/sci/ - Science & Math

>>10485174
Because they make many calculations much easier.

>mathematics is how much apples has Joey given to Bobby
Are you fucking 8?

>>10485174
We should about unicorns too because they are useful tool for solving equations and interesting part of cryptozoology. Sometimes you can visit land of fantasy and hard problems of rainbow analysis become easy if you call your unicorn friends.
Also you are retarded if you think that numbers exists in physical reality.

>>10485197
Says the guy who imagines up fake numbers. That is a level of delusion rivalling intersectional wymyn stydies.

>>10485207
The set of natural numbers: what you can count on your fingers and toes, by definition.

The set of integers: whole numbers including negative values.

Rational numbers: the numbers expressed as a ratio of two ingeres. A fraction where the denominator is not equal to zero. Integers are elements of this set.

Irrational numbers: numbers that are not logical.

The set of real numbers: all numbers which exist. The rational numbers and irrational numbers.

The set of complex numbers: numbers with a real part and an imaginary part that does not exist.

please stop posting hot girls on /sci/

>>10485174
>Why do we need to learn about complex numbers if they are imaginary?

Electrical engineering.

Next question.

You don't have to, but if you don't your not gonna make it very far into the electricxal engineering curriculum because the math's become way too hard if you DON'T use complex numbers.

>>10485228
So if I rub an ebonic rod with cat fur will the charge be the square root of -1? No?

>>10485236

That has nothing to do with electrical engineering. Please refer to last 100 years of literature and not your own ass.

>>10485228
This^ thanks based anon

>>10485174
The numbers don't exist because math doesn't exist.

EVERYONE NEEDS TO WAKE UP RIGHT NOW

>>10485174
Because of some idiot named Euler who decided to put e to an imaginary power

>>10485174
Real numbers don't exist in reality, either.

You don't need "need" to do anything, anon.

>>10485228
Oh also
[eqn]i\hbar\frac{\partial \psi}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \psi}{\partial \mathbf{x}^2} + V(\mathbf{x},t)\psi[/eqn]

>>10485174
>those liver spots on her thigh
Literally unfuckable

>>10485217
Where's my -6 finger?

>>10485217
[math] \displaystyle
\boxed{ \mathbb{O} \;
\boxed{ \mathbb{H} \;
\boxed{ \mathbb{C} \;
\boxed{ \mathbb{R} \;
\boxed{ \mathbb{Q} \;
\boxed{ \mathbb{Z} \;
\boxed{ \mathbb{N}}}}}}}}
[/math]

You can represent a 2d plane using only one number as the coordinate. Also phasors

How is this /sci/ material?

Complex analysis enables you to solve problems involving real numbers. Hence, it's useful.

>>10485174
It helps you solve trig problems since you can rewrite trig functions in exponential form

>>10485174
How will math majors LARP as contributing to society if they're unable to extend their subject to literal made up bullshit and pretend that solving problems within the made up bullshit matters?

>>10485174
How can anyone on this board with a 3 digit IQ fall for this bait

>>10485497

It does matter, see electronic engineering.

The device you are shitposting on right now is working because of complex numbers.

>>10485174
They aren't imaginary, they are as real as all other consistent number systems and they objectively exist in the Platonic realm

Imaginary numbers pop up in physics all the time. This is representation but just more complex than representation as objects. Numbers obviously don't exist irl retard.

>>10485517
Yeah this thread is the type of shit I'd expect to see popup anywhere but /sci/. Unbelievably low iq content.

>>10485517
>>10485529
>>10485553
>>10485557
seething

>>10485529
Where is the platonic realm? Is that where virgin mathematicians dwell?

Thats why people hate the term imaginary number, they have their existence in our world in a sinilar way to irrational numbers.

>>10485217
Show me one atom of natural jumber. Or molecule of zero. Show me length exactly of √2. Numbers are social construct. And you are discriminating me

>>10485573
Irrational numbers have a physical or geometric representation. Pi is the circumference of a circle, e is a rate of change. What is i? Draw a geometric representation of i for me. No, the real vs imaginary coordinate thing doesn't count.

>>10485591
>No, the real vs imaginary coordinate thing doesn't count
why not retard

>>10485189
Are you a retard

>>10485591
Complex numbers have an algebraic representation. [math]i[/math] is a root of [math]x^2+1[/math].
Working in algebraic closures is often nicer than working in plain fields.

>>10485664
x^2 + 1 has no roots because it is an upward facing parabola shifted up 1 unit so it does not touch the x axis. It has roots only in the unicorn space of imaginary bullshit.

>>10485734
Parabolas have nothing to do with algebra.

