/sci/ - Science & Math

sage

I had this thought, too. Let's party like it's 40AD.

it has been thought of before and it works fine

> Where does my math break down?

it doesn't: The rule that everything squared is positive only applies to the set of reals - your numbers including X forms a new bigger set without that rule

Maybe you should call it i instead of X.

http://en.wikipedia.org/wiki/Imaginary_unit

>Where does my math break down?

1 = sqrt(1) = sqrt(-1 * -1) = X * X = -1

OP's math is just as retarded as division by zero.

>>5865861
> implying sqrt(ab)=sqrt(a)sqrt(b)

>>5865866
Did you fail algebra?

>>5865866
You fucking idiot.

<span class="math">\sqrt{ab} = \sqrt{a} \sqrt{b}[/spoiler]

OP are you fucking retarded? You think you can just magically come up with some negative square root and expect all of math to work, when even great minds like Euler and Gauss couldn't do it?
>lrn2axioms
Get real dude.

>>5865867
>>5865887
>im I funny yet?
Ironic shitposting is still shitposting

what education system were you put through? it's fucking called i for imaginary number.

1/10 because i replied

>>5865861
I am actually quite confused by this

>>5865908
They're right though, which is why it's so confusing

>>5865823
The square root of -1 is i, you incompetent niggardly subhuman.

<span class="math">\sqrt{-a}=i\sqrt{a}[/spoiler]

DAT ALGEBRA

>>5865930
nice and simple, good job

>>5865861
they say sqrt(ab)=sqrt(a)sqrt(b) is only valid for reals

I stopped caring about math after I read OP's post. 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.

>>5866654
Go back to your weed and parties young man, you have entered the wrong room.

captcha: the dynabot

>>5866654

every time I laugh

>>5865861
this is confusing

>>5865951
this is also confusing. I thought complex numbers still worked the same as any other number. Are there other properties that break down too?

I have no clue who's trolling in this thread, but in case anyone doesn't know; that totally works out perfectly and it's called i, the imaginary unit.

>>5866720
>I thought complex numbers still worked the same as any other number. Are there other properties that break down too?
ln() and exponents. its not that it doesn't work, its that the functions are multi values and you have to alow for that.

I used to believe in imaginary numbers. For years I did not understand why people would stop and stare at me in the street. Children would run up to me, laughing, and throw dung in my face. I carried on, oblivious to the reason for my public humilation. Then one day a close friend told me why. I didnt understand, imaginary numbers were just so useful, they solved so many problems, especially in engineering. I, foolishly, ignored his advice and continued to use a mathmatical concept cooked up out of nothing to account for what should have been a blindingly obvious flaw at the core of our mathematics. I soldiered on, solving wonderously complex equations with the use of imaginary numbers. All the time I had this vague , sort of itching, discomfort in my anus. I ignored it, but as I continued to work the pain became worse, You could imagine my surprise when one day, in frustration at my increasing rectal irritation, I hurriedly pulled down my pants, pulled up a mirror behind me, and bending down so my head was firmly between my knees, I stared straight into the gaping hole that was my anus. What I saw horrified me. Besides all the wingnuts I caught a glimpse of something so terrifying that my mind almost refused to believe it. But somehow I managed to retain control of my senses and forced myself to observe the crawling horror that was so inflamming the delicate tissues of my sphincter and the passages within. It was an imaginary number dildo. How could I have missed it? There it was! Working its way rthymatically up and down my arse! Oh sweet Jesus the trauma was almost too great for me to bear. But I held on to my sanity. Drastic action was obviously needed. Quickly I read up on Clifford algebra. Within minutes the pain had gone! The dildo of imaginary numbers had vanished! I was saved!

>>5867695
>I have no clue who's trolling in this thread
well I know the one person who got trolled though

>>5867709
Haven't seen that copypasta for more than 2 years. I almost forgot about it.

>>5865823

>>5865951
>they say sqrt(ab)=sqrt(a)sqrt(b) is only valid for reals

a = b = -1 is a real number

>>5865861
>>5865912

sqrt(1) =/ sqrt(-1 * -1)

-1^2 = 1
1 =/ -1^2
1 = 1^2

>>5866720

see
>>5868730

lel /sci/ is easily trolled

Why is it called the imaginary unit? All numbers are imaginary.

