/sci/ - Science & Math

[Anonymous No.14687077]

>formula connects five of the most important numbers in mathematics using four of the most important mathematical operations and relations – addition, multiplication, exponentiation and equality.
Absolutely breathtaking. Time to pay your respects chud, say something nice about this formula.

[Anonymous No.14687083]

>>14687077
>five of the most important numbers
there is only one number in that picture

[Anonymous No.14687086]

>>14687083
here we go again

[Anonymous No.14687089]

>>14687077
Does look good.

[Anonymous No.14687091]

What? that's this with an extra step. I think the more general form has much more significance.

[Anonymous No.14687093]

e^iπ = -1

[Anonymous No.14687098]

>>14687091
Both are gay. Euler can suck on 30cm ruler. There's a number for you to think about tonight.

[Anonymous No.14687103]

>>14687077
It is nice, shame the messenger is a complete cock piece of a child though.

[Anonymous No.14687106]

>formula connects five of the most important numbers in mathematics

>The number 0.
Not a number. Could be considered a representation of infinity.
>The number 1.
A number, but there are arguments it doesn't have to be one. Also can be a representation of infintiy.
>The number π (π = 3.141...).
Pi is not a number. But could be a representation of infinity.
>The number e (e = 2.718...), which occurs widely in mathematical analysis.
'e' is not a number. But could be a representation of infinity.
>The number i, the imaginary unit of the complex numbers.
'i' is not a number. But could be a representation of infinity.

>using four of the most important mathematical operations and relations

>addition. An operation but there are arguments it dosent have to be one. Could just be considered as the successor function

>multiplication
Not an operation as it is repeated addition which is not an operation.


>exponentiation
Not an operation as it is repeated multiplication which is not an operator.

>equality
Not an operation as it dosent change anything.

fuck this brainlet shit

[Anonymous No.14687107]

Imaginary numbers are an abomination. I understand why they exist, but I still hate them.

[Anonymous No.14687109]

>>14687083
e, π, and 0 are all numbers. i can only be compared to a number if you strip the dimension away and measure it as 1

[Anonymous No.14687127]

>>14687083
based

[Anonymous No.14687140]

>>14687083
>there is only one number in that picture
but there are arguments it dosent have to be one

[Anonymous No.14687144]

>>14687109
>e, π, and 0 are all numbers

[Anonymous No.14687150]

>>14687144
my bad: e, π, and 0 are each numbers. i'd have a hard time typing out all numbers

[Anonymous No.14687159]

>>14687150
if these are so called "numbers" as you say, would you mind writing these "numbers" down ?

[Anonymous No.14687162]

>>14687106
>the number 1
>A number, but there are arguments it dosent have to be one. Also can be a representation of infinity.

[Anonymous No.14687164]

>>14687162
0.999...=1 which is a representation of infinity

[Anonymous No.14687168]

im not even trolling i dont know much about math, but how can 0.999999999... be equal to 1? they are two distinct numbers no?

this means that 0.99999999... is not less than 1? that doesn't make logical sense, because 0.9999.... is smaller and you can plainly see it, sure the amount it is smaller is very very small but you can still logically see that 0.999... is smaller than 1 and that they are not equal?

pls help

[Anonymous No.14687169]

>>14687144
They are all numbers, they are not all of the numbers. I know, English is hard

[Anonymous No.14687172]

>>14687159
He did

[Anonymous No.14687177]

>>14687159
here i even put it in order for you like space invaders coming down

0
e
π

[Anonymous No.14687180]

>>14687177
>0
not a number

>e
not a number

>π
not a number

[Anonymous No.14687184]

[Anonymous No.14687194]

>>14687180
>0
>not a number
not an argument

>e
>not a number
not an argument

>π
>not a number
not an argument

[Anonymous No.14687198]

>>14687106
this is peak comedy

[Anonymous No.14687200]

>>14687107
>Anon hasn't taken an geometric algebra course yet

[Anonymous No.14687203]

>>14687168
1 / 3 = .333...
1 / 3 x 3 = .333... x 3
1 = .999...
in fact you can literally turn any repeating decimal into a fraction using this method.

[Anonymous No.14687210]

>>14687077
>i
>number

[Anonymous No.14687324]

Every number is equally important. Even 73.

[Anonymous No.14687336]

amateur hours. this is where the real beauty lies

[math]i^i = e^{-\pi/2}[/math]

[Anonymous No.14687349]

This thread again? At least make the bait less obvious by not using words like chud or breathtaking.

