/sci/ - Science & Math

[Anonymous No.11351812]

well /sci/?

[Anonymous No.11351823]

>>11351812

How can a side have a length of 0

[Anonymous No.11351827]

>>11351812
well what? the square root of 0 is 0.

[Anonymous No.11351832]

>>11351812
>what is distance in complex plane
are you all niggers on this board?

[Anonymous No.11351835]

>>11351827
no it's undefined

[Anonymous No.11351848]

>>11351835
False, zero is the only number with one single square root.

[Anonymous No.11351849]

>>11351848
No.. It's the only number which has a undefined square root

[Anonymous No.11351854]

>>11351848
The square root is a function and has only one output for each input. Thus square root of 9 isnt 3 and -3, its ONLY 3.

[Anonymous No.11351861]

>>11351835
x^2 = 0
0*0 = 0
therefore the square root of 0 is 0

[Anonymous No.11351865]

>>11351854
9 has two square roots because 3 squared equals 9 and -3 squared equals 9.

0 squared is 0 therefore the square root of 0 is 0

[Anonymous No.11351875]

>right triangle on complex plane
>one leg has length 1
>othe leg has length 1
>the hypotenuse has length sqrt(2)
[eqn] |1+i|=\sqrt{1^2+1^2}=\sqrt{2}\neq0 [/eqn]
wooooaaaaaah dude

[Anonymous No.11351880]

>>11351854
Define square root as a function from the complex numbers to sets of complex numbers, so every input has several outputs.

[Anonymous No.11351882]

>>11351865

you are wrong.

-3 to the power of 2 equals to 9, but square root of nine doesn't equal -3.

Just go on Wolfram Alpha right now and type in "sqrt(9)" you get one (1) answer, there's no ambiguity.

This is high school maths.

[Anonymous No.11351885]

>>11351865
>9 has two square roots
No is doesnt. sqrt(9) is absolutely not equal to -3, by definition. That's not to say that (-3)^2 isn't equal to 9. This is an important distinction.

[Anonymous No.11351887]

>>11351882
>but square root of nine doesn't equal -3.
y^2=x
(-3)^2=9
(3)^2=9

[Anonymous No.11351894]

>>11351885

[Anonymous No.11351898]

>>11351887

There's no ambiguty.

Listen here mate;

the EQUATION y^2 = 9 has TWO solutions.
The first solution is +sqrt(9) which is equaivalent to +3.
The second solution is -sqrt(9) which is equivalent to -3.

Observe that sqrt(9) = 3 is not a contradiction to your statement.

You have to distinguish between these two cases;

y^2 = 9 --> equation with two solutions
sqrt(9) --> one and only one answer (3)

[Anonymous No.11351903]

>>11351898
I understand it, but can you prove it?

[Anonymous No.11351905]

>>11351894
Hey, look! The very next sentence! Fucking retard.

[Anonymous No.11351906]

If you dont believe me go to any calculator you can find and input "sqrt(9)" not a single one of them will respond with -3.

[Anonymous No.11351909]

>>11351898
>y^2 = 9 --> equation with two solutions
>sqrt(9) --> one and only one answer (-3)
FTFY

[Anonymous No.11351910]

>>11351903

it's not something you prove it's a definition.

Sqrt(9) is defined as the positive solution to
the equation x^2 = 9 and that's that.

[Anonymous No.11351914]

The pythagorean theorem says:
In an inner product space, if v and w are such that <v, w> = 0, then ||v+w||^2 = ||v||^2 + ||w||^2.
There is no notion of norm which is complex valued, unless you take a space equipped with a sesquilinear form which is not positive definite.

[Anonymous No.11351919]

>>11351905
Wow, words have different meanings when you add more words like principle. Great job anon.

[Anonymous No.11351925]

>>11351812
Someone didn’t study inner products nor Euclidean distance.
>>11351854
The square function is the onto map from the reals to the reals. You prove that every positive real has a unique positive n-th root in a basic analysis class. However, you learn through the fact that the reals are a totally ordered field that for any [math] x \in \mathbb{R}_{> 0}, (-x)^2 = x^2 [/math]. It is clear to us that when we say square root of y, we mean any number x such that [math] x^2 = y [/math] unless specified otherwise

[Anonymous No.11351931]

>>11351925
based

[Anonymous No.11351936]

>>11351919
Good thing this is the common usage of sqrt()!

