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/sci/ - Science & Math

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8570042 No.8570042 [Reply] [Original]

I think I just discovered new mathematics. What happens if we have a function like this:


f(x)=x.cos(x)

Yes that "." between the x and cos(x) is a decimal, but what will it look like if you graph it? How would you take the derivative or integral of something like this? Maybe I just thought of new math?!

>> No.8570054

Compare this to x + cos(x), x =/= πn...

>> No.8570060

>>8570042
so x + [cos(x) / 10]?

>> No.8570065

Really made me think

>> No.8570068

Senpai are you actually retarded?

>> No.8570069

>>8570042
What're you going to name it?

>> No.8570074

Obvious bait, but i'll bite.

I started doing this in middle school for fun. You didn't discover anything.

>> No.8570083
File: 439 KB, 1085x680, 1433753049841.jpg [View same] [iqdb] [saucenao] [google]
8570083

>>8570069
"Anon's Dot"

>> No.8570092
File: 68 KB, 720x514, 1482805932857.jpg [View same] [iqdb] [saucenao] [google]
8570092

f(x)=x+0,1cosx

>> No.8570104

>>8570042
I must know what you're majoring in.

>> No.8570106

>>8570042
So let's see, f(1) = 1.0.5403...
Oh wait, that doesn't make any fucking sense.

>> No.8570150

>>8570106
Or does it, what if decimals have decimals, called sub-decimal integers?

>> No.8570160

>>8570042

You're just adding cos(x) to x if x is an integer and if it isn't then you're gonna get like 5.4.cos(5.4) which is nonsense...

>> No.8570166

>>8570042

How old are you?

>> No.8570167

>>8570160
>>8570166
Actually, they are sub-decimal integers as per Anon's Dot hypothesis, see >>8570150.

>> No.8570170

>>8570150
You made me laugh OP. You are still retarded though.

>> No.8570172

>>8570060
This falls apart if x > 10, needs to be defined as some kind of piecewise function with increasing powers of 10 in the denominator

[math]x + \frac{\cos{x}}{10}[/math] if x < 10
[math]x + \frac{\cos{x}}{100}[/math] if 10 <= x < 100

etc

>> No.8570196

>>8570172
What? Why would it fall apart?

>> No.8570225

>>8570060
/thread

>> No.8570269
File: 5 KB, 687x523, 4chan.png [View same] [iqdb] [saucenao] [google]
8570269

as I see it

>> No.8570300

>>8570104
comp sci. its my 1st year

>> No.8570304

>>8570300
>Hello guys. Today we are going to learn about concatenation in Java. Here is the task: Write a """program""" that takes two numerical strings and then concatenates the digits of one string as the decimals for the first string, and returns this new string

>HOLY FUCK I JUST INVENTED NEW MATH CALL THE PRESS

>> No.8570349

I don't think STEM is for you, have you considered switching to Women's Studies or some other major that only requires a single digit IQ?

>> No.8570354
File: 54 KB, 531x773, stephen.jpg [View same] [iqdb] [saucenao] [google]
8570354

>>8570150

That's just called the next decimal place.

retard.

>> No.8570362

>>8570269

Is the function differentiable at pi/2?

>> No.8570371

>>8570042
this poor OP has got to wish so hard that he could delete this post... poor guy.

lets sadistically bump this over and over so his shame wont archive.

>> No.8570372

>>8570371

good idea.

>> No.8570374

>>8570371
>lets sadistically bump this over and over so his shame wont archive.

nice

>> No.8570384

In all seriousness, I could get behind this notation. I'd love to write 0.cos(x) instead of cos(x)/10.

>> No.8570410

its actually a good idea.

never thought of that.

but u are mistaking the decimal as some sort of operation.

>> No.8570486
File: 84 KB, 1506x897, BIG IF TRUE.png [View same] [iqdb] [saucenao] [google]
8570486

this is almost as breakthrough as -1/12 op

>> No.8570491
File: 144 KB, 1505x896, 23.png [View same] [iqdb] [saucenao] [google]
8570491

so this... is the power.. of anon math..

