Alright, give it your best shot to justify this fucking bullshit

Alright, give it your best shot to justify this fucking bullshit.

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en.wikipedia.org/wiki/Extended_real_number_line
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1. Prove an algebraic closure of R exists

2. Fundamental Theorem of Algebra

i is a 90 degree turn, -1 is a 180, 1 is a 360

One can not justify blatant lies

MATH WAR NOW

LSD

>1. Prove an algebraic closure of R exists
>Th-there's roots of this polynomial in a field that is completely detached from reality!
So autistic mathfags circlejerking is an argument now?

No such thing as a continuous square root function on [math]\mathbb{C}[/math]

first bullshit: what do you need to do twice to get a rotation by 180 degrees ? that's right motherfucker, rotation by 90
second bullshit is not true

I like you. You know the math. You are just baiting people who are insecure about their knowledge of math (e.g. engineers and other "wtf i love science" types). Keep it up.

That's like one guy saying
>let's use the expression "house" to denote that thing we live in,
and another guy complaining and wanting to justify introducing a word that he hasn't heard before.

The real problem here, OP, lies with your Platonic view of numbers. You act as if e.g. natural numbers are just something in the world and working with rational, real or complex numbers, or whereever you set the bound (or quaternions, octernions, hyper real, surreal, polynomial rings, SU(2), or any compact Lie groups) need justification.

I haven't even done Analysis, pal.

[eqn]\mathbf C \,\sim\, \mathrm{Vect}_\mathbf R \left[ \begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix},\, \begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix} \right][/eqn]

I said you know the math. The math involved here is 10th grade math. I didn't say you're working on class field theory.

Are irrational numbers real?

yes, by definition

>describe a natural phenomenon with math
>set up differential equation
>negative square root
>"fuck! oh well, I'll just assume it makes sense to continue on, we'll set $sqrt(-1) = i$"
>all i's cancel out
>get a solution with real values
it just werks

it's well defined

>believing in reals
>Bullshitting your way to to imaginary numbers

i is a number with the property of its square being equal to -1, there's nothing to justify. I think we can define whatever we want in math and work with it as long as certain conditions are met, though I'm not sure because I'm not a mathematician.

I see an engineer after my own heart
Can't solve all odd ordered polynomials without them, despite the fact that EVERY odd ordered polynomial will have at least 1 root

...

kek

x < 0
Justify this bullshit.

>0

You first

you done fucked up

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.

le wildberger face

lel

>If your equation can only be solved by inventing numbers that can't exist

Mathematics is simply a catalog of objects and their properties. Examples of entries in the catalog of mathematics include:

irrational numbers
imaginary numbers
complex numbers
transcendental numbers
hyperreal numbers

All of those entries exist. None of those entries "exist" any more or any less than any other entry in the catalog.

Now, some of those types of number might be more useful for a certain domain. For example, if you were keeping the books of a business, the rational numbers would be just fine for your purposes. But usefulness is not a requirement for inclusion in the catalog of mathematical objects. Mathematicians simply seek to understand and document patterns, that's all.

> "the correct answer is whatever the correct answer is"

That's not the way complex numbers work. The idea is that IF i^2 = -1, THEN the complex number system can be defined. Notice the crucial word "IF". You're free to refuse to accept that i^2 = -1 -- no harm, no foul. The complex number system only comes into play ***IF*** you first define i^2 = -1. For convenience, they call i a "number", but if you don't like that, then you're free to refuse to call i a number and simply treat it as an abstract variable with the property that i^2 = -1, and if you do, then absolutely nothing will change about complex mathematics.

It's a definition. There is no need to justify a definition.

If I said "I define the square root of -1 as potato," you could say that's a stupid choice, but you can't ask me to justify it because it's just a choice I made.

What the fuck did you just fucking say about complex numbers, you little bitch? I’ll have you know I stopped caring about math when I was introduced to the concept of imaginary numbers, and I’ve been involved in numerous secret raids on Al-Gebra, and I have over 300 crocks of shit. I am trained in equations that can only be solved by inventing numbers that can't exist and I’m the top math deity in the entire US academic forces. You are nothing to me but fucking wrong. I will wipe you the fuck out with math the flaws of which have never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of algebra solutions across the USA and your IP is being traced right now so you better say "the correct answer is whatever the correct answer is", maggot. The math that says the pathetic little thing transcribed to words. You’re fucking dead, kid. I can be anywhere, anytime, and I can mark you wrong in over seven hundred ways, and that’s just if you write it down in english instead of ancient math runes. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Logical Math Corps and I will use numbers that never lie to their full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy flaws your little “clever” human construct was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit complex numbers all over you and you will drown in it. You’re fucking dead, kiddo.

Engineers gotta deal with control theory. Phasors, settling times, root locus, and the like all include the practical use of i.

Just because you can write something algebraically doesn't mean it's solution exists. Can I create a "special number" "f" to make x+1 = x valid?

There, f is a special number, defined as the number such that f+1=f.

That's essentially what I is. The square root function does not take negative numbers. Anything derived from I is pointless. Cope, mathfags.

>the square root function does not take negative numbers
uh, user?
it does...
the square root of a negative number is just the square root of it's absolute value times i. That's what it's defined as!
You autistic retard.

All maths is imaginary and made up.

So why can't I define the special number system as multiples of number f that allows me to let any transformation of g(f) = f+1 = f?

It's the same pretentious rulebreaking as complex numbers.