[Anonymous No.11351938]

>>11351936
see >>11351925

[Anonymous No.11351945]

>>11351936
Good thing we don't structure every conversation around the 1st definition of a word in Merriam Websters. You can have multiple meanings for a word and you can have multiple square roots for a number.

[Anonymous No.11351958]

o = sqrt2. what don't i understand?

[Anonymous No.11351979]

>>11351861
>0^2=0 therefore sqrt(0)=0
Doesn't follow m8

[Anonymous No.11351991]

>>11351875
Why absolute value?

[Anonymous No.11351995]

>>11351991
That's not absolute value, that is "norm." That is how length is defined.

[Anonymous No.11352012]

>>11351812
>uses i, has 0 knowledge about complex plane
>>11351835
doesn't know what square root is
>>11351854
>>11351882
doesn't know the definition of square root, talks functions without defining domain/codomain, doesn't know why teachers don't like negative square roots in primary school

[Anonymous No.11352055]

>>11351861
does this mean the square root of 1 is 1 because 1^2=1?

[Anonymous No.11352062]

>sqrt(-1) = i

[Anonymous No.11352069]

>>11352062
agreed. [math] j [/math] is obviously the imaginary unit.

[Anonymous No.11352071]

>>11351848
you are forgetting about -0, retard

[Anonymous No.11352081]

>>11351848
-1

[Anonymous No.11352088]

>>11352071
There is no negative zero. The notation of negative zero only indicates a limit reaching zero from the negative direction.

[Anonymous No.11352090]

>>11352088
shut the fuck up retard
-0 = 0
-0*-0=0

[Anonymous No.11352092]

>>11352069

based EE chad

[Anonymous No.11352102]

>>11352055
Yes, and it's positive so it's the principal root

[Anonymous No.11352131]

>>11352069
>>11352092
samefag

[Anonymous No.11352173]

See dichronauts for discussion of physics in a universe with negative distance

[Anonymous No.11352176]

>>11351812

[Anonymous No.11352177]

>>11352090
>[eqn]-0 \cdot -0 = 0[/eqn]
That's what a square root is, retard

[Anonymous No.11352185]

>>11351823
If the left of this is imaginary in the real sense, you can replace it with 1. Thus. A straight line.

[Anonymous No.11352193]

>>11351823
it doesnt
>>11352131
lolnofaggot. I'm not EE either.

[Anonymous No.11352222]

>>11351812
Lrn to geometry faggot

[Anonymous No.11352223]

>>11352177
nope you fucking idiot
-0*(-0) = -0

[Anonymous No.11352261]

len(-i) = len(i)
len(-i) = -1(i^2)
len(-i) = -1(-1)
len(-i) = 1
len(i) = 1

if the triangle was reflected about the z axis you wouldn't say the bottom side has length -1

[Anonymous No.11352268]

>>11352261
* y axis

[Anonymous No.11352401]

>>11352071
>>11352088
Assuming we’re not talking about the standard metric topology on the reals and not anything like the line with two origins or the double origin topology:
[math] -0 = -1 \cdot 0 = 0
+0 = 1 \cdot 0 = 0
\Rightarrow 0 = +0 = -0 [/math]
This appeals to the basic commutative ring structure of [math] \mathbb{R} [/math].

[Anonymous No.11352405]

>>11352401
Whoops forgot to space correctly. Meant this:
>>11352071
>>11352088
Assuming we’re not talking about the standard metric topology on the reals and not anything like the line with two origins or the double origin topology:
[math] -0 = -1 \cdot 0 = 0 [/math]
[math] +0 = 1 \cdot 0 = 0 [/math]
[math] \Rightarrow 0 = +0 = -0 [/math]
This appeals to the basic commutative ring structure of [math] \mathbb{R} [/math]

[Anonymous No.11352682]

>>11351812
[math]1^1 + √(-1)*√(-1) = 0^2[/math]
[math]1 + -1 = 0 [/math]

[Anonymous No.11352694]

>>11351812
OMG anon, you're such a genius. Let me guess, engineering, right?

