/math]

The most indisputable theorem of all, nobody has ever found a way to combat it. It's the hardest cock in the scientific world. It rams its way through all knowledge.

>>11450858
This is actually not intuitionistically valid.

>>11450858
if it's a theorem then you can prove it right?

>>11450919

>>11450873
That's the joke, it'€ bullshit

>>11450919
To quote that based other anon, "it is a self-evident law of thought"

>>11450927
wow it really is simple
why intuitionistic brainlets don't get it

>>11450747
the unsolvability of the quintic by radicals

>>11450927
Absolutely based. Intuitiautists BTFO

>>11451057
X^5 - 2 =0
X = sqrt^5(2)

>>11450927
P | ~P
https://programming.dojo.net.nz/study/truth-table-generator/index

>>11450747
This is now a mathfag hate thread.
Get off my science board you lonely nerds

>>11450747
>>11450775
>>11450791
>>11450858
>>11450932
>>11451177
>>11451188

[math]P ≠ NP[/math]

>>11451207
>>11451210
>banjo duel intensifies

>>11451210
posting image using software created by mathematician on computer invented by mathematicians which runs on logic invented by mathematicians

yeah... totally just autistic masturbation

>>11451207
>>11451210
>seething low IQ mathlet produces low IQ, unfunny memes
Colour me surprised

>>11451231
cope and seethe autist

>>11450927
That's a semnatic interpretation of the statement.

Showcasing a model isn't a proof, just like an example isn't a proof of the general case. Giving me a commutative group doesn't proof that all groups are commutative. Truth values are a meme, we're talking about derivability of formal statements here. To say I ate eggs Benedict for breakfast today doesn't mean "the container of truth values associated with 'I ate Eggs Benedict for breakfast' holds that one or that other value inside it." Show me proof of me having eaten Eggs Benedict, don't show me 0-1-containerized applications of the pigeonhole principle.

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

>>11451303
https://en.wikipedia.org/wiki/Universal_approximation_theorem

>>11451278
this post doesn't make any sense. that post exhibits that all semantic interpretations of the relevant logic result in a true valuation of the sentence P or not P.

This one. Looks like a bit of a mess at first sight, is absolutely beautiful and easily re-deriveable once you REALLY get it.

>>11451388
I agree with the second sentence, but why do you say the first doesn't make any sense?
I'm saying that, when arguing about the validity of a statement in a formal logic, showcasing how it plays out in two-valued semantics isn't a strong argument in my mind. There's enough universally quantifyable statements that a provably undecidable and thus can have no demostrable proof value each of it's instances. E.g.
https://en.wikipedia.org/wiki/List_of_undecidable_problems#Problems_about_matrices
To say a proposition _is_ like a container holding either of two truth values is begging the question from the get-go.
Adopting LEM just hides nice math and has no gain except for shorter formulas. And for any statement A provable with LEM, there's also a statement B such that LEM+B=>A imediatenly, e.g.
https://en.wikipedia.org/wiki/Double-negation_translation

Anyway, I was just shitposting from the start, in the sense that it doesn't quite fit the topic of the thread (it's just always fun to discuss the topic on /sci/, although where it leads to is questionable.)

My favorite "theorem", if I think about it, is probably some nice but completely analysis result..

>>11451424
use [math]A\choose C[/math] next time.

>>11451388
I agree with the second sentence, but why do you say the first doesn't make any sense?
I'm saying that, when arguing about the validity of a statement in a formal logic, showcasing how it plays out in two-valued semantics isn't a strong argument in my mind.
There's enough universally quantifyable statements that a provably undecidable and thus can have no demostrable proof value each of it's instances. E.g.
https://en.wikipedia.org/wiki/List_of_undecidable_problems#Problems_about_matrices

To say a proposition _is_ like a container holding either of two truth values is begging the question from the get-go.
Adopting LEM just hides nice math and has no gain except for shorter formulas. And for any statement A provable with LEM, there's also an intutionistically statement B such that LEM+B=>A imediatenly, e.g.
https://en.wikipedia.org/wiki/Double-negation_translation

Anyway, I was just shitposting from the start in the sense that it doesn't quite fit the topic of the thread (it's just always fun to discuss the topic on /sci/, although where it leads to is questionable.)
My favorite "theorem", if I think about it, is probably some nice but completely basic analysis result..

>>11451480
> just make half of the people here guess what the hell this weird notation is this
not everyone's into probstats/combinatorics

>>11451488
you're obviously correct to the point of pedantry. it doesn't matter, because normal mathematicians don't question their semantic framework, we just work in the same one all the time. i guess there are some operator algebraists who look elsewhere. everyone else is a logician.

>>11451507
literally everyone knows that notation and learns it in early high school

>>11451518
hm?
depends on the country, I guess...

>>11451303
https://ncatlab.org/nlab/show/universal+coefficient+theorem

>>11451529
i would be astounded if another american tells me they didn't learn binomial coefficients before university

>>11451568
- Not an american.
- Have learned binomial coefficients, basic statistics, basic combinatorics, and the related formula at school.
- Did not learn the choice function notation at school.

I think different countries just have slight differences in preferred notation and/or educational programs.

>>11451278
>To say I ate eggs Benedict for breakfast today doesn't mean "the container of truth values associated with 'I ate Eggs Benedict for breakfast' holds that one or that other value inside it."
Yes it does.

>>11450858
>Implying his set of axioms is complete

>>11451664
I see. So you thought it would be unusual for someone to know the standard notation?

test

Gauss-Bonnet theorem
Hasse-Minkowski theorem
what are some other based 2-name theorems?

>>11453904

Bolzano-Weierstrass

>>11450747
Rule 110 is universal.

>>11453904
For me, it's Borsuk-Ulam

>>11450791
Thanks for this. Really neat

Generalized Stokes

>>11451507
Bruh rly

>>11450747
>classification of finitely generated modules over a PID
>Whitehead's theorem
>fundamental theorem of Galois theory
>Hilbert's Nullstellensatz
>Sylow's theorems
>Fermat's little theorem
>every integer has a prime factorization
>homomorphism theorem
>De Rham's theorem
>existence and uniqueness of the tensor product

>>11450858
>le law of excluded middle meem

>>11455181
>trigger everything and everyone : the post

>>11453904
Riemann-Roch theorem.

>>11453904
Atiyah-Singer index theorem.

>>11451568
americans don't even learn pre-calculus until university

>>11450747
Strong normalization of System F.

Inclusion-Exclusion

>>11455275
Oh that's a good one.

>>11455268
That too.

>>11451231
COLOR ME 4 AMIRITEEEEE111!!!

>>11450848
I'm an experimentalist, so I prefer 1~10

>>11453904
Gauss-Bonnet is fucking great. Good choice.