/sci/ - Science & Math

>>11954084
Obvious bullshit

>>11954084
the square root of a negative number is really just undefined.

>>11954096
It's undefined if you can't concieve of 2X2 matrices yeah.

>>11954108
there is no number, N, such that N added N times will give you its additive inverse.

>>11954118
N = i

>>11954121
you cant just be making stuff up. thats hocus pocus not mathematics

>>11954108
We're talking about numbers, not about matrices. -1 is not a matrix, so its root shouldn't be a matrix. And you can't even take the root of a matrix unless it's diagonalizable.

>>11954084
What’s wrong you can set it equal to that. Nothing inherently wrong with doing so.

>>11954125
They didnt make it up. There’s a canonical ring isomorphism between the set of complex numbers and the reals modded out by the idea generated by x^2 = -1.
Why do the math illiterate act as if people haven’t done proofs studying this?

To all those who believe in "imaginary numbers": Tell me what is the numerical value of i in decimals?

Pi is 3.1 and e is 2.7. How do I enter i into a calculator?

>>11954142
i isn’t in the set of reals without you first modding out by an ideal. Either way, many calculators can do calculations with i. In the complex numbers, i is the imaginary unit, so its decimal form could be represented by a vector of real decimals (0, 1)

[math]
\displaystyle
a+ib \leftrightarrow
\begin{bmatrix}
a&-b \\
b&a
\end{bmatrix}

[/math]

Why is it obvious and why is it bullshit?

>>11954165
It’s a meme format now that someone did this with 0.99... = 1

>>11954125
well it's not a real number, that's for sure.

i isn't even a number it's a letter jesus christ

>>11954135
it's a 1x1 matrix. like how many matrices are just tiny tensors.

>>11954183
And tensors are just arrays

You are right. As -i is forgotten. (-i)*(-i)=-1 too.

take your meds

>>11954216
You first, muh neighborhood at infinity hat
You’re part of the problem

>>11954142
>Pi is 3.1 and e is 2.7. How do I enter i into a calculator?
Easily. There is two ways to do it with my calculator. See the red-circled buttons to accees these menus.

>>11954125
>you cant just be making stuff up. th
didnt we make all the other numbers up too?
i isnt any more made up than 1/2
1/2 is the solution to 2x - 1 = 0
i is the solution to x^2 - 1 = 0
>>11954142
>Tell me what is the numerical value of i in decimals?
0.0 + 1.0 * i

>>11954135
>>11954148
Learn about matrices first bro.
Complex numbers can be used to think about rotations. They are applied in electrical engineering, optics, etc.. anything with waves, so everything.

There is nothing more "Real" about the reals. They are numbers, logical constructions. Also the complex numbers extend the reals, and unify things like square roots (that produce two values) into one object.

>>11954216
shut the fuck up imposterfag

[math]i\neq \sqrt{-1}[/math]
retards need to stop spouting this definition, when the real definition is:
[math]i^2 \equiv -1[/math]

>>11954248
>Complex numbers can be used to think about rotations.
Not really, just a coincidence that some complex numbers are similar to rotational matrices.
>They are applied in electrical engineering, optics, etc.. anything with waves, so everything
Only as helpful tool in the middle of calculations. Physics problems should start with real numbers only. Also solutions should be given with real numbers only. Want to describe rotation in 2D? Use 2D vectors and possibly 2x2 real matrices.

>>11954121
>>11954237
>durrr it’s just defined that way
1/0=u
(1/0)*3=3u
There, I just defined 1/0 according to your smooth brain

>>11954276
No
If i'm describing a rotation I will use complex numbers just to spite brainlets who can't into 2x2 matrices

>>11954262
there is no real number that satisfies that equation

>>11954278
what is 0*u? is it 1? is it 0?
stop using this retarded example because it doesn't follow the rules of multiplication

>>11954276
>Only as helpful tool in the middle of calculations. Physics problems should start with real numbers only. Also solutions should be given with real numbers only. Want to describe rotation in 2D? Use 2D vectors and possibly 2x2 real matrices.

Hahaha and what are real numbers huh? do you think a continuous line infinite in both directions but infinite also in its microscopic scale exists?

