/sci/ - Science & Math

>>10760396
>SQRT (-1) is an illegal number so it is a huge mistake to use it.
Prove it

>It amounts to mathematical fraud.
Prove it

>Those that that have such egos to think they are above mathematical law will be condemned to mediocrity
What mathematical laws say that sqrt(-1) can't be done?

>No truths can be found and no are problems are solved if one pursues the route of the imaginary, complex theoretical pseudo mathematician
Electrical engineering, aeroelastic flutter, and oscillation damping disagree with you

>>10760396
Stupid troll, shut up moron

>>10760404
>Prove it
Prove that it isn't

>Prove it
Prove that it doesn't

>What mathematical laws say that sqrt(-1) can't be done?
Give me a number, such that multiplied by itself gives as -1. Protip, you can't

>Electrical engineering, aeroelastic flutter, and oscillation damping disagree with you
These are all empirical branches of science. Where all discovery has been made by experimental approaches. The inclussion of SQRT (-1) in this branches is a ploy by pseudo-intellectual mathematicians to gain recognition.

>>10760396
Confirmed for failing calculus II.

>>10760415
Shut up moron, your iq is low and you are stupid.

>>10760396
>You can't just invent numbers that don't exist.
Boy, you're in for a surprise

>>10760415
>Give me a number, such that multiplied by itself gives as -1. Protip, you can't
i

Shut up you piece of click clack without a clock

To everyone saying that i'm wrong, try to explain this.

We know that:
[math]i^{2} = -1[/math]

But then we have:
[math]i^{2} = i*i = \sqrt{-1} *\sqrt{-1} = \sqrt{-1 * -1} =\sqrt{1} = 1[/math]

So you are implying that 1 = -1. Pathetic.

>>10760396
[math] \mathbb{C} = \mathbb{R}[x] / \langle x^2+1 \rangle \\
i = x+\langle x^2+1 \rangle [/math]

>>10760441
i isn't exactly a sqrt(-1), because sqrt(-1) can be both i and -i. Think of it this way:
Imagine ordered pairs of real numbers (a,b) with operations + and • which are defined as (a1,b1)+(a2,b2)=(a1+a2,b1+b2) and (a1,b1)•(a2,b2)=(a1*a2-b1*b2,b1*a2+b2*a1) where + and * are addition and multiplication of real numbers. Observe that (0,1)•(0,1)=(-1,0) and that operations on pairs (x,0) closely resemble that of real numbers. Now, we call (a,b) a complex number and write it as a+bi. (0,1) = i. Even though it is entirely possible to use complex numbers with only ordered pairs of reals, a+bi notation is way more convenient to use. It is commonly used in AC electronics, signal processing etc.

>>10760473
Damn when you put it like that it actually makes sense. Thanks i guess anon.

>>10760396
lol coping undergrad failing math 1

>>10760441
Can you prove that [math] \sqrt{a} \cdot \sqrt{b}= \sqrt{a\cdot b} [/math] for both a,b<0?

>>10760493
can you prove that it isn't?

>>10760528
>can you prove that it isn't?
You prove that [math] \sqrt{a} \cdot \sqrt{b}= \sqrt{a\cdot b} [/math] for positive numbers via [math] (\sqrt{a} \cdot \sqrt{b})^2= a\cdot b [/math], after that you have to prove that [math] \sqrt{a} \cdot \sqrt{b} [/math] is positive. If you drop this last part you can have [math] \sqrt{a} \cdot \sqrt{b}= -\sqrt{a\cdot b} [/math], which is the relation we have to use for [math] i^2[/math].

>>10760488
>when you put it like that
That's literally the standard definition. Do people seriously post math threads without knowing shit about math?

>>10760396
You clearly don't have any clue what the formal notion is. If we have a unital commutative ring, like R[x] (the ring of polynomials with coefficients in R) we want to be able to find the roots of elements. But we can't find a root of x^2 + 1. So we can throw in that root into R to get a larger field. This is equivalent to taking the quotient R[x]/<x^2 + 1>, i.e. modding by the principal ideal of "polynomials with a factor of x^2 + 1". It is a basic argument to prove that such a ring is in fact a field since x^2 + 1 is irreducible and thus the ideal is maximal, and the isomorphism with your current notion of C is very clear. Merely send 1 to 1 and x to i. This is how one formally defines the complex numbers.
You can see that x=i is in fact a square root of -1, since x^2 + 1 = 0 under the quotient.

>>10760396
It's just a tool, and it turns out that it was invented in a way that it's pretty useful ^^

>>10760404
>>10760405
>>10760418
>>10760431
>>10760457
>>10760491
>>10760600
>>10760605
mfw all this people respond to obvious bait

>>10760396
the absolute state of /sci/

>>10760396
>You can't just invent numbers that don't exist.
does 2 exist ? does -2 exist ? does 1/2 exist ? does pi exist ?

>>10760756
>does 2 exist ?
yes
>does -2 exist ?
yes
>does 1/2 exist ?
yes
>does pi exist ?
NO

>>10760415
> electrical engineering is empirical
yeah, no. electrical engineering is not the same as being an electrician, retard.