[Anonymous No.14687354]

>>14687324
indeed, 73 is the first prime with 9 quadratic residues in a row, spanning from -4 through 4

[Anonymous No.14687357]

>>14687107
learn signals or radio theory

[Anonymous No.14687384]

>>14687180
Hahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha

[Anonymous No.14687405]

>>14687077
This is hte most beautiful formula ive ever seen

[Anonymous No.14687408]

>>14687336
That's only one possible value.

[Anonymous No.14688098]

>>14687077
I don’t get why people are amazed by this.
It’s literally something akin to 1-1=0 on a number axis but for complex plane.

[Anonymous No.14688103]

>>14688098
Did you guys fail a fucking calculus 1 course?

[Anonymous No.14688104]

>>14687109
>i can only be compared to a number if you strip the dimension away

[Anonymous No.14688126]

>>14687077
Oops, sorry Euler.

[Anonymous No.14688211]

>>14687077
Subtract 1 from both sides and suddenly you only have 4 numbers and 3 operations. Checkmate.

[Anonymous No.14688220]

>>14687168
>how can
because 1/inf=0

[Anonymous No.14688253]

>>14687077
Learn the difference between [math] =[/math] and [math] \equiv[/math], cuck

[Anonymous No.14688257]

>>14687168
Check the archive, anon. You may find one or two threads on the topic.

[Anonymous No.14688310]

i like when the funny numbers do stuff

[Anonymous No.14688372]

>>14687168
Putting aside all the shitty arguments for why 0.999... = 1
0.999... is larger than any number x such that x < 1.
It cannot be any number that is smaller than 1 but it's no larger than 1 as well.
On the real number line, there's only 1 number that meets those criteria and that is exactly 1.

[Anonymous No.14688473]

[math]
\begin{bmatrix}
\cos(\pi)& -sin(\pi)\\
sin(\pi)& \cos(\pi)
\end{bmatrix}+\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}=\begin{bmatrix}
0 & 0\\
0 & 0
\end{bmatrix}
[/math]

[Anonymous No.14688540]

>>14688220
this

[Anonymous No.14688747]

>>14688104
are the distances from 0 to i or to 1 the same or different or incomparable?

[Anonymous No.14688917]

>>14688747
Same

[Anonymous No.14689696]

>>14688747
Same distance, but i and 1 follow 2 different directions : 90° one from the other.

[Anonymous No.14689847]

>>14688917
>>14689696
why did anon make fun of me then :(

[Anonymous No.14690133]

>>14689847
He didn't, just added clarity from an assumption that isn't necessarily true, just standard choice

[Anonymous No.14690141]

>>14689696
Distance doesn't have direction, displacement does. Didn't think we would need to address this on a /sci/ board

[Anonymous No.14690165]

>>14687106
based and redpilled

[Anonymous No.14690206]

>>14690133
he didn't add clarity, he just posted a retard image >>14688104

[Anonymous No.14690219]

>>14687091
That's like saying a box truck has more significance than a Lamborghini. Yeah you're probably right, but the Lambo is sexier.

[Anonymous No.14690256]

>>14687083
>>14687106
>>14687180
>>14687210
>what are integers
>what are irrational numbers
>what are imaginary numbers

[Anonymous No.14690319]

>>14690256
>what are integers
points on the number line that are ruler marks of 1 away from 0
>what are irrational numbers
points on the number line that aren't an integer divided by an integer away from 0
>what are imaginary numbers
points that aren't on the number line

[Anonymous No.14690326]

>>14690206
Then you cited the wrong post

[Anonymous No.14690388]

>>14690326
no, but if i pretend i did will you answer the question?

[Anonymous No.14690517]

>>14690388
It's because there are multiple ways of comparing two pairs of coordinates. Distance is the simplest that loses information. For your interest, look into different distance metrics https://towardsdatascience.com/9-distance-measures-in-data-science-918109d069fa
There are many other ways of comparing values and combining vectors (addition, multiplication, etc) but this will get you started into thinking why you might choose one over another

[Anonymous No.14690543]

>>14690517
thanks, but i think we got our wires crossed somewhere. i was asking what's "retarded" about pointing out that you can't compare i to a number without stripping away the dimension component. i don't think we connected on that

[Anonymous No.14690570]

>>14687106

You never give up do you.
Keep taking your meds!

