/sci/ - Science & Math

>>10238814
Define "true".

>>10238814
t. Social science major

>>10238820
This is why mathematicians need to be rounded up by the state.

If you really believe that sums to negative 1, why don’t you hand me two dollars, then 4, then 8, and so on and let’s see if I end up out a dollar. Fucking homo. God damn when people brag about doing math like this it makes me vigilantly angry, you’re literally not doing anything that’s real or true. Fuck anyone that actually believes that shit. How gullible can you be?

>>10238814

the left sum doesnt even converge, how can it be -1

LMFAO

>>10238825
If one agrees with the assumptions and axioms of Rammanujan summation then yes, I do believe it, but you don't have any idea of what that is, so you approach it with your "intuition" instead of any real mathematical rigor or any knowledge of what exactly leads to that result so you flail and foam at the mouth when someone uses words aren't actually completely familiar with in a way you aren't used to.

>>10238828
It does converge for very small infinities

>>10238833
“Mathematical rigor” is literally just making up nonsensical definitions and then following them to their logical conclusions. It’s not hard to do. Again, it’s got nothing to do with the real world and is just fake bullshit, and the fact that people that spend their days contemplating this shit (like yourself) think it makes them superior to those who don’t us the primary reason they should be rounded up and forced to do real labor. Fuck EVERYONE who does math like this.

>>10238825
All math is arbitrary. The specific formula you posted is only true if you assume that divergent sums can have finate solutions or that general operations can be applied to infinate numbers. The reason why that solution is not an issue is that nothing in leads to a contradiction assuming that the properties of number sums do not hold for infinate sums (eg. 1+1+1/2+1/6+1/24+1/120... is irrational despite how every individual point on the sum on the way to infinity is rational) which is not an absurd assumption. Using these assumptions you can create logical explanations for some otherwise illogical identities that are not equivalent for certain values (eg. Zeta(-1)=-1/12 as opposed to not existing as the sum definition would imply assuming you are using one of the many identities if zeta which are equivalent for all non negative integers.). Overall these sorts of sums exist to logically explain parts of math that otherwise don't make sense.

>>10238841
Oh I see, you're one of those people, carry on then.

>>10238851
Adding on to what I said prior the same methods used to get the formula you posted are also used to obtain the sum of the series 1,0,1,0,1,0 and set it equal to 1/2, which is used to get the infamous -1/12 which, unlike what you said does have real world application, as shown by the casimir effect's derivation. So yes these infinate sums do have uses.

>>10238814
Isn't it the same thing as a for loop in programming?

>>10238841
>Fuck EVERYONE who does math like this.
Nigger

>>10238841
>they should be rounded up and forced to do real labor
These retards would fuck that up, too. Line them up next to a trench. Sounds extreme until you realize that they don't spread bullshit like OP's pic because they're stupid. They do it because they are evil and want to fuck up our progress.

>>10238851
>All math is arbitrary.
Then none of it is wrong, you faggot.

>>10238926
For convenience sake we set the standard of math to be that equvilance and non equvilance exist and hold true.

>>10238814
Divergent series are a meme

>there are people out there who devote their ENTIRE LIVES to researching adding up little fractions

holy fuggn gek get a life you autists and do something real/useful

>>10238814
wait, but this isn't true lol
where did you get this picture from?

it should be

SUM 2^n = 2^(n+1) - 1

How the fuck did you manage to forget the 2^(n+1)?

>>10238814
>>10238825
>>10238841
>>10238925
>>10238926
>>10239331
Cry me a river, brainlet.

>>10238814
>I'm too retarded to undertand it

>>10238814
>Be op
>Be that retarded

>>10239352
You are even less familiar with the topic than the OP, brainlet.

>>10238814
math went full retard when chinks and pajeets started doing it. it's a good thing i stopped believing in it early on

>>10239430
>didn't understand math so he quitted and blamed others

We all know what you did there, don't need to hide

>>10239433
at least i'm not brainwashed into believing absurd things

>>10239409
wow, you guys are really fucking stupid
can't believe i was baited into replying to this thread

>>10238825
>define "true"
>this makes me angry, this isn't true. you are gullible
?

>>10238814
The day you'll realize that the Riemann hypothesis is about finding the correct way to do such summation.
Ramanujan wrote 1+2+3+...=-1/12 because he knew that it was the real shit.