Or.. is it... just a helpful tool. oh..

>>11954278
cool, youve just made a number system thats very inconvenient to use, since we need to drop all sorts of nice properties
but its still a thing, we just dont use it because of how much of a pain it is
unlike the super easy and useful complex numbers
https://en.wikipedia.org/wiki/Wheel_theory

imagine getting filtered by complex numbers of all things. if this is the case then there are other boards that are more your speed.

I dont understand the underlying philosophical motivation to reject the complex numbers.
Is is some dumbfuck brainlet idea that numbers "have to have a physical correspondence" or something? What is it? Why does the imaginary unit cause brainlets to seethe?

>>11954135
[0 -1; [0 -1;
1 0] x 1 0] = -1 + 0 = -1

>>11954344
complex numbers have a physical correspondence in every vibrating phenomenon you can think of the real displacement and the imaginary displacement (as momentum)

>>11954084
You need to be 18 to post here.

>>11954352
Yes, so even the idea that complex numbers don't have a physical correspondence doesn't work.
So why do brainlets seethe at the imaginary unit? What is the underlying philosophical motivation to reject the complex field?

>>11954360
desu it's the name

they usually have no issue with the reals, when there is plenty of issues with the real numbers and that's why it took so long to develop them

>>11954372
>getting filtered by a name
pretty sad anon. I feel sad for them

>>11954331
The riemann sphere is metal as phuck

>>11954323
Thank goodness i is a complex number.

>>11954410
you cant just make up numbers at whim. that's magical thinking. not rigorous mathematics

>>11954457
I can and will. I just invented a number that made your mum a man.

>>11954457
>not rigorous mathematics
how is it not rigorous
I can make 1/2 from the integers by taking the Quotient Ring Z[x}/(2x - 1)
I can make i from the integers by taking the Quotient Ring Z[x]/(x^2 - 1)
I can make i also from the reals by taking R[x]/(x^2 - 1)

>>11954255
you really are getting it wrong a lot calling me an imposter so much lately.

>>11954457
It is rigorous. Read up on ring theory and injecting elements into the set via quotient rings and identifying elements with the first isomorphism theorem.
Someone will say “wahhh it’s really the solution to x^2 - 1 = 0” but we can rigorously identify this this by adjoining an element which has the same properties as though x = sqrt( -1 )

>>11954328
>do you think a continuous line infinite in both directions but infinite also in its microscopic scale exists?
See picture.


There are no limits in space. Also no smallest possible lenght over zero. Planck's lenght is just a result from dimensional analysis of physical constants and only a popscientist claim it as smallest possible lenght.

>>11954492
that was you? why would you tell someone to take their meds?

>>11954262
If i2 = -1, then √i2 = √-1, so i = √-1

>>11954360
>Yes, so even the idea that complex numbers don't have a physical correspondence doesn't work.
Well it works. Just lazy fuckers use complex numbers as a result or start problem with it. Complex numbers are just a helpful tool and brainlets thinks they have some physical or even mathematical significance.

>>11954492
>>11954504
it's not him, and i'm a different anon who also called out the obvious imposter acorn in a different thread last night. acorn seems to have a high verbal iq, it's obvious to anyone who has read a lot. the imposter acorn(s) use comparatively bland language. the only other possibility is that acorn has multiple personalities and some of them have lower verbal iqs than others

>>11954084
It is.

>>11954627
no, i has a length of 1. the hypotenuse is √2

You will love quaternions.

>>11954551
LITERAL FUCKING RETARD

>>11954664
>i has a length of 1
so what, if i^2≡−1

>>11954738
so the jpg is wrong

>|x| = -1 has no solution
sounds familiar

>>11954513
If i =sqrt(-1) then i*i=sqrt(-1*-1)=sqrt(1)=1, so i=1, so 1=sqrt(-1), so sqrt(-1)=-1. But sqrt(-1)=i and we deduced i=1, and we now have - 1=1.