[Anonymous No.14690576]

>>14690543
Look into cosine distance, that basically only compares the dimension component

[Anonymous No.14690700]

>>14687184
would smash

[Anonymous No.14690704]

>>14688220
1/inf is not a valid fraction

[Anonymous No.14690770]

>>14690704
Express it in terms of limited and learn what limits actually mean. Don't just think about it as we're getting close so we'll call it this value. No, it actually is the value.

[Anonymous No.14690900]

>>14690770
it isn't the value because you cannot construct a fraction out of something that isn't a number or is a placeholder for a number, it doesn't make any sense

[Anonymous No.14691030]

>>14690900
1/∞ isn’t a fraction

[Anonymous No.14691196]

>>14687083
based retard

[Anonymous No.14691250]

>>14687077
its useful for solving problems in the complex field, and for making some stuff with trigonometry so i like it

[Anonymous No.14691264]

>>14687106
now the square root of 2 isnt a number , bruh

[Anonymous No.14691282]

>>14687077
wow truly the Keanu Reeves of mathematicla formulas
kill yourself

[Anonymous No.14691469]

>>14687077
hmm yeah its breddy gud i guess so

[Anonymous No.14691496]

>>14687083
>1
Not a number, just the default dimension
>0
Not a number, just the absence of a number
>e
That's a letter. Irrational numbers are not real.
>pie
That's a food. see above
>i
Also a letter and literally imaginary

Where's the number? Retard.

[Anonymous No.14691519]

>>14687077
What about 1-1=0
Simpler (more elegant) than ops formula
Relates 0 and 1 without having to use e or pi
Uses subtraction, a beautiful operation
Uses 1 twice because 1 is so important and beautiful

[Anonymous No.14692141]

>>14690900
>you cannot construct a fraction out of something that is a placeholder for a number
Right because 1/x doesn't exist because x is a placeholder for a number
Ever hear of algebra?

[Anonymous No.14692159]

>>14690704
ok, Qanon

[Anonymous No.14692224]

>>14691030
that's literally what i just said

[Anonymous No.14692229]

>>14692141
oh no i missed a second 'not' in my sentence and you are so argumentative that you have to perceive me as being wrong instead of giving me the benefit of the doubt that maybe i made a simple typo. you know exactly what i was trying to say. you cannot make a fraction out of something that isn't a number or something that isn't**** a placeholder for a number. you knew exactly what i meant you fucking sperg

[Anonymous No.14692269]

>>14692229
Kek

[Anonymous No.14692291]

>>14687077
You only have 2 numbers there + and =

[Anonymous No.14692321]

is it sad that this equation is the most beautiful thing that ive ever seen in my life?

[Anonymous No.14692480]

>>14690319
kek

[Anonymous No.14692489]

>>14692291
based

[Anonymous No.14692624]

>>14689847
I think you're equating C with R^2

[Anonymous No.14692895]

>>14687106
The post that destroyed /sci/

[Anonymous No.14692915]

>>14687106
Can you give some examples of numbers?

[Anonymous No.14692946]

>>14692915
Prime numbers

[Anonymous No.14692956]

>>14692946
1 is a prime number

[Anonymous No.14692990]

>>14692956
Troll harder

[Anonymous No.14693019]

>>14687106
The post that killed /sci/

[Anonymous No.14693105]

Pifags must be destroyed:
e^(iτ)=1

[Anonymous No.14693225]

>>14687203
that only because we have base 10
if we had base 12 (1,2,3,4,5,6,7,8,9,X,E,0)

1 / 3 = 0.4...
1 / 3 x 3 = 0.4 x 3
1 = 1
does 1 = 0.EEEEEEEEE ?

[Anonymous No.14693276]

>>14693225
>1 / 3 = 0.4..
Already a mistake in your first line (funnily enough you got it right in your second line). In base 12 it would be:
1/3 = 0.4

>does 1 = 0.EEEEEEEEE ?
Yes, but it does not follow from your calculations.

[Anonymous No.14693436]

>>14687077
It’s a great way to identify mindless cheerleaders. If someone presents you with this equation just ask them what the nth roots of unity look like.