>>10238814
>It’s got nothing to do with the real world and it’s not even true.

"Do not ask whether a statement is true until you know what it means."
-Errett Bishop

if its not true then fucking disprove it.
[math]
A=1+2+4+8+...\\
A=1+2(1+2+4+...)\\
A=1+2A\\
A=-1
[/math]

>>10239352
how the fuck did you manage to forget to show that 2^inf isn't 0

>>10239439
Why don't you stop saying vague shit and actually shows some of the "absurd things" you're talking about.

>>10239516
>that “proof” that it equals -1
Holy shit no wonder math majors are all unemployed. What a bunch of useless trash

>>10238825
>being stupid enough to think that an infinite process can terminate

>>10239573
it was a demonstration you retard, it wasnt meant to be serious, but please, actually disprove the summation
i bet you fucking cant

>>10239516
BASED GENERALITY OF ALGEBRA POSTER.
>>10238825
Nice pasta.

>>10239573
>no wonder math majors are all unemployed
Continue believe this old story retard. A math major is paid more than you 99% of the time.

>>10238841
>“Mathematical rigor” is literally just making up nonsensical definitions and then following them to their logical conclusions
that's true
>It’s not hard to do
this is not true
>it’s got nothing to do with the real world
this is not true
>Fuck EVERYONE who does math like this
everyone does math like this, because centuries of trial and error proved that it's simply the most efficient way to do math

>>10239580
>>10239516
this guy >>10239573 is completely correct
your """proof""" is fucking retarded
you call yourself a math major but fail to realize there are infinities that are smaller than other infinities
That shitty second summation you substitute on the right hand side that you call """A""" should be called A' or A* since it will literally always be one term smaller than A.

You want me to disprove it AGAIN?

A = 1 + 2 + 4 + 8 + ...
A = 1 + 2(1 + 2 + 4 + ...)
A = 1 + 2(1 + 2(1 + 2 + 4 + 8 + ...))
A = 1 + 2(1 + 2(1 + 2(1 + 2 + 4 + 8 + ...)))
A = 1 + 2(1 + 2(1 + 2A))
A = 1 + 2(1 + 2 + 4A)
A = 1 + 2 + 4 + ... + inf*A
You will literally have an infinite summation of positive integers no matter what, idiots
You can't just take some notation and pretend like it's a true infinite sum when in reality one sum is literally always smaller than the other

Riddle me this. Which sum is bigger?
2 + 4 + 8 + ...
OR
1 + 2 + 4 + 8 + ...

I swear to god if you morons claim both sums are equal to each other, we're gonna have a problem. Your stupid fucking arguments rest on the premise that both sums equal each other

>>10239632
>since it will literally always be one term smaller than A.
thats not how different sizes of infinity work dude, adding or subtracting a finite number (one term) from countable infinity is still countable infinity.
the entire "disproof" in that sentence is built on a misunderstanding of the sizes of infinity

A = 1 + 2 + 4 + ... + inf*A
you have a last term in a series thats infinite, thats invalid and i never did that
if you looked just one step before
A = 1 + 2(1 + 2 + 4A)
A still equals -1 here.

Riddle me this. Which sum is bigger?
2 + 4 + 8 + ...
OR
1 + 2 + 4 + 8 + ...

-2
OR
-1

-1 is bigger.

>Your stupid fucking arguments rest on the premise that both sums equal each other
no, my arguments literally dont

>>10239580
>takes a fat shit on sheet of paper
>”hehe...disprove that my shit isn’t a literal shit...bet you can’t, kid”
The entire math population needs to be eradicated so we can start over. Even the physicsfags aren’t this bad. At least they occasionally do something useful

>>10239516
in the second line you're using associativity of infinite summation and in the fourth line you're using commutativity. both properties hold only when the sum is (absolutely) convergent, but that's what you're trying to show in the first place. circular reasoning.

>>10239661
i said disprove the summation, not my demonstration, learn how to fucking read

>>10239667
>but that's what you're trying to show in the first place.
im not trying to prove convergence

Yeah I know i cant use those, but the actual proof is apparently beyond the scope of ops understanding
so im just trying to show him that it isnt contradictory like he thinks it is.