>>11954125
but math *is* making stuff up

>>11954751
How is it wrong when it shows that
> i has a length of 1

>>11954806
He’s trying to imply it’s arbitrary and not rigorous. Neither of these are the case.
Notice how none of these naysayers respond to the posts about ring theory and adjoining elements. They’re either shitposting or literal highschool knowledge brainlets who reee at stuff they don’t understand

>>11954276
>Not really, just a coincidence that some complex numbers are similar to rotational matrices.
>just a coincidence

>>11954627
To extend the Pythagorean theorem, which is defined for nonnegative side lengths, you have to use the usual inner product with the complex conjugate to get “length,” which would then be i(-i) = 1

>>11954815
1^2 + 1^2 ≠ 0^2
1^2 + 1^2 = √2^2

>>11954762
>i =sqrt(-1) then i*i=sqrt(-1*-1)=sqrt(1)=1
non sequitur

>>11954276
>Only as helpful tool in the middle of calculations. Physics problems should start with real numbers only. Also solutions should be given with real numbers only. Want to describe rotation in 2D? Use 2D vectors and possibly 2x2 real matrices.
This is why people make fun of physishits. Smarter than engineers but not as useful, and yet not nearly as informed or smart as people who actually know the math.
Complex numbers are well defined as their own “canonical structure” in math, useful in many other contexts other than physics, and are interesting in their own right as a pure object.
You guys don’t even know what you don’t understand but act like you do lmao

you'd think this is horeshit until you understand its applications with electric shit. i've heard electrical engineers deal with this nonsense constantly

>>11954835
>I’ve heard
You sound like a highschooler
What is so mystical about the complex numbers that they sound like “bullshit?”

>>11954839
on a surface level, if you have no clue what practical applications there are, the entire concept seems like a waste of time
i'm not saying it is, but i remember doing things with imaginary numbers way before i knew what the fuck they were used for

>>11954827
I thought i^2 = -1

>>11954829
um no sweaty it proves that i*i is both 1 and -1 which is a proof by contradiction that i doesn't work

>>11954627
The Pic That Saved /sci/

>>11954856
i thought we agreed that the length of i is 1

>>11954867
i^2 isn't the length of i

>>11954735
>>11954834
You are just wrong. You make yourselves clowns by claiming complex numbers are something more than they actually are.
>and are interesting in their own right as a pure object.
No absolutely no. Only to serve real science. Yes its good you mathfags have problems with complex numbers so we real scientists can use these results in the middle of our calculations to help them.

But real scientists start and end with real numbers.

>>11954860
prove sqrt(a*b) = sqrt(a)*sqrt(b)

>>11954872
correct

>>11954867
Is it so convenient that you i can equal 1 when you want it to or there's some rule when exactly √-1 equals 1?

>>11954883
no u

>>11954885
length, i goes up length 1

>>11954888
I can't prove something which isn't true. I can give you a nice counter example though, wanna see it ?

>>11954826
I'm sorry, kid, but it looks like a pilpul to me.
I know your tribe have corrupted linguistics and physics. So excuse my belief that you've also corrupted math (here and in ramanujan summations)

>>11954892
sure

>>11954889
why not length i?
also did you just pull it out of your ass or there are actually books which are saying just that?

>>11954895
ignore fancy words, if you draw a line from 0 to i the length is 1

>>11954896
sqrt(-1)*sqrt(-1) = i*i = -1 but
sqrt(-1*-1) = sqrt(1) = 1

>>11954901
see>>11954906

>>11954906
how do we know that?

>>11954908
prove it

>>11954910
because it's a line segment connecting the points (0,0) and (0,1) ?

>>11954910
just look at a graph of i

>>11954912
>>11954913
so how is i ≠ 1?

>>11954911
sqrt(-1) = i by definition of sqrt in complex numbers
i*i = -1 by definition of i
-1*-1 = 1 since both 1 and -1*-1 are additive inverses to -1, therefore they're equal
sqrt(1) = 1 again by definition of sqrt in complex numbers

>>11954918
i goes up, 1 goes right

>>11954918
why should it be 1 ?

>>11954926
so does y
>>11954934
because otherwise we have a contradiction.

>>11954936
>because otherwise we have a contradiction.
what contradiction

>>11954936
>so does y
i agree