[Anonymous No.14693447]

>>14693436
ircc they look kinda like this

[Anonymous No.14693994]

>>14693447
I was looking for "they're the vertices of regular n-gons" but your answer is good, too

[Anonymous No.14694586]

If you divide Euler's Identity by 12 you get the sum of all natural numbers. Incredible

[Anonymous No.14695185]

>>14694586
If you divide 0 by 12 you get the sum of all integers
What's your point?

[Anonymous No.14695551]

>>14687106
>>multiplication
>Not an operation as it is repeated addition which is not an operation.
lol no. The incompleteness of Peano arithmetic is a consequence of defining multiplication as an operation. If you only have iterated addition (i.e. Presburger arithmetic) then incompleteness doesn't apply.

[Anonymous No.14695553]

>>14695551
semantic incompleteness, to be more specific

[Anonymous No.14695563]

>>14695551
What about vector multiplication? Cross product to be specific

[Anonymous No.14696604]

>>14687083
You know what? Maybe 4chan isn't such a good format for discussions. Some opinions like this one are just worse than others and should be hidden or buried because they add nothing to the discussion aside from trolling and making you falsely think that some people unironically believe this.

If only there was a way to vote on which posts should be more visible and which posts should be less visible. And maybe the comments should be sorted so the more visible ones are displayed more up and less visible ones are displayed more down. And we could maybe call them upvotes and downvotes.

If only...

[Anonymous No.14697113]

>>14695563
Can you define a cross product without making any reference to the dot product?

[Anonymous No.14697157]

>>14697113

[Anonymous No.14697185]

>>14697113
Who even uses a dot product to define or justify a cross product?

[Anonymous No.14697189]

>>14687083
kek schizo posts are the best

[Anonymous No.14697209]

>>14697157
What I should have asked is if it's possible to define cross product without reference to addition, not dot product.

tbqh I took a single linear algebra class in 2007 and I don't remember most of it. I don't know for sure if the cross product would entail incompleteness without the dot product. My guess is yes, because semantic incompleteness (as in Gödel's Incompleteness Theorems) is a consequence of a language's capacity to express self-referential statements. If you have two operations and one is an iterated form of the other, then (I think) that's sufficient for self-reference.

If you had just cross products but not vector addition, then (maybe) you could have semantic completeness.

[Anonymous No.14697211]

>>14697185
Because I'm stupid and meant addition, see >>14697209

[Anonymous No.14697224]

>>14697209
What's the issue with self-reference? It's called shorthand or implicitly specifying an iterator instead of passing additional information like
In terms of python type basically asking for sum([1 for i in range(5) for j in range (8)]) instead of simply 5*8 to avoid self-reference

[Anonymous No.14697235]

>>14697224
>What's the issue with self-reference?
How much do you know about Gödel's First Incompleteness Theorems and its proof? (Not trying to start a pissing match, I just want to know where to start.)

[Anonymous No.14697239]

>>14697235
Literally nothing or just seems strange that relying on things you've already defined is bad. Just looking for big picture ideas instead of getting lost in the weeds and taking too long to understand the depths otherwise yeah I'd look it up. I'm also assuming he's a mathematician and has good work to say instead of all the AGI bullshit going around. Just from what you said here it started sounding more like the latter than the former

[Anonymous No.14697243]

>>14697239
AGI bullshit and things like Fermi's paradox. Good physicist but pointless discussions to follow from that idea

[Anonymous No.14697249]

>>14697224
The short answer is, the theorem is usually expressed as something like "any consistent system capable of a certain level of arithmetic will contain theorems it can neither prove nor disprove." The capacity for self-reference satisfies the "certain level of arithmetic " condition.

[Anonymous No.14697252]

>>14697249
Fair enough, but to toss out something because it is complex enough to contain something unprovable isn't good justification to ignore the things that can be proved or to try proving what seems reasonable

[Anonymous No.14697253]

>>14697249
>>14697252
But all this is probably moot anyway since your initial post I cited was replying to a troll anyway

[Anonymous No.14697254]

>>14697239
>I'm also assuming he's a mathematician
and logician, and he did some stuff on epistemology but I think it wasn't published during his lifetime.
>and has good work
He's arguably the most influential mathematician of the twentieth century.

[Anonymous No.14697266]

>>14697252
>to toss out something because it is complex enough to contain something unprovable
I mean there are good reasons for studying things like Presburger arithmetic, but you're correct that this isn't a reason to abandon self-referentiality. It's just that you have to accept that it leads to things like "This statement is false."