Correction to be more rigorous:

g(f,x,y) = xf + 1y = xf + y
So any special number can be written in the form xf + y

Circuits

decent response but I'm afraid you've failed to recognize that you've replied to a copypasta

>Can I create a "special number" "f" to make x+1=x valid?
you can, actually.

en.wikipedia.org/wiki/Extended_real_number_line

>numbers that can't exist,
aight

what is the projective line, the post

fucking brainlet

why has nobody pointed out that irrational numbers make even less sense than i

> i doesn't exist but pi does

leave

because i doesn't exist in the sense of counting apples, but it can be used to model some physical phenomena. It's useful. Literally the only justification needed (other than appreciation for the math itself).

The only numbers that exist are the natural numbers. Anything else is math faggot wankery that doesn't represent reality

Oh, and don't get me started with the "negative" numbers. They make no sense at all, you can't count non-existing or "negative" objects. Utterly bs.

NJW pls go.

The study began when the search for roots of polynomials gave us imaginary numbers. The quadratic formula requires a square root to be taken, and thus cannot be used if the discriminant is not a square in the field you're working in. However, mathematicians blew imaginaries in quadratics off as an anomaly at first...when we started studying cubics we discovered every real number has two imaginary cube roots. Anyway the field of real numbers was algebraically extended to the complex numbers so that all of its elements would have squares and any element would work in the quadratic formula. It turned out that all roots of any polynomial can be found in the complex plane so we're kind of done extending that field now

I don't even believe in fractions. How can you have half of a single thing?

How Can i Equal Root Of Minus One If -i Equals Root Of Minus One

It can be understood as a multivalued function.

That's easy.

Solve the equation x/4 = 3. You'll find that no such solution exists for whole numbers. So you have to invent fractional numbers in order to solve the equation.

Now solve x + 2 = 0. You'll find that no such solution exists if you only know positive numbers. You need to invent negative numbers to solve this.

Now try x^2 - 2 = 0. Once again, you'll find this impossible if you only know rational numbers. You have to invent real numbers in order to get a solution.

Lastly, try x^2 + 1 = 0. You have to invent complex numbers in order to solve it. Once you do, it has the solution +/- i.


If that's not enough, then pick up any electromagnetism, optics, or quantum mechanics textbook and you'll see complex numbers everywhere. Physics is impossible without complex numbers, which means the electronics in the everyday world are impossible. If the technology you use to shitpost isn't proof enough, then you should probably kys.

Sorry, I'm retarded. 4x = 3 not x/4 = 3.

>people actualy believe this
complex and imaginary numbers are used in so many different ways for real-life applications like eigenvalues and shit

You have 6 friends and 3 apples to give them. How do you divide the apples so that every one gets an equal amount?

This is literally preschool math.

Of course you could look at it as "you have 6 halves of an apple" instead of 3 apples, but that's the definition of a fraction. 6 halves is by definition 3.

Complex numbers have tons of applications.Specially in EE

So if the square of something is something times itself.And to get -1 from a product you need 1 and -1 then the square root of -1 is not constant

Isn't that why it's considered an imaginary number? As it's a number that doesn't exist within our reasoning.

Why I have to justify shit? Numbers are constructions based on arbitrary axioms. You can define whatever bs you want, i is useful though

(y = sqrt(x)) == (y^2 = (sqrt(x))^2)

If the sqrt(-1)=i, then sqrt(-2)=?

Yes.It just seems to be weird from a formal point of view

(((Complex numbers))),

Are you fucking retarded? ALL numbers are made up. 1+4 = 5 doesn't make sense in the "real" world either. Math is a human invention so we can define whatever we want. What's special about math is that we're defining everything so that it is consistent with some axioms we came up with or other solutions. And since our universe also seems pretty logical (that's actually where we got our definition of "logic" from) the maths we come up with can abstractly describe our universe to some degree. Kys your thread is bullshit

Why shouldn't it exist?

>1+4 = 5 doesn't make sense in the "real" world either.
Put 4 fingers of your right hand in your ass and 1 finger from your left hand in your ass.How many fingers do you have in your ass?

Can't really, it's maths based on a created "complex plane" being justified with maths based on the real plane

Prove 1 = 1.

Animals can count

what's wrong with it?

Are you fucking retarded?

Just define a dot product in [math]\rm I\!R^2[/math] in such a way that that [math](x,y)\cdot(x,y) = (x^2 - y^2, xy + yx)[/math]

You just got BTFO small baller brainlet

No. 'Fingers' aren't equal objects. There's different kinds of them and every fucking finger on this planet is unique. There are no equal things so saying 4 fingers + 1 finger = 5 fingers is just an abstraction that has nothing to do with reality. It's just how the human mind processes things.

we have this thread every day and you all retards don't get bored of arguing about it. kill yourself

Why am I reading this garbage thread.

Yes, you can make up numbers. So long as the "made up" numbers don't break any of the other rules we have set forth. When adding i we make sure it doesn't break the field axioms. And well, if it doesn't, then we've got a new mathematical object that behaves nicely! Nothing stupid like making a number so that 1+x=x.

this

>0i=0

>0*2=0

really makes you think

it's almost like numbers are abstractions and intagible objects! THATS CRAZY

no 0i = -0

I'm with u. To many shit tier retards posts. Must be the Trump effect.

>when we started studying cubics we discovered every real number has two imaginary cube roots.
this never happened because it isn't true

the name "imaginary" was a mistake. brainlets can't into abstract thinking.

Factor the polynomial X^3-c for a real number c.

this is not the same question and one day I hope you understand why

The thing that bugs me is how to differentiate i from -i, when the square of both is -1.

this guy is a dickhead, we build things whit that "bullshit"

sqrt(2)i

That's a good question. The upshot is that it really doesn't matter so long as you just pick one and are consistent.

-i = -1*sqrt(-1)
so (-i)^2 = (-1*sqrt(-1))*(-1*sqrt(-1)) = (-1)*(-1)*sqrt(-1)*sqrt(-1) = 1*-1 = -1