>>10760904
Engineering in general is empirical, you fuckin moron. Hell, the entire physical SCIENCE of electrodynamics is empirical.

>>10760824
Okay you fucking retard, give me a 2. Don't give two OF something, give me a "pure" two.

>>10760396
I will not "admit" to something that is obviously not true.

>>10760930
*reaches into platonic realm*
here you are

>>10760396
The only reason i and -1 exist is because of squareroots. The definition of a squareroot is flawed and incomplete, and the "root" of your problems.
While imaginary numbers like i and negatives have undeniably proven their worth, the exact meaning of what an "squareroot" is still needs to be reevaluated, especially given its lack of commutativity and production of multiple equivalent values.
>inb4 "why does the squareroot need to be commutitative?"

>>10760938
>unary operator
>commutative
besides that, why the fuck would it need to be commutative? Whatever the fuck that means here.

[math]\sqrt{-1} = -i[/math]
[math]\sqrt{-1}^2 = (-i)^2[/math]
[math]-1 = -1[/math]
therefor [math]\sqrt{-1} = \pm i[/math] or in short, it's all a fucking meme

>>10760938
>the exact meaning of what an "squareroot" is still needs to be reevaluated
z -> z^2 is a two-sheeted covering C* -> C* of Lie groups. a squareroot is the fibre. to get "the" squareroot amounts to picking a section, this is not possible globally as the covering is not trivial. nothing to be "reevaluated", this is all there is to it.

>>10761019
That's true but [math]\sqrt{}[/math] denotes the absolute value of square root, so root(-1) only equals i

>>10760396
>he believes in sqrt()
brainlet. i exists as an extension of the fundamental theorem of algebra. That is all that is needed. """Square Root""" is a convenience, it doesn't really exist.

I bet you believe division exists too.

>>10760528
Yes, of course. In fact, you essentially proved it yourself with the argument in >>10760441. If it was true, then we'd have a contradiction. Therefore it cannot be true.

>>10761043
>That's true but ...
Not really; the post you're replying to is misleading at best. Their logic goes the wrong way. They assumed a conclusion and deduced a truth. That's not a proof unless all the steps can be done in reverse (i.e. all statements are "if and only if"). In this case, the middle statement does NOT imply the first statement, so it's not a proof at all.

>>10761060
It's valid logic for the square root function. (But not the principal root function of course)

>>10760396
>SQRT (-1) is an illegal number
can we invent a new set of numbers larger than the imaginary ones called ILLEGAL numbers pretty please?
I need this in my life

>>10760396
>You can't just invent numbers that don't exist
Then how can you have math at all nerd?

>>10760396
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.

Niggers, all of you

>>10761723
brainlet niggers, you and op

>>10761707
[math]\pi + i_\text{fish}[/math]

One illegal number.

>>10761723
>"imaginary" numbers
*yields extreme utility in everyday applications of science and engineering*
Huh, looks like they're just as real as "real" numbers afterall

>>10760396
>wave and oscillation don't exist
weakest bait I've seen in a while

>>10761750
You know you can describe these with sines and cosines, right?
>inb4 sine and cosine are complex exponentials

Moron's like OP are why mathematicians now admit that calling [math]\sqrt{-1}[/math] "imaginary" was probably a mistake.

And oh, OP, about numbers... they're ALL imaginary!

>>10761759
Have fun trying to write the frequency response of an LC circuit down without complex exponentials

>>10761746
>"God" doesn't exist
>*yields extreme utility in everyday applications of life and human existence*
Huh, looks like He's just as real as anything else afterall

Lmao faggots [math]i=\sqrt{-1}[/math] is literally a wrong definition, because roots must have one solution. [math]i^2=-1[/math] is correct.

>>10761764
>Moron's like OP are why mathematicians now admit that calling −1−−−√ "imaginary" was probably a mistake.
Exactly like this. If only people listened to Gauss and called them lateral numbers. OP and his followers are brainlets who cannot grasp that "imaginary" numbers are as areal and natural as any other.

>>10761019
You can write down the same thing for square roots of positive numbers as well. What's your point? The squaring is not an injective function.

>>10761775
Is your crux with imaginary numbers literally just that they're called imaginary?

>>10761775
God does exist, and I'm sure glad He's not the pathetic, degenerate false one the chr*stians call "father"

Why do retards have problems with "imaginary" numbers but not negative or irrational numbers? They are as imaginary.

>>10760441
[math]
\sqrt{-1} \cdot \sqrt{-1} \neq \sqrt{-1 * -1}
[/math]

>>10761707
[math] \displaystyle
\boxed{ \mathbb{O} \;
\boxed{ \mathbb{H} \;
\boxed{ \mathbb{C} \;
\boxed{ \mathbb{R} \;
\boxed{ \mathbb{Q} \;
\boxed{ \mathbb{Z} \;
\boxed{ \mathbb{N}}}}}}}}
[/math]

>>10762661
they have imaginary in the name, that's literally the only reason