[Anonymous No.11352706]

>>11351812
It makes sense if you're viewing the triangle from the side

[Anonymous No.11352734]

>>11351812
The complex plane is the empitome of dumb mathematicians that can't see the bigger picture. Perhaps if they had a bigger brain they would see a better solution than i as a hack job.

[Anonymous No.11352751]

>>11352185
>-1 = i

[Anonymous No.11352821]

>>11352734
But it isn’t...complex analysis is a deep field that reveals many methods and deep facts that further analysis and explore number theory, theoretical computer science (see analytic combinatorics), physics, engineering, etc.. That and complex analysis plays waaaaay nicer than real analysis. Many of the theorems are cuter, easier to see, are more intuitive, and feel natural, which makes sense since the complex numbers are a natural field extension.

It’s peak engineering brainlet to think the imaginary numbers are anything but amazing. Even physicists prefer it to the reals

[Anonymous No.11352941]

>>11352090
Suppose -0 =/= 0
Add 0: 0 + -0 =/= 0 + 0
Left side: 0 is the additive inverse of -0, which means
0 =/= 0 + 0
Right side: any element plus the additive identy is equal to that number, which implies
0 =/= 0
Hmmmmmm?

[Anonymous No.11352972]

>>11351812
weird looking slice of 'za, bro

[Anonymous No.11352979]

(0)^2=(i)^2+(1)^2
0=-1+1
0=0
QED
there's obviously nothing wrong with this triangle

[Anonymous No.11353277]

>>11352821
I'm not saying imaginaries aren't useful, quite the opposite. There's a broader concept at play, but as is the way with mathematicians in history; they choose the narrowest part of it, make it contrived and limited, give it a fun name, and pretend it's genius.

Dumb mathematicians never learn.

[Anonymous No.11353279]

>>11351832
theyve never gone beyond first year calc or something. people like this have not yet been introduced to mathematics which is not seen in your everyday life

[Anonymous No.11353281]

>>11352979
Except for the fact that 0 DNE sqrt(2)

[Anonymous No.11353282]

>>11353277
>i dont know any math or physics or engineering or applications at all, btw

[Anonymous No.11353297]

>>11353282
Actually Anon I went to the top uni in my country (often, the world) for maths two years early and scored an early retirement from making millions in finance with algorithmic trading before that sector became popular.

Any more sarcastic greentext you'd like to offer?

[Anonymous No.11353300]

>>11351812
z = 1+i
|z| = sqrt(Re(z)^2 + Im(z)^2)
Re(z) = 1
Im(z) = 1
--> |z| = sqrt(2)

[Anonymous No.11353305]

>>11353297
>lying on an anonymous swahili cockerel boiling blog

[Anonymous No.11353328]

>>11353305
Exactly, I have very little reason to do so.
>>11351875
Big yikes there buddy.

[Anonymous No.11353387]

>>11352751
i = 1*exp(i*π/2).
i^2 = 1^2*exp((i*π/2)*2)
Side length = sqrt(1^2 + 1^2*exp(I*π))
Side length = sqrt(1 + 1*cos(π))
Side length = sqrt(1 + 1) = sqrt(2)

Do you understand yet or do you need it broken down further?

[Anonymous No.11353540]

>>11353281
What in all fuck are you on about? (i)^2 is -1, and (1)^2 is 1. -1+1=0. 0^2 is 0, so the triangle works out.

[Anonymous No.11353729]

>>11353328
You can't actually expect anyone to take your opinion of complex numbers seriously if you call the complex norm "big yikes"

[Anonymous No.11353731]

>>11353540
What the fuck are YOU on about? The vector that joins 1 and j in the complex plane is 1+j. The magnitude of 1+j is sqrt(2).

[Anonymous No.11353935]

What is the modulous for $500?

[Anonymous No.11353944]

>>11351823
>how can a squared number be equal to -1
that's how, retard

[Anonymous No.11353980]

>>11351823
how can a side have a length that can't be measured?

[Anonymous No.11353989]

>>11353944

but the lenght of that number is not -1 so the image is false. The length is defined in another way.

[Anonymous No.11354103]

>>11353729
>Using the English language as a crutch because he can't use mathematics
Big yikes to you too, buddy

[Anonymous No.11354156]

>>11353989
that's your opinion. I'm of the opinion that infinite sets don't exist and yet here we are.