>>10485174
science is as imaginary as complex numbers you faggot
objective reality doesn't exist as you see it so why not just kys, its imaginary after all

>>10485174
>Bobby doesn't get i apples from Joey.
No, but Bobby can have 4+3i volts over his circuit element. And offshore roughneck Joey can easily load 8-2i kN onto his string. Complex numbers are just like normal cartesian vectors but with some extra very useful properties. They are as " real" and "exist" just as much as any other number.

>>10485591
But they did have a physical interpretation, retard. See >>10485760

>>10485174
This guy gets it.

I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>>10485786
jfc
I guess literal brainlet engineers are better at math than you

obvious bait

>>10485560
I'm not angry, fren, I'm trying to enlighten you
>>10485564
It exists as the superclass in which this physical universe derives it's laws to function, as a subset.
Also engineer majors are 95% men while math is about 50/50, so it's quite humorous for a lowly engineer brainlet to call a math chad a virgin.

>>10485802
fuck off with your platonic shit

>>10485806
>fuck off with the truth
I will not.

>>10485174
Please look into Fourier transforms, faggot

>>10485256
That is the Schrodinger equation!!

>>10485174
No one who uses math for their work actually needs to argue with you in order to go on with their lives.

If you can't recognize the factual usefulness of mathematics then I have the feeling no amount of explanation would allow you to understand.

>>10485932
Real numbers are useful but imaginary numbers are not because they are made up.

>>10485957
real numbers are just as made up as complex numbers. Both are just extensions of our number systems to satisfy the Fundamental Theorem of Algebra.

None of them are "made up" they are not human inventions or human dependent.

>>10485973
>platonist nigger

>>10485973

>>10485979
There has not yet been a single argument against it
>>10485981
Not an argument

Stay seething

>>10485991
you haven't made a single argument

>>10486005
Not in this thread, but in a others, and guess what? Not a single counter argument.

>>10486005
Plenty of arguments have been made ITT that complex numbers are "real"

The last hundred years of physics have depended on the mathematical properties of complex numbers. The complex numbers themselves are never observed in measurements, but the mechanics of the theory depends on them crucially.

Say goodbye to your MRIs, PET scans, molecular modeling, lasers, electron microscopes, semiconductor physics, etc.

>>10485174
Complex numbers are just real numbers in 2D

>>10486038
This.

Complex numbers are 2d vectors that multiply together exactly the way you would intuitively expect vectors to multiply, not that unsatisfying dot product vector """multiplication""" bullshit

Literally just define (a,b)*(c,d) = (ac-bd, bc+ad) and you can easily see the multiplication sums the angles from the positive x axis and multiplies the distances from the origin. Then you just put an "i" next to the second coordinate and say it's square is -1 as a shorthand for remembering the definition formula. Numbers with an i are not less real, it's quick shorthand for an extra structure you put on some vector quantities.

>>10485588
you go girl !

>>10485504
op picture helps
sex sells

>>10485217
>Irrational numbers: numbers that are not logical.
>The set of real numbers: all numbers which exist.

oh my god thank you

>>10485174
Engineers and electricians use i all the time, fuck off and learn something instead of shitposting.

>>10485174
watch and learn, unless you are a brainlet with the attention span of a gnat, in which case keep on shitposting brother
https://youtu.be/T647CGsuOVU

>>10485174
i honestly cant tell if this is a shit posting thread or an honest inquiry into the reason for why we have certain machinery in mathemetics. Well, simply put, mathematics is an arbitrary language with the property of self coherence. Maths are developed in order to deconstruct and generate sophisticated systems in an effort to find solutions to difficult problems. Fundamentally, what makes a language or tool useful is it's ability to create solutions and ease of use." imaginary" numbers are such an example of a useful tool. if you want to learn more about abstract mathematics read up on abstract mathematics, number theory, fundamental mathematics or logic.

But who am i kidding. this is likely just a shit posting thread

>>10485217
The only thing that you got right was the natural numbers. Proof OP is a brainlet and still uses fingers to do basic arithmetic.

>>10485217
Here's how it actually works:

>have nothing of interest
>don't count things, numbers don't exist to you
>have a bunch of interesting things for whatever reasone
>would like to count them
>invent naturals to do so
>can add them and multiply them, even exponent them
>it makes sense with the language you use
>having x and y = having x+y
>having x of y = having xy
>having x ys of ys times kinda means having y^x, but language has its limitations
>only the greatest scholars of your society use exponentiation anyway
>life goes on
>lose all your shit
>describe your situation of having nothing
>zero is now a number
>that's neat it sort of still works with adding and multiplying
>have a bunch of shit and nothing else
>x+0= x lmao
>have none of this shit
>0x=0 lmao
>again, exponentiation is tricky, and nobody but the best and brightest use it anyway, so it's not that big of a deal when they settle the debate of how 0 behaves as a base and an exponenent
>probably defined so that notation of exponents makes sense in algebraic scenarios
>Anyway, people are getting really tired of saying things like, "the number of things i need more than I have to get what I want," and, "enough parts of the whole to put together this many times to make the whole" So subtraction and division are defined on the Naturals, respectively
>the greatest minds (not you) are probably inventing roots and logs as well
>people naturally divide things amongst themselves, like land, food, livestock, money etc.
>some things, like livestock, are hard to agree on what a fractional part is, so they are only defined with integer quotients, or remainders
>some things, like land (provided your society has measurement), can be divided in any way (it's easiest as squares and rectangles), so we now have positive rationals, like one half or two thirds of an acre of land
>but someone must pay for this land
>and perhaps he must go into debt