People who jack themselves off to immediate applications of their work are generally completely devoid of creativity and inspiration in their work. I’ve noticed they define scientific jobs more like “doing a task” rather than “understanding what’s going on.”

Anyway it sounds like you’re an engineering student salty about calculus 2. One only has to squint to see applications of purer math once we’ve studied it sufficiently enough. Summation over infinity is tricky and not super intuitive (even less so than integration at times). In calculus 2 they try and give you various tests/algorithms to plug and chug (limit comparison is bread and butter:: given a sequence of terms [math] a_n [/math] find [math] b_n = \Theta ( a_n ) [/math]. The behavior should be more or less the same. Students still fuck it up. I feel like “it has no applications (that I can see)” is the laziest, most immediate excuse for “i don’t get it, this sounds stupid.” Would you give up signal analysis and communication towers just because you don’t believe in imaginary numbers? Would you give up body scans because you don’t believe in positrons and annihilation?

>>10239728
* [math] b_n \in \Theta (a_n) [/math]

>>10239593
Tbh, huge topics in maths really do have no real world application. Not to say that's a bad thing though as physicists are famous for stumbling into problems they can't solve just to find out that some mad mathematician has developed a whole field of maths which turns out to be the exact solution to their problem.

>>10238833
I'm with you. But let's not pretend that the origin of these misunderstandings is that they are using the same fucking notation that is used for "normal" sums

>>10239847
That it's not *

>>10238814
That’s just using the formula for a converging geometric series and ignoring the general formula for a geometric series. I agree it’s wrong because the sum on the left diverges, so that picture is not a true sum.

>>10239847
You do realize that we have different definitions for adding whole numbers, rationals, reals and complex numbers. But using different notation would be overly pedantic and a total waste of time.

We analytically continue sums just like we extend other definitions to larger domains. This isnt strange or unintuitive, its how we do all math.

>>10238814
You seem upset.

>>10238814

> he still thinks in base 10
> he still hasn't adopted the 2-adics

lmao!

>>10238851
>The specific formula you posted is only true if you assume that divergent sums can have finate solutions or that general operations can be applied to infinate numbers.

Wrong. Its true when you work under a different norm or metric on the real numbers than the usual one. look up p-adic numbers. this result is specifically using the 2-adics.

>physishits and engisneers SEETHING in this thread
ahahahah oh wow

>if it not my intuition it wrong
fuck non-mathematicians, youre all stupid

>>10240005
Litterally what i just explained.

>”ayyy bruh *takes a puff of weed* what if I give you 1 apple, then give you 2 apples, then 3 apples and keep going....”
>”damn bruh sounds like I’d have a lot of apples * hits blunt * “
>”no bruh....you’d actually have -1 “
>”yoooo.......YOOOOOOO!”

>>10238814
Yes, it isn't.

But you are missing the point, probably because you are retarded.

>>10240086
>He doesn't trust his intuition
How can you even do mathematics? The claim is also formally wrong inside of the standard analysis definitions, exactly what my intuition tells me.

>>10239587
>A math major is paid more than you 99% of the time
But when you include the remaining one percent, the math major's total pay is only -1/12.

>>10240631
Top kek

>>10240591
>The claim is also formally wrong inside of the standard analysis definitions
nope, there is no standard. Complex anal is cooler than real anal anyway, they have analytic continuation

And i didnt say that i dont trust my intuition, I do. But other people have wrong intuition so they shouldnt trust theirs.

>>10239920
Well that's true.. It's just that these ones for some reason got out of hand

>>10239516
Let's get rid of -1 and just use the other thing instead. Let's find something like that for all the negative integers and just get rid of these un-integers. And complex numbers are proably not needed either, or zero. Let's go back to roman numerals or even unary notaton.

>>10239632
the same thing you're arguing is a problem is the same method used to find other infinite sequence's answers, and predict them accurately, you're a brainlet and you need to unironically kill yourself.

>>10241137

Consider why negative numbers "exist" in math. Its simply because some asshole forgot to account for all the items they represent in the first place. Nothing wrong with the minus operation, mind you, so long as you dont try to subtract anything greater than what exists in the first place. Thats where math gets all fucked up, people doing dumb shit like that.