[Anonymous No.11354190]

>>11351835
/sci/ absolutely seething

[Anonymous No.11354241]

>>11352081
(-i)^2 = -1

[Anonymous No.11354262]

>>11354103
>>11353297
>>11353277
It’s very clear to everyone here that you are lying lmao, seeing as you don’t know mathematics nor history. Nobody pretended it was “genius.”

[Anonymous No.11354263]

>>11353277
>contrived and limited
There’s a plethora of really nice and natural representations of complex numbers, and you don’t really even make any reference to i if you use the canonical matrix representation.
If you feel complex numbers feel contrived, then you have next to no idea what you’re talking about

[Anonymous No.11354271]

>>11353944
>>11354156
Even in a type construction you would need a positive definite Hermitian form to make sense of extending the Pythagorean theorem. So yes, you would in fact say the sides have length 1 and hypotenuse sqrt{2}.
Not believing in infinite sets isn’t a get out of jail free card to accepting canonical and well made mathematics.

[Anonymous No.11354294]

>>11354263
>you don’t really even make any reference to i if you use the canonical matrix representation
Now you're getting there, brainlet. Nearly understanding the truth. Now let me drop this nugget on you: Matrices are also contrived, and there is better way of expressing the underlying arithmetic association. What would you represent "i" with then?

[Anonymous No.11354321]

>>11351979
yeah it does

[Anonymous No.11354324]

>>11351812
well what?

[Anonymous No.11354326]

>>11351849
no

[Anonymous No.11354327]

>>11351854
nah 3 and -3

[Anonymous No.11354328]

>>11354294
You don't know any math whatsoever

[Anonymous No.11354329]

>>11351936
no it isn't.

[Anonymous No.11354331]

>>11351898
>>11351910
nope

[Anonymous No.11354338]

>>11352821
define deep, cute, inuitive, and natural.

[Anonymous No.11354341]

>>11353297
kek

[Anonymous No.11354343]

>>11353731
nah

[Anonymous No.11354355]

>>11351812
Why would people even enter this thread without having familiarized themselves with the complex plane?

[Anonymous No.11354356]

>>11354355
But anon, then there would probably be like ~4 responses in this whole thread.

[Anonymous No.11354357]

>>11353297
Why would anyone just go and lie on the internet? Obviously this Anon is telling the truth about being a 6'4" swole 19 year old millionaire with a 24" dick.

[Anonymous No.11354362]

>>11354355
Where do I start?

[Anonymous No.11354372]

>>11354294
>matrices are contrived
Completely untrue, especially if you’ve ever done any sort of basic proof linear algebra. Matrices are one of the most natural structures out there. Actually given your misconceptions on how to do inner products and distaste for basic matrix representation, I think it’s safe to say you really haven’t taken basic undergrad linear nor know what you’re talking about.
>underlying arithmetic
It’s the same arithmetic...
>how would you represent i?
http://www.sosmath.com/matrix/complex/complex.html

[Anonymous No.11354403]

>>11354338
>deep
Containing many theorems on which many others are proven. This typically extends to other fields as well. No, I’m not trivially talking about set theory or univalent foundations which are necessary to address how we write in the first place, but results that are common in the math canon that we use all the time. For example, we have generalized heine-borel in analysis
>cute
Nontrivial facts fall out of simple yet novel ways to look at old theorems. In a basic analysis, you would go through continuity arguments to prove IVT, whereas in a topology class, it’s almost a direct consequence of connectedness. The latter is cute.
>intuitive
Many proofs in courses from complex analysis make direct appeal to the structure of the elements of the plane rather than more contrived methods. Now, I enjoy stretching my reasoning when working over fields like the reals, but there’s no denying the complex numbers play way nicer given how a lot seems to pop out from their construction.
>natural
Many methods you use when reasoning over complex numbers come up when doing new problems. Similarly, even arithmetic over the complex field is so easy, especially when considering polar form

[Anonymous No.11354410]

>>11354328
>>11354372
This is why I am smart and achieve, and you are dumb and wank.

[Anonymous No.11354430]

>>11354403
how many is many?
what is simple? what is novel? why is connectedness cute?
what is play nicer?
what is natural?