>>5865823

>>5865837

lol'd

>>5869213
+1

>>5868747
except 12, 12 is surprisingly real.

>>5868747
no they're not. All reals are complex.

>>5870571
just particularly simple complexes

>>5870536
Why?

8/10 OP

>>5865823
>We all know there are no square roots of negative numbers because every number squared is positive.
Stopped reading here.

>>5871008

I don't know that might be a nine, it was executed almost perfectly. Maybe I'm just saying that because of the person who responded that it wouldn't work

>>5870536
>12
I think you meant -1/12.

>>5871012
Why did you stop reading? You should have read the rest of the post. OP developed an interesting theory.

>>5865823

because it has been though of, and X in your description is the number i

>>5873202
I have never heard of that number before. How am I able to count to it?

>>5865823

yea lets pretend it exist. hmm maybe the name imaginary number could be a name ? since we are just pretending .sci is going to be famous for this :D

>>5873779
You can count to i. The gaussian integers are countable.

>>5875388
How am I able to do it?

>>5876195
Go in spirals around the origin of the complex plane.

>>5871008
>implying we were trolled and not just playing along to see if we could get someone to fall for it

>>5866713
>someone's new

>ask teacher if the square root of i continues, like it's j, and the square root of -j is k
>she has no idea what the fuck I'm talking about
Fucking women

>>5877714
Nobody else does either, that is stupid rambling nonsense that demonstrates a clear lack of understanding of any basic principle of i.

>>5877714
Maybe you should have specified what you're talking about.

>>5877714
Quaternions?

>>5865861
sqrt(1) = +/- 1

>>5880036
-1 is the anti-number of 1.

>>5865906
I stands for current fucktard. Try j

>>5880677
>-1 is the anti-number of 1.

I like the term "anti-number". It sounds more impressive than "inverse".

>lets pretend you can divide by zero
>any number n divided by zero equals Ω
>this allows us to divide by zero
>Why has nobody thought of this before?

>>5865823
>It feels weird just like dividing by zero or infinity.
No, there's a huge difference. The imaginary number "i" works fine with the 4 basic operations. The same doesn't happen if you just define some symbol to equal 0^-1.

>>5882125
>>Why has nobody thought of this before?
The OP is clearly intellectually superior to the majority of the population.

>>5882184
>works fine with the 4 basic operations

What are the 4 basic operations?

>>5877714
<span class="math">\sqrt{i} = \left( \frac{1}{2} + \frac{1}{2}i \right).[/spoiler]

Try squaring it to verify. The complex numbers are algebraically closed, so you may take square roots, cube roots, etc. to your heart's content.

>>5884423
Hey can you tell me how you derived that? Obviously squaring it checks out, but how did you get there?

>>5884474
If you study complex analysis you'll learn that every complex number can be uniquely represented in the form <span class="math">re^{i\theta}[/spoiler], where r is a real number (non negative) interpreted as the "radius" of the complex number (i.e. the distance from the number in the complex plane to the origin) and <span class="math">e^{i\theta}[/spoiler] is interpreted as a rotation counter-clockwise in the complex plane by <span class="math">\theta[/spoiler].

To convert from a complex number <span class="math">a + bi[/spoiler] to the form <span class="math">re^{i\theta}[/spoiler] we have the following easily verified formulas:

<span class="math">r = \sqrt{a^2 + b^2},[/spoiler]
<span class="math">\theta = \arctan{b/a}.[/spoiler]

Converting back is left as an exercise (or can be google searched). Once a complex number is in the form <span class="math">re^{i\theta}[/spoiler], its nth root is easily seen to be <span class="math"> \sqrt[n]{r}*e^{i\theta /n} [/spoiler]. Converting back to Cartesian coordinates yields the "normal" looking nth root of the desired complex number.

Performing this process on the number i gives the number above.

>>5884484
N.B. Of course the term "nth root" is ambiguous, as technically speaking there are n distinct "nth roots" of a number in an algebraically closed field, but the one given is easily seen to be one of them. The others are generated by multiplying it by other nontrivial nth roots of unity.