>> No.8570492
File: 78 KB, 1507x889, CARL FRIEDRICH GAUSS.png [View same] [iqdb] [saucenao] [google]
8570492

it looks like a bad 90s haircut

>> No.8570493

F(X) = X+0.1cos(x)

>> No.8570501

>f(x)=x.cos(x)

You have to show how it works.

Hey guys x#cos(x) it does something but idk what, and I certainly can't think deeply enough to graph it myself, so show me how it does something. # does (something familiar) so maybe I just thought of new math?!

>> No.8570698

>>8570493
/thread

>> No.8570703

I havent laughed this hard at a thread in weeks

>> No.8570706

>>8570042
o i am laffin

>> No.8570712

>>8570042
Therem: If x is an infinite decimal that does not equal a finite decimal then x.cos(x) = x

First consider the arbitrary integer [math]a_1[/math]

[math] f( a_1 ) = a_1 + \frac{cos(a_1)}{10} [/math]

Then add a non zero decimal [math]a_2[/math]


[math] f( a_1.a_2 ) = a_1.a_2 + \frac{cos( a_1.a_2)}{100} [/math]

Then notice that

[math] f( a_1. a_2 a_ 3 ... a_n) = a_1. a_2 a_ 3 ... a_n + \frac{cos( a_1. a_2 a_ 3 ... a_n)}{10^n} [/math]

Then compute


[math] \lim_{n\to\infty} f( a_1. a_2 a_ 3 ... a_n) = \lim_{n\to\infty} a_1. a_2 a_ 3 ... + \frac{cos( a_1. a_2 a_ 3 ...)}{10^n} = a_1. a_2 a_ 3 ... [/math] [math] \square [/math]

Fuck, thanks for the PhD thesis OP. I had been stucked in this shit for months. No idea what to prove. You gave me an easy answer, my paper is already up in arxiv. I will gift you this first theorem I proved though.

>> No.8570747

>>8570712
where did the 10^n come from?
also e*cos(e)=/=e

>> No.8570758

>>8570747
>also e*cos(e)=/=e

Yes but e.cos(e) does equal e. I just proved it.

>> No.8570763

>>8570747
Where is the faulty reasoning though ? His function is not clearly defined ?

>> No.8572139

>>8570371
agreed

>> No.8572148

>>8570060
kek

we have a winrar

>> No.8572162

>>8570371
kekklez

>> No.8572168

>>8570384

top kek

>> No.8572184

>>8570042
This is the worst idea since -1/12.

>> No.8572205

>>8570354
Or are they infinitesimals?

>> No.8572211

>>8572205
K

;^)

>> No.8572214

>>8570042
op i just want to say i've never thought of this before and its pretty cool.

lateral thinking and creativity is the path of the genius, and even this doesnt lead to something new its a unique way of thinking about things which is just what we need.

glad you posted it, and dont mind the braindead robots who can't compute, creativity left them long ago, we can only pity them now.

>> No.8572225

>>8570042
like this?

x+c/10+o/100+s/1000+(/10000+x/1000000+ )/10000000

>> No.8572259

This entire thread reminds me of this

https://www.youtube.com/watch?v=tmRHy3cu31M

>> No.8572369 [DELETED] 

f(x)=x.cos(x) =/= x + (cos(x)/10)

if you have

imagine doing it with

f(x) = x.3x

then f(x) = x + (3x/10)? I think not

>> No.8572376

>>8570712
The interesting thing comes when you're using non repeating rational numbers. Then the function get's really weird.

>> No.8572381 [DELETED] 

OP here

here's my thereom


let f(x) = g(x)

g(x) = n(x).T(x)

if and only if T(x) < 1

T(x) are functions like cos, sin, tan etc...

You cannot use the notation if it's something like:

f(x) = x.3x because

f(x) = x.3x =/= x + (3x/10)

QED

>> No.8572384
File: 23 KB, 200x300, 1483039066376.jpg [View same] [iqdb] [saucenao] [google]
8572384

>>8570042

Dude, weed.

>> No.8572401 [DELETED] 

OP here

here's my thereom


let f(x) = g(x)

g(x) = n(x).T(x) = n(x) + (T(x)/10)

if and only if T(x) < 1

T(x) are functions like cos, sin, tan etc...