>>10487886
>so whoever is in charge of recording debts must figure out how much is to be paid
>but he must do arithmetic to figure out exactly how much is owed and how much has been paid for
>and not all debts are settled by currency
>anyway he's figuring out his shit and he comes to a problem
>differences are only defined on naturals, and now you need negative numbers
>but how can you have negative of anything?
>it doesn't matter since this is just a technique to make computation easier
>for all intents and purposes, negatives are a debt, and debts can be settled by paying back positives
>and the great minds of your time prove all the properties work neatly
>it's the same thing with imaginary numbers
>the smart people use them so whenever their calculations lead to the square root of a negative number, they don't have to stop and figure out how to work the problem a different way
>they just say root -1 is i, and hope that eventually they will square their problem again and all imagination will be checked by reality
>but you're not a great mind, so you wouldn't know

>>10485228
They're "imaginary" but they represent real quantifiable things. You can use polar coordinates/math to do everything the j-operator accomplishes, it just takes extra steps to convert everything back and forth.

Using imaginary numbers is more of a trick to keep track of things that are more intuitively explained using two separate coordinate systems at the same time but you just want to use one for simplicity. Hence they're not exactly imaginary, they're an artifact from how you simplified the problem you're solving.

>>10485174
Complex numbers are literally just a better way of expressing Cartesian coordinates dumb ass, there’s nothing less real about them

>>10485174
Don't worry OP, you won't ever use complex numbers. But one of the smart kids might

>>10487933
>Using imaginary numbers is more of a trick to keep track of things that are more intuitively explained using two separate coordinate systems at the same time but you just want to use one for simplicity.

EXACTLY this. This guy gets it. That's why they're useful for dealing with propagation of waves for example, which constitutes nearly fucking everything.

Calling them "imaginary" was the most dumb shit thing anyone ever came up with because if they were smart they would have anticipated dumb shits like >>10485174 latching onto the turn of phrase to make stupid arguments.

Also you can check out Quarternion numbers for extending this concept into 4 dimensions, which is useful for things like quantum mechanics and computer graphics.

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

>>10485497
>imaginary "proof"
You forgot to use the complex conjugate when computing that hypotenuse; pythagorean theorem is really to square root of a times its complex conjugate added to b times its complex conjugate. It just so happens that for real numbers that's the same as squaring them.

>>10485217
>Irrational numbers: numbers that are not logical.
There is nothing illogical about irrational numbers

>>10487933
>>10488008
I agree with you two. the name "imaginary" is VERY WRONG in terms of linguistic description, a better name could be "intensity" or even better "magnitude"...
the term "imaginary" is a relic from that argand paper.

Real numbers are the problem my son.

t.wildberger

>>10485657
He's right you know, even for harmonic oscillations equations it's easier to go by complex numbers

>>10485981

http://m.wolframalpha.com/input/?i=abs%28i%29+×+-1

Higher math is such a scam.

>>10489066
The term confuses the definition of extra dimensions. You can plot a vertical and horizontal number line, but thats a grid with parameters (X, Y), not (Re, Im)

Because the numbers are not imaginary.
Also
>i instead of j
lmaooo

>>10490068
Pure math niggers utterly BTFO by this post

>>10485174
Real numbers dont exist in reality either.

>>10485174
You never know if these threads are shameless bait or some high school brainlet who's having a hard time with his homework.

>>10485957
The device you shitpost on literally uses complex numbers to operate. Either you believe that complex numbers are bullshit, or you can use your computer. You can't do both.

>>10487933
>>10488008
>>10489066
>>10489895
The term "imaginary number" was explicitly made and propagated by retards like OP some centuries ago to discredit the concept and make it look absurd. Gauss suggested "lateral numbers" instead, which would have worked much better IMO.
Unfortunately, the former term won out, and it and the misconception fundamental to it persist to this day. At least people who actually do math for a living know the term is bullshit, but it managed to fool pretty much everyone else, which only serves to bring down the perception of math as a whole.