I have 10 apples and I owe you 11 apples.

10 apples minus 11 apples....

WHAOH! Wait on there asshole! Its impossible to have a negative apple. You dumb asshole!

So really what you mean to say is...

There are n apples in existence of which you have n - 11 + 10

So lets say there are only 22 apples in existence at this very moment.

Then 22 - 11 +10 = 21.

YOU HAVE 21 FUCKING APPLES!

Well okay, how about me then?

To give you more apples than I currently possess I have to take at least one from the pile of n.

See kids? It all makes sense if you aren't an asshole about it.

>>10238814
A lot of things in m*th are flawed, even up to the foundations themselves. Like for an example, what exactly is x/0 without pulling the usual "uhh dude you just cant bro XD" or going into abstract bullshit like limits or infinities
But hey lets just pretend that it's all fine and automatically conclude that since the natural numbers apply in reality, everything we build on top of them, no matter how flawed or autistic the thing we're building actually is, automatically applies as well

>>10238841

FUCK YEAH!

But make it real hard labor. Digging holes. Then get them to fill the holes back up with the shit they just dug up. Then dig it out again.... FOR 16 HOURS A DAY FOR 20 YEARS!

These cunts should be made to pay dearly for their crimes.

>>10241137
>what is simplification
i never argued in favor of writing -1 as 1+2+4+8+...
what point are you even trying to fucking make.

>>10241184
any rational number, [math]\frac{a}{b}[/math] is just the solution to [math]a=bx[/math]
the equation corresponding to [math]\frac{1}{0}[/math] is [math]1=0x[/math]
which is never true and has no solution, easy fucking peasy
[math]\frac{1}{0}[/math] doesnt correspond to a solution, so it isnt a thing

aint no flaws that obvious in math

>>10241197
Hey I can do that too
[math]\frac{1}{0}[/math] should be [math]1 = 0x[/math] and has no solutions, therefor [math]\frac{a}{b}[/math] is not the solution to [math]a=bx[/math]
You can't just try to establish a universal set of rules if those rules have arbitrary exclusions to fit your agenda

>>10241184

Fuck yes Bro! Keep fighting the good fight against these assholes!

1 = 0x

0 = 0x - 1

0 = -1

>>10241201
youre braindead

>>10241197
>>10241202

>>10241206
cope

>>10241205
>>10241209

>>10241201
>arbitrary exclusions
its not arbitrary, 0 is an absorbing element of multiplication
so 1=0x has no solutions, since 0x = 0
and 1 = 0 is a false statement

there isnt a number that cancels out 0 even if you write down 1/0
"1/0 _should_ be 1=0x"
youre just making shit up and
youre just ignoring the properties of the numbers we're using
kys

>>10241085
>nope, there is no standard.
There is, all major definitions are pretty much agreed, up to equivalency.

This claim is FALSE unless you redefine = to something that is NOT the definition of equality for real numbers.

>Complex anal is cooler
It is heavily based upon standard analysis, just like literally everything that has analysis in its name, this is such a dumb thing to say from you...

>>10241184
Are you retarded? You aren't shitting on math as you might suspect you are shitting on physics.

>But hey lets just pretend that it's all fine and automatically conclude that since the natural numbers apply in reality, everything we build on top of them, no matter how flawed or autistic the thing we're building actually is, automatically applies as well
Physics and engineering completely and utterly BTFO.

>>10241219
Again, you're trying to exclude a specific case in your set of rules so you maintain the validity of that set of rules, without even considering the fact that the set of rules might be flawed in the first place if it doesn't apply for everything, when it should as that is math's point.

Take basic addition and subtraction with integers and forget about all the abstract bullshit above it for a second. However you try to spin it, you simply cannot find a dysfunction of that set of rules: 1 - 1 is 0, 0 - 1 is -1, (-1) - (-1) is 0 and so on, and the exact same rules apply for every possible case in existence. There is no special treatment for the zero and no arbitrary exclusions in special cases, and most importantly, it obviously applies to reality. This is what math is supposed to be, and if the rules you create do not work like that, they're probably inherently flawed or non-existent
Or on the other hand, multiplication and division might exist in reality, but we just haven't found the set of rules around division with zero much like we didn't find the set of rules around squaring negative numbers until the 16th century