[Anonymous No.11354449]

>>11354271
You know what, you're right that's not an excuse.
Here's an actual valid reason: my triangle lives in a Minkowskian space with signature (-,+) and there's nothing you can do about it.

[Anonymous No.11354454]

>>11354410
you're not smart and you don't achieve.

[Anonymous No.11354456]

>>11354271
nah fuck your math bitch lmao

[Anonymous No.11354459]

>>11354454
Mad that I'm already retired at 29? Must feel bad being poor and stupid :)

[Anonymous No.11354471]

>>11354459
you're 14 and you've never gone outside lmao

[Anonymous No.11354488]

>>11354471
Actually Anon, I am unironically a Chad and am very attractive. At my university we have something called "formals" which I use to pick up slutty chinks, sometimes even two at once.

[Anonymous No.11355109]

>>11354488
nope you're not and you don't attend uni :)

[Anonymous No.11355118]

>materials science paper
>HRTEM clear enough to make out and quantify lattice spacing
Yep, I'm thinking it's kino

[Anonymous No.11355370]

>>11351991
The other guy didn't mention that norm means distance function. In this case it's the Euclidean distance, but it could be the Manhattan distance or another function that satisfies the properties of a metric.

[Anonymous No.11355376]

>>11355109
I feel like you're telling me your life story with all this projection, Anon. Go see a therapist.

[Anonymous No.11355382]

>this thread again where nobody knows how complex numbers work
it's all so tiresome.

[Anonymous No.11355456]

>another brainlet complex numbers thread

Here's a question: sqrt(-1) has two square roots. Which one is i and why?

If you can't answer this basic question then go back to /b/ and stop spreading your retardation here

[Anonymous No.11355473]

>>11351885
>This is an important distinction.
t. if I say it like I know what I’m saying I’m right

retard

[Anonymous No.11355488]

i=-1 1+-1=0

[Anonymous No.11355551]

>>11354449
damn he got us, nothing we can do about light-like distance

[Anonymous No.11355559]

2.

[Anonymous No.11355573]

>>11351812
who the fuck is the nigger that keeps posting this

[Anonymous No.11355618]

>>11355376
seething lmao

[Anonymous No.11355621]

>>11351885
3 and -3

[Anonymous No.11356993]

>>11351823

[Anonymous No.11357004]

>>11353279
I've never gone beyond calc and even I know about this. Is that actually the answer though?

[Anonymous No.11357123]

>>11353279
>>11357004
retards, complex distances can actually exist and are also defined in physics https://en.wikipedia.org/wiki/Minkowski_space , you are not absolutely bound to take the norm
it's just a matter of which convention is used

[Anonymous No.11357151]

>>11357123
The Minkowski "metric" isn't actually a metric in the mathematical sense. The value of an actual metric between two points can only be nonnegative, equaling zero if and only if the two points are the same. Hence, d(a,b)=norm(a-b) qualifies as a valid metric, while d(a,b)=(Re(a-b)^2 + (i*Im(a-b))^2)^(1/2) does not over the complex numbers.

[Anonymous No.11357171]

>>11357151
My mistake, the half power is left out of the Minkowski metric. The point stands.

[Anonymous No.11357228]

>>11351812
Uhh, so, you're telling me that the area of the circle depends on the orientation of the measurement..? uhh.. okaaaay

[Anonymous No.11357467]

>>11354362
A math book. Obviously.

[Anonymous No.11357474]

>>11351812
having a side length of i is like having a side length of -1, they are both extensions of the number line that do not exist in geometry

[Anonymous No.11357516]

>>11351812
It's impossible for this to be a right triangle.

[Anonymous No.11357619]

>>11357516
What if it's in the complex plane partially?

[Anonymous No.11357723]

>>11357516
The angle opposite of the hypotenuse is indeed 90 degrees. Following the cosine law:

[math]c^2 = a^2 + b^2 - 2ab\cos{x}[/math]
[math]0^2 = i^2 + 1^2 - 2i\cos{x}[/math]
[math]2i\cos{x} = -1 + 1[/math]

The above can only work for [math] x = \frac{\pi}{2}[/math]

[Anonymous No.11357747]

>>11351812
assuming space itself is distorted then i would equal 1 if its a isosceles right triangle