/sci/ - Science & Math

>Riemann destroyed

>>11147238
practical and inuitive

One more time for the nosebleed section
>imaginary numbers

>>11147246
>practical and inuitive
as it usually is when making shit up

>>11147255
>are just as "imaginary" as "real" numbers

>>11147258
is this some kind of pottery? because it is real in my mind.

>>11147258
They are.

>>11147262
im lost for words.

>>11147238
what about them?

>>11147265
>what about them?
>imaginary numbers
>imaginary numbers

>>11147263
Literally every statement about imaginary or complex numbers can be rephrased in terms of real numbers and will mean the same thing.

>>11147272
a train can derail into a pit of horse manure and still go somewhere

>>11147276
Moron

One more time for the folks still waiting in line outside
>imaginary numbers

>>11147270
uhh what? the name? yeah it's a bad name since they are totally real insofar numbers in general are but we're stuck with it it seems

>>11147282
>>11147280
im lost for words

>>11147257
yeah, electrical impedance and boundary layers and 2D rigid body mechanics are totally made up

>i

>>11147272
so? complex numbers makes the analysis easier, and they lie on an equally rigorous foundation

If you can imagine, you can pretend

imaginary numbers exist, unlike your girlfriend

>>11147304
/codeblock/based/codeblock/

>>11147285
multiply by -1 means "change the number's direction to its opposite - or in other words, rotate the number's direction by 180 degrees"
multiply by i means "rotate the numbers direction by 90 degrees"
rotate the direction twice = multiply by i*i = multiply by -1
as expected since i is defined by i^2= -1
nothing surreal about it

>>11147301
I agree with you. My point was that they are no more imaginary than the reals.

>>11147310
>rotate the direction twice
*twice by 90 degrees

>>11147310
multiply by -1

OP is a pajeet who can't into 12th grade maths. Pathetic.

>>11147319
I have been found out.

>maths

>square root
>square
>root

>trigonometry
>trig
>o
>nometry
>nometry

Thats all for now I imagine. stay based!~

Im going to finish the sentence.
Imaginary numbers are ..... beatiful. (๑๑)

>>11147238
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.

>>11147354
Now tell me why you should be able to rotate a number's direction by 180 degrees but not by 90 degrees >>11147310

>>11147386
Because numbers lie on a line, not on a plane, retard. There's no angles on 1D spaces such as a line. You can only say that multiplication by -1 "rotates" a number 180 degrees because rotating a 2D vector by 180 degrees is the same as multiplication by -1.

>>11147573
>Because numbers lie on a line, not on a plane, retard
But complex numbers do lie on a plane. What's the problem with that?

I don't understand what's so hard to understand about imaginaries.

>>11147354
The only reason we keep imaginary numbers is because it just so happens that they work well in many fields in engineering and physics.

And they just so happen to work well when trying to solve complicated equations and analyzing infinite series.

Why get rid of something that works well?

>>11147654
I'm not the guy youre talking to and im not anti imaginary, but...

just because something is a good tool, if its meaning or motivation isnt understood, its reasonable to be wary. Yes it provides answers, and solutions, but thats only because we've embedded it into our existing logic structures. like youre talking about serieses and physics well, the function e^z is literally just an extention of the real function based on logical constraints. it conforms to the reals because its made to, but understanding why its a good choice is essential, any arbitrary system can conform to another if you nitpick hard enough

also, if you're using an object as an intermediary step in physics, it needs to represent something, or else youre making a nonphysical claim to support a physical system, throwing the whole thing into doubt, or potentially implying i is somehow physical

>>11147667
>if its meaning or motivation isnt understood
the meaning and motivation of the imaginary unit is very, very well understood.

>>11147627
>numbers do lie on a plane
This makes no sense. Your so called complex "numbers" are merely vectors.

>>11147667
Youre a fucking retard. Shut the fuck up.
Mathematics doesnt need to conform to any reality at all.
If it happens to have the ability to model and predict reality then it's great (and it often does)
If it doesnt it doesnt mean its invalid.

Your lack of understanding doesnt imply a lack of sense. Hammer that in your skull.

>>11147677
>Your so called complex "numbers" are merely vectors.
The complex numbers are also a field. So they are vectors and a field and they represent quantity of a sort. Sounds a lot like numbers to me.

>>11147238
Don't ride the root function below zero.