>>5884487
Thanks bro. I am actually studying calc by myself, so that's a little beyond me right now, but it's good knowing.

>>5884500
Algebraic manipulation of complex numbers isn't out of reach at the high school level, but having a firm intuition and doing some serious math with them is probably a bit more advanced.

For example, one powerful tool of complex analysis is that it allows for the evaluation of complicated REAL valued integrals (you'll learn what those are in calculus if you haven't yet) - something very important and applicable. There is literally no overstating how important complex numbers are to applied and pure mathematics, despite the initial "but they're imaginary and make no sense!" discomfort some people have to them.

>>5884423
>>5884484
Oops, the correct equation should be:

<div class="math">\sqrt{i} = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i.</div>

This one should square to i. Check your work.

>>5884518
Thanks, I think this is right...I kinda suck at math.

>>5884509
>There is literally no overstating how important
Complex numbers are a pseudo-intellectual mental masturbation that is not needed for anything.

>>5884810
Highschooler detected

>>5884509
>but having a firm intuition and doing some serious math with them is probably a bit more advanced.

How much intuition am I supposed to have?

>>5885892
Why do you think that? It only requires an elementary school level of understanding to reach the conclusion.

>>5880696
>jimaginary jumbers

>>5884509
>For example, one powerful tool of complex analysis is that it allows for the evaluation of complicated REAL valued integrals

Can it help me solving triple integrals?

Someone has been keeping at least 35 threads alive
by bumping them twice a day. Compare the post times of
>>5870504 >>5873196 >>5873779 >>5875388 >>5876195 >>5877654
>>5878860 >>5880024 >>5880677 >>5882102 >>5882728 >>5884198
>>5884810 >>5887306 >>5888686
to the post times in other threads.
It's clear most of these are the same person.
The threads being bumped:
>>5858447 >>5861383 >>5862983 >>5863249 >>5865823 >>5866853
>>5867452 >>5867640 >>5868097 >>5868460 >>5868538 >>5869504
>>5869595 >>5869759 >>5869946 >>5872951 >>5873166 >>5873829
>>5874378 >>5874727 >>5875025 >>5876410 >>5876819 >>5878449
>>5878607 >>5878684 >>5878722 >>5880041 >>5880453 >>5880775
>>5881738 >>5883998 >>5884116 >>5884625 >>5885545
Write to moot@4chan.org if you want it to stop.

>>5887314
>jimaginary
That is not a real word.

>>5889536
Of course not. The humorous rhetorical device she was using is called "neologism".

>>5890578
She was just jusing her jimagination.

>>5890578
Please explain. I do not see the humor.

>>5891327
Word play or wordplay[1] is a literary technique and a form of wit in which the words that are used become the main subject of the work, primarily for the purpose of intended effect or amusement.

>>5893026
ITT: summer fags fail to answer questions because they think they have something worth saying

>>5893026
Do you find it amusing? I do not.
>>5893037
She is being very helpful and answering all my questions in an enlightening manner. Please stop shitposting.

>>5893773
>Do you find it amusing?

I have to admit I chuckled. Nevertheless I agree that childish humor is inappropriate on a serious science and math board.

>>5893037
How was it not an appropriate answer to the question?

While you're at it, why not invent a solution to 1/x = 0 as well?

>>5896911
x = weight of your mama

>>5865823
I thought that the square root of -1 is i, the immaginary number.

I thought that the square root of -1 is i, the imaginary number.

>>5896966
y=mx+b
Now what do I do?

>>5897812
Now you solve for x.

>>5897002
The square root of -1 is X. Did you even read the OP?

>>5899252
How do I do this?

>>5899252
>>5901025
Does anyone know?

>>5901850
It is an unsolved problem in mathematical equation theory.

>>5903245
I heard that Atiyah was working on this.

>>5903972
Do you think he can solve it? This problem is definitely not as trivial as index theorems or K theory.

>>5905470
I am not sure. How non-trivial is it?

>>5906268
Approximately a 9 on the non-triviality scale.