[Anonymous No.14697269]

>>14697253
I have an autistic crush on this theorem so an opportunity to discuss it is never moot. Thanks for indulging me, Anon.

[Anonymous No.14697273]

>>14697269
I mean we can discuss in more depth, like if there's any indicators that something is unprovable, etc, but those aren't the theorem but more a corollary (no idea what those follow up words mean and which is appropriate) but at least it's related. I get his theorem is more an existence theorem than applicable to specific statements. What other conditions are necessary and sufficient for a language to contain unprovable statements? Does that necessarily generalize to an inability to determine truth value?

[Anonymous No.14697387]

>>14697273
>if there's any indicators that something is unprovable
That's the halting problem. Turing proved that there's no general solution, but you're asking about a heuristic not a solution. Interesting question. I have no idea.
>I get his theorem is more an existence theorem than applicable to specific statements
Well there are infinitely many unprovable theorems of Peano arithmetic, and some non-trivial ones have been identified. e.g. https://en.m.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem

But the unprovable statement from his proof, which was roughly equivalent to "This statement is unprovable," has interesting properties. Its similarity to the Liar Paradox, "This statement is false," is obvious.

But to an Intuitionist, they're not just similar, they're the same statement. Because to an Intuitionist, the truth of a mathematical claim is equivalent to a mental construct proving that claim, (truth <==> proof).

Well the claim "this claim is unprovable," which proves the 1st Incompleteness Theorem, is itself isomorphic to the 1st Incompleteness Theorem. You have to already know the theorem in order to prove the theorem. (truth <==> proof).

>What other conditions are necessary and sufficient for a language to contain unprovable statements?
I know Robinson arithmetic is also incomplete and is weaker than Peano, but I don't remember how it's weaker off the top of my head and I'm too lazy to look it up right now as this post is already pretty long.
>Does that necessarily generalize to an inability to determine truth value?
Unfortunately this crosses the line of active work that I can't discuss.

[Anonymous No.14699284]

>The mathematician Carl Friedrich Gauss was reported to have commented that if this formula was not immediately apparent to a student upon being told it, that student would never become a first-class mathematician."

ITT: brainlets

[Anonymous No.14699451]

>>14687077
The proof is ugly. I will never like this formula.

A beautiful proof is more important than a beautiful statement. There are ugly statement with beautiful proof (for example IMO 1994 problem 6 is ugly problem but has a beautiful proof) and I like them because the proof is beautiful. I never like a beautiful statement with ugly proof.

[Anonymous No.14699456]

>>14699451
>The proof is ugly
which one?

[Anonymous No.14699479]

>>14699456
How to prove this beautifully?

sin(x),cos(x),e^x can be written as infinite sum sum a_nx^n

[Anonymous No.14700023]

>rotates 1 by half a turn on the complex plane
>OMG IT CONNECTS ALL THE NUMBERS I HECKIN LOVE SIENSE

[Anonymous No.14701624]

>>14687168
>sure the amount it is smaller is very very small
the whole problem here is HOW small. Because no matter how tiny you go, we can STILL demonstrate that we'd be off the value by some finite amount. For example:

hmmm 0.99999999... must have some finite difference between itself and 1, even if its really small! This is the same as saying that at some point the 9s must stop repeating so that we can measure a finite difference. That is, eventually 0.9999... = 0.999...99a0000.... where a is the last nonzero digit in the decimal expansion, and then 0.9999 = 1 - 0.000....00a00000. But by definition, there will never be any point at which we can measure this difference, because the real difference will continue to be smaller and smaller and smaller no matter how small of an initial difference we pick.

[Anonymous No.14702522]

>>14693447
only good post in the thread. keep it up anon

[Anonymous No.14702674]

>>14690219
Cos and Sin are definitely sexier than pi

[Anonymous No.14702689]

Philosophy/Sophistry are not science, maybe >>>/lit/ or >>>/x/ are more your speed.

[Anonymous No.14702696]

>>14702674
You like your functions to let it all hang out like that, I get it. A bit lurid for my tastes. I like a function that leaves something to the imagination. To each their own.

[Anonymous No.14702699]

>>14702674
>>14702696
Functions, equations, whatever. Shit.

[Anonymous No.14702951]

>>14687077
we out here doin real shit nigga

[Anonymous No.14703204]

>>14691496
kek

[Anonymous No.14705607]

>>14687083
true, and that number is zero. The left side is equal to zero so the only number in that picture is 0.