>>10241234
Dude, the rules of addition and distributivity are the reason 1/0 doesnt exist
Its a basic consequence of the field axioms, and i dont even need to use the multiplicative inverse axiom to show 0 is an absorbing element

from the field axioms, multiplication distributes over addition for all a, b, c
a*(b+c) = a*b + a*c
so a*(1+0) = a*1 + a*0
a*1 = a*1 + a*0
0 = a*0 by the existence of the additive inverse of a*1
so for any a, 0 = a*0
so no number exists within a field that satisfies 1 = 0*x

>>10241241
Ignore him anon. People dealt with making sense of this by using abstract algebra and analysis years ago. The person you’re responding to refuses to listen and (I bet) refuses to learn any more math that would make immediate sense of his grievances.

>>10241184
You would take the complex conjugate you dolt. Even if you didn’t, what the 0 tells you is that the hypotenuse doesn’t lie on the full real plane. That being said, we like our distance function to be real, so complex conjugation is how you find length in terms of reals. Was that really that hard to follow?

>>10241252
True, thanks anon.
good night everyone
and merry kurisumas

>>10241241
>Dude, the rules of addition and distributivity are the reason 1/0 doesnt exist
Yeah dude multiplication and division are totally not flawed its all that nasty addition's fault that 1/0 dysfunctions

>>10241252
>>10241254
>maybe if I just close my eyes it might go away

>>10238814
Anyone who takes issue with some part of math because "it's got nothing to do with the real world and it's not even true" clearly does not know the first thing about mathematics. The fact that you can go through school and still make this argument is a testament to the failure of your education system.

>>10239728
>>10240005
These guys get it.

>>10241182
There's probably something profound about compound interest that can be said about the sum of an exponential function being the basic unit of debt.

>>10241219
Though being mathematicians we could introduce a new symbol.
I will all this symbol :D, 0*:D = 1.
Now we have a solution 1=0x => x = :D.
and now OP can sleep happily knowing 1/0 = :D

It doesn't converge in some standard theories sense. But that's about it.

>>0238825
This is not a counter-argument in many way. For one, you can't complete this process of giving out money, unlike the process of summing infinite terms, modeled by mathematical theories about exactly doing that. In the
>>10238814
>real world
the's no infinite adding up. In "fantasy" theories like that of the real numbers (which are convenient and have a huge load of practical applications and are thus used often), you can deal with the infinite. And in some of those theories, those sums have this and that value, and in others it doesn't. That's it.

>>10241791
based

It doesn't converge in some standard theories sense. But that's about it.

>>10238825
This is not a counter-argument in many way. For one, you can't complete this process of giving out money, unlike the process of summing infinite terms, modeled by mathematical theories about exactly doing that. In the (>>10238814)
>real world
the's no infinite adding up. In "fantasy" theories like that of the real numbers (which are convenient and have a huge load of practical applications and are thus used often), you can deal with the infinite. And in some of those theories, those sums have this and that value, and in others it doesn't. That's it.

>>10241231

>>10241845

> it converges in some theories

oh look mom its a retard

>>10243606
It does equal -1 as a 2-adic number as someone else stated earlier itt

>>10238814
Translation: "I do not understand analytical continuation and that is your fault".

>>10241184
Late to the party. Gödel already found flaws in all of mathematics.

>>10238814
You’re a dumb motherfucker

>>10238814
Haha brainlet OP can't into p-adic analysis

>>10238825
>>10238841
>>10239430
>>10239573
lol stay mad brainlet

>>10238825
>This is why mathematicians need to be rounded up by the state.
Why should they always be rounded up? Shouldn't half of them be rounded down?

>>10238814
>>10238825
>>10238841
>t. Economist

>>10239661
>"useful"
t. Brainlet that can't appreciate the purity and beauty of knowledge for it's own sake.

>>10243606
what?
that was a plain factual statement

>>10238814
>sum is equal to -1
what the fuck

t. undergrad who got a b in linear alg.

The absolute state of /sci/-schoolers.