You cannot use the notation if it's something like:

f(x) = x.3x because

f(x) = x.3x =/= x + (3x/10)

3x is never less than 1

QED

so maybe I'm onto something, maybe we can replace the + operator using only decimals, we must first define some rules for it to work though like my theorem

>> No.8572403

OP here

here's my thereom


let f(x) = g(x)

g(x) = n(x).T(x) = n(x) + (T(x)/10)

if and only if 0 < T(x) < 1

T(x) are functions like cos, sin, tan etc...

You cannot use the notation if it's something like:

f(x) = x.3x because

f(x) = x.3x =/= x + (3x/10)

3x is never 0 < T(x) < 1

QED

so maybe I'm onto something, maybe we can replace the + operator using only decimals, we must first define some rules for it to work though like my theorem

>> No.8572406

But that get's me thinking.. what if we actually graph a function like

f(x) = xcos(x).x

>> No.8572410

>>8572406
It will look like the line y=x but with discontinuities jumping everywhere.

>> No.8572412

>>8572410
or let's make it weirder

f(x) = xcos(x).xtan(x)

>> No.8572415

>>8570712
kek

>> No.8572420

>>8572412
I think you're still just getting the function xcos(x) with discontinuities every place that xcos(x) is non-repeating rational number. The positioning of the discontinuities would be interesting though.

>> No.8572426

>>8570172
You don't know what the range of cosx is do you bb

>> No.8572428

>>8572420
so then I just invented new math, it gives us random discontinuities which is probably useful for random analysis and probability, what should we call this new maths?

>> No.8572433

>>8572428
You need to take into account that it will be quite different for different base systems.

>> No.8572437

>>8572426
I think he's accounting for x having a decimal string of it's own.

>> No.8572440

>>8570712
Wouldn't this work for other funcions too besides cos, sin etc? Because since a is a natural number between 0 and nine, the maximum number it could generate is 9.99999... so for any kind of function, if you calculate the limit as n approaches infinity for f(a_n) the number a(1).a(2)a(3)... would eventually converge to 10 while 10^n would approach infinity and the term disappears. So you could generalize this theorem a little more I think

>> No.8572441

>>8572433
how would you know?

>> No.8572451

>>8572441
Because it affects the position of decimals (not always base ten you know what I mean). Moving and appending decimal points should make it base dependent.
Just a hunch could be wrong here.

>> No.8572462
File: 48 KB, 500x444, haircut.jpg [View same] [iqdb] [saucenao] [google]
8572462

>>8570492
wtachu mean boi

>> No.8572463

>>8572428
You also haven't accounted for the f(x) in
g(x)=x.f(x)
being negative. you need a convention like abs(f(x)) of the the negatives reduce the decimal string, wither a a wrap around like
2.(-2) = 2.8
or 2.(-2) = 1.8

>> No.8572468

>>8572463
maybe... but that negative could potentially mean something, we just have to experiment and find out if it means anything. It might mean something different.

>> No.8572494

>>8572428
Could call it Appended Base Expantion

>> No.8572852

>>8570042

what about [math] x \sin ( \frac{1}{x} ) [/math]

>> No.8572862

so x=cos.&6^ > y%? I'm totally into your new math
can you comprehend mine a little?
2x=y7 squared man2 power of 4% -=)ldrt:D

>> No.8572888

>>8570042
Something like this. It's a slightly waved straight line.

>> No.8572891
File: 114 KB, 640x960, image.jpg [View same] [iqdb] [saucenao] [google]
8572891

>>8572888
Forgot to attach pic. Nice I got trips

>> No.8572901

>>8570384
It's called 0.1*cos(x)

>> No.8572934

>>8572891
No dude fuck that shit, plot this:

f(x) = xcos(x).xtan(x)

>> No.8572937

You all are fucking retarded. Cos(x) is less than 1 for all non-pi multiples of pi. ".cos(x)," as you have so loosely called it, would simply be the identity function for all non-pi multiples of x. At pi-multiples, ".cos(x)" would cycle through the values .1, 0, -.1, and 0. I shouldn't kill this thread, though, so that the retards can have their containment thread.

>> No.8572949

>>8572934
Is the point decimal or multiplication?

>> No.8572969

>>8570362

Does it look differentiable at pi/2?