>>5865823
Go to hell, square root of -1 is the imaginary number, it's not even funny.

>>5907920
Why are you insulting and ignoring the OP? The square root of -1 is X.

>>5908596
In fact the number X does not exist as demonstrated by >>5865861

Interesting thought, OP. I'll show it to my professor and ask for his opinion.

>>5910142
I do not see how this negates the existence of X. That post assumes it is a number, but it is actually a mathematical letter.

>>5912837
How do we do math with letters? What rules do they follow?

>>5914199
It will be hard to explain unless you understand high level mathematics like long division.

>>5865823
cool what else did you learn at community college today?

>>5914856
I doubt this kind of cutting edgy PhD research math will be taught in community college.

>>5914856
Why would they teach falsehoods and nonsense at CC?

>>5917450
There are zero falsehoods in the OP. She is sharing her avant-garde ideas about number theory.

>>5919105
It has been disproved in >>5865861

>>5920420
Lies. All of them.

>>5920420
You mean the non-argument (i.e. fallacy) that >>5912837 has refuted?

>>5921208
Oh, I did not see that refutation. Thanks.

>>5921208
The link does not work.

>>5921208
The post doesn't exist anymore. What was the poster saying?

>>5924144
I would also like to know this.

>>5865823

go post this on /v/ or something. you'll blow their minds

but yes, this already exists and is called the imaginary number or more simply "i"

>>5925516
I don't think the anti-intellectuals on /v/ would understand advanced math.

>>5925516
Anything imaginary is not able to exist.

>>5925516
>this already exists
>imaginary

contradiction

Even if the math turned out to be valid, there are still no uses for such a number.

>>5926501
Video games use a lot of mathematics.

>>5932195
Playing them does not involve any math.

>>5930931
Yes there is.

>>5933676
What can be asserted without evidence can be dismissed without evidence.

>>5934737
Solutions to ordinary differential equations of degree 2 or higher, in the case where the characteristic equations have non-real roots.
#rekt

>>5934745
When the characteristic equation cannot be solved, the diff eq has no solutions.

>>5935920
yes it dus

The DE
x" + x = 0
has the characteristic equation
r^2 + 1 = 0,
a quadratic with two imaginary roots, but using Euler's identity yields solutions x = Acost + Bsint, where A and B are arbitrary constants.

Please apply yourself.

>>5865823
so... x = i ?

>>5936294
You cannot have two letters in one equation. You cannot solve for both of them simultaneously.

>>5865823
it's like dividing by infinity. Just so weird. It's not that it's wrong, because clearly no one can disprove, but it's just weird and Mathematicians like to "steer in the clear".

>>5936276
How is it possible? Does that mean the method of characteristic polynomials is flawed?

>>5939360
It is an unsolved problem in differential equation theory.

>>5940619
Will it ever be solved?

>>5942522
The best mathematicians are working on it.

>>5944375
Where can I see their work in progress?

what about magical numbers

get this, if i is an imaginary number, then maybe -1 is actually an imaginary letter

>>5946510
/sci/

>>5946587
Thank you. I didn't know this.

>>5946566
Just as stupid as irrational/imaginary/illogical/inconsistent numbers.

>>5865823

Ha! Next you'll be telling me that the length of an isosceles right triangle with unit legs isn't expressible as a ratio of two integers.

5/10 OP made me respond.

>>5884423
Wallis' formula

>>5949570
How is this related to the thread?

>>5865823
It works in some theoretical applications but has no reasonable basis for real life.

>>5865839
He can call it whatever the fuck he wants to you fucking moron maybe I'd call it P but that doesn't make it any more valid retard.

>>5950041
I cant legitimately tell if you're retarded or trolling. i is what is known as a complex number or the square root of negative 1

>>5950290
His point was that it's just a notation. It makes no fucking difference what you call it. You could draw a mini mona lisa for every imaginary unit for all it matters.

P.S. Mathmos tend to call it j.

>ctrl+f "pasta"
>1 result and it doesn't refer to the OP

Seriously you guys, we've had this exact same post like 10 times already (and I mean word for word down to the last period). Stop fucking responding to it.