>>10238836
>small infinity
oh fuck off

for 32-bit integer we have:

#include <iostream>

int main()
{
int sum = 0;
int power_of_2 = 1;
for (int i = 0; i < 32; i++)
{
sum += power_of_2;
power_of_2 *= 2;
}

std::cout << sum << "\n";
return 0;
}

output:
-1

Well, what can I say...

t. applied

Sum = 1 + 2 + 4 + 8...
Sum = 1 + 2(1 + 2 + 4 + 8 +...)
Sum = 1 + 2Sum

Solutions = {-1, infinity}

ez

>>10241201
don't you know that anything multiplied by 0 is zero?

>>10243779
"If you keep adding positive numbers they become negative because of this little trick I do with arithmetic :^]"
wow so fucking beautiful and pure

>>10238814
Is this from that one Jewtuber everyone keeps shilling despite not being able to explain anything properly?

>>10239740
This.
"Doesn't apply to real life" is just saying "most of the primates here on earth are incapable of ever actually comprehending this so it's gonna take a while for anyone to figure out how to use it".
I think that the attitude that some mathematicians have is wrong because being able to come up with that kind of stuff isn't actually a superiority over ordinary people. Rather it's a culmination of success for humanity as a whole. The right circumstances is what separates the 200 IQ "troubled genius" that cries every night and never actually accomplishes anything, or the 200 IQ prodigy who dies from polio at 9 a hundred years ago that no one will ever remember, from the 200 IQ fields medalist. So we owe revolutionary mathematical progress to humanity as a whole to be so diverse as to provide these circumstances at the rate that it does, not just the fields medalist who, frankly, got lucky.

>>10239995
Every base is base 10.

>>10244854
>he thinks analytic continuity is adding

Well, at some point there happens integer overflow.

>>10245058
>”In mathematics, summation (denoted with an enlarged capital Greek sigma symbol
∑
\textstyle\sum) is the addition of a sequence of numbers; the result is their sum or total.”

Fucking retard

>>10244983

>>10245293
woosh

It is not true using the elementary school definition of addition. Using this definition, the series can truthfully be said to diverge.

There is a definition of summation for which this is a true statement. Mathematicians use the same symbol because it makes sense to us (there is a strong precedent for generalizing definitions in this way).

Feel free to use your own notation if you like, but if you are encountering this level of confusion you are probably not prepared to tackle these topics.

Seemingly unintuitive mathematics has proven useful in the real world time and time again. I wonder what are the contributions of the brainlet OP to society.

>>10238814
Based get, and yeah that's for retards. Only sub-70 IQ retards are good at math

>>10243958
Clever

>>10245280
Nope, you're the retard here.

>>10241184
makes sense that there is no length of that triangle sincethe complex plane is not within the real plane therefore you can't connect them both

think about it like this: what is the distance between your minecraft house and your GTA 5 house? none, there's no way to compute it unless you develop a way to connect them both

>>10245854
But there's a difference between "no distance" and "distance of 0", with the latter implying that they're on top of each other

>>10245864
Since you're a fan of practical applications, I used a more practical example. The counter-argument you gave is a mathematical one which I cannot refute based on the nature of the explanation.

What does a length of 0 mean in real life? It doesn't exist in that dimension. What does nonexistant distance mean in real life? Means there is no distance.

>>10241184
by definition, lengths are taken from the nonnegative (possibly extended) real numbers. So you can’t have a line segment with length i.

And why are you so butthurt about not being able to divide by zero. No one ever said that the point of math is for every operation and formula to be defined on every possible number or mathematical object.

>>10245833
>>10238814

>>10241234
>>10241234
>>10241234
The definition of division that we have has served us pretty well. It got us to the moon, for instance. Dividing by zero doesn’t make sense with the definition of division, and you don’t fucking need to do it anyway. Why exactly is it bad that division isn’t defined for every number?

What math is supposed to be... according to God? Dumbass math is supposed to be whatever is the most useful or interesting.

>>10239728
based

>>10238885
Are you retarded, anon?

>>10243779
>it’s own sake
>it is own sake

>>10248474
the apostrophe is also used to show possession.

ie
"anon's stupidity" is not "anon is stupidity"
but is "the stupidity of anon".

>>10247354
>t. doesn't know English

>>10250040
Shit. Meant to quote >>10250012

>>10250040
using "it's" still isnt wrong

t. not retarded

>>10239661

actually lolled at this, semi-applied non ghey mathematicians aint that bad

>>10245280

are you demented?