>>11147677
But they have the nice feature where you can rotate them by multiplication. Vectors don't have that.

>>11147673
>>11147678
neither of you are getting the point of what im saying, as i said, i am not anti imaginary, im just explaining how one could be confused by it

also, to the second poster, i agree that math doesnt need to conform to physics. but in using math to model physics... you need to stay true to physics. also, cool the aggression man

I could wax lyrical about the beauty of complex analysis. Never forget that [math]\mathbb{C}[\math] is the algebraic closure of [math]\mathbb{R}[\math].

>t. analysisfag

>>11147686
if anything, numbers are bounded
infinity isn't

>>11147687
Numbers are scalars, not vector. Not matter what you babble about fields, this is how it is.
>>11147710
brainlet

>imaginary numbers

>>11147740
Why is C such a special closure? I could per se enclose R in a set called R* where sqrt -1 = "P" a kind of dead end value that doesnt interact with anything else

>>11147272
ok big boy
solve x*x*x -5*x+1=0
without imaginary numbers
(all three answers are real)

>>11147779
real numbers literally form a vector space

>>11147781
? [math]0\neq|1+i|[/math]

>joining the thread about complex numbers
>as if it were still a thing
i have to say, i love zoomers. at least you guys are following in our footsteps. having the same debates we had as undergrads 8 years ago, on the same exact website. things never change.

>>11147790
What about the number 7? Is it a vector space? Retard.

>>11147796
it literally is a vector space

(0,7)
(7)

>>11147796
is is a member of a vector space, yes

>>11147781
the hypotenuse having a side length of 0 is irrational retard

>>11147800
wtf is (0,7)

>>11147806
a vector in R2

>>11147802
Is 7 itself a vector space? Retard.

I prefer to call them capacitive or inductive numbers depending if they are positive or negative.

>>11147813
no. good thing i didnt claim it was.
>>11147816
based

>>11147810
wtf is R2

>>11147810
>>11147821
also what is a vector

>>11147821
the set of 2-tuples such that both components are real numbers

>>11147775
No, you are wrong. Numbers aren't "anything." Numbers are "elements of ordered sets." You can find this definition on Wolfram as well as I can, and this is the commonly accepted definition of what a number is. Infinity is absolutely an element of an ordered set if you define it with the ordering relation "greater than every real number."
>if infinity is anything
>then it's the thing that means you're wrong

You people are so fucking insistent on your declarations that words mean what you think they ought to mean rather than what the dictionary says they mean. Get a brain moran.

>>11147821
google it

>>11147824
an n-tuple of independent numbers or a pointy thing in ND space

>>11147824
a member of a vector space. a vector space is a collection of objects that satisfy certain axioms.

>>11147818
>backpedalling
pathetic mathfag

>>11147844
i didnt backpedal

>>11147833
what is a vector space; what is an axiom?
>>11147826
>>11147831
the only tuple i know is from programming (I did a python/java boot camp)

is this similar?

>>11147857
that doesnt look very similar to me

an axiom is a thing you suppose is true as the basis of your logical world, like the rules of a game

a vector space is a space that has independent slots that only interact with corresponding slots of other vectors aka axes or coordinates or dimensions, in simplest terms. so XYZ coords are a vector space and so are apple, orange, banana coordinates

a single vector can be a vector space, like (7) or (7,3) or (5,6,7,8) or you can have a vector space including lots of vectors like (x,y,z) where xyz are real numbers

>>11147868
in python a tuple would be pic related
https://www.w3schools.com/python/python_tuples.asp

>>11147857
actually lemme correct myself

your fizbuzz thing might be slightly related to vectors, in that multiples of three and five are dimensions held separately

>>11147886
ah, its kind of like that. its a tuple that can only contain floats and each position only matches up with its counterpart.

>>11147813
Depends, is '7' the character representing the identity element?

>Homotopy type theory

>>11147821
wtf is wtf

>>11147827
>greater than every real number
<idiot mode on>
inf is number
inf is bigger than any number
inf is bigger than itself
<idiot mode off>

hurr durr

>>11147827
>words mean what you think they ought to mean rather than what the dictionary says they mean.
>moran.
topkek

>>11147238
All numbers are imaginary

So how do you get zero from 14.38412308431872423 whatever times i plus 1/2?

>imaginary
complex