>> No.8572980

>>8572937
Kind of bizarre you are calling everyone retarded when thats the last thing I would have guessed as the meaning of this undefined nonsense, especially when you talk with terms like "would simply be" as if theres a canon way to interpret things made up on the spot.

>> No.8572986

>>8572937
>non-pi multiples of pi

>> No.8573038

>>8572437
But that still doesn't matter.
For any
[math] x \in [\mathbb{R}] [/math]
x.cos(x) will also yield a real (obviously)
Because cosx is always <,= 1 I'm 99% positive that x + (cos(x)/10) == x.cos(x)

>>8570758
e.cos(e) is ~ 2.71828182846.-0.91173391478696509789371731780543184525041342921569540133
If you resolve the decimals how I think you would (correct me if I;m wrong)

That's still quite literally cos(e) + e, which isn't e so you clearly haven't proven it unless I'm demonstrably wrong that
x.y =/= x + .y

>> No.8573080
File: 2.93 MB, 1440x2560, Screenshot_20161226-220908.png [View same] [iqdb] [saucenao] [google]
8573080

Can you use it on this? Notice the intersections in the triangles and the triangle of pascal

>> No.8573085

>>8573080
Is this your architecture drafting practice?

>> No.8573101
File: 10 KB, 236x271, 24522d4933eaf78bacb372cdc62d8b2e.jpg [View same] [iqdb] [saucenao] [google]
8573101

>>8573085
No, its a sketch. I'm working on perspective calculation. I think it has something to do with this.

>1=(0+1;2-1;3-2; till infinity)

And 1÷3= .3333333333333333 (till infinity)

>> No.8573102

>>8572986
Good reading comprehension, faggot.

>> No.8573104

>>8573101
>>1=(0+1, 2-1,3-2,... till infinity)
First, shouldn't it be
1=(1-0, 2-1, 3-2,... An-1 - An)
Second...
Why?

>1÷3= 0.3333333333333333...
>Infinitesimals

>perspective calculation
desu no idea what that means.

>> No.8573105

>>8572969
Did you have to be rude to people senselessly?

>> No.8573109

>>8572376
>non repeating rational numbers

...also known as the irrational numbers?

>> No.8573455

>>8573109
1/3 is repeating, 1.3 is not repeating if there are an infinite amount of decimal places OPs function is the same as the input.

>> No.8573484

>>8573455
1.300000....
?

>> No.8573491

>>8573484
No different from 1.3 physics get out.

>> No.8573497

>>8573491
>physics
1.30000... is the full number.
every rational number repeats.

>> No.8573512

>>8570042
That's actually easy to solve.

A better example of a "new" branch is:

x^x factors.

>> No.8573515

>>8573497
well the see this
>>8570712
and everything in this thread is useless

>> No.8573527

>>8570172

[math]
f(x) = x + \frac{g(x)}{10^{\lfloor log_{10}(g(x)) \rfloor + 1}} = x.g(x)
[/math]

pleb

>> No.8573537

>>8570042
How does the first part of x.cos(x) work?

let x = 1.451032, then cos(x) = 0.1195

so x.cos(x) = 1451032.01195

would that be correct?

why cant we just do x = 1.45103200000000000000 and have the number be

x.cos(x) = 1.45103200000000000000.01195

>> No.8573539

>>8573537
edit

x.cos(x) = 145103200000000000000.01195

>> No.8573549

>>8573537
OP didn't think much about it but it is better for . to be a concatenation.

So if x is 1.451032 and cos(x) is 0.1195 then
x.cos(x) = 1.45103201195

>> No.8573572
File: 57 KB, 490x653, sheriff.jpg [View same] [iqdb] [saucenao] [google]
8573572

>>8570172
But that's wrong, you mongoloid

>> No.8573596

>>8573549
Isn't that what it was from the begining

>> No.8573614

>>8573549
so the magnitude of cos(x) will vary widely depending on the digit length of the number x.

wouldnt this mean that if you did the exact same function evaluation in a different base value would you get a different number?

converting x = 1.451032 to base 8 you would get an infinitely long number which is 1.3467332522271420461521675... if the calculator I used was right.

so that would mean the magnitude of cos(x) would be infinitely small.

>> No.8573625

>>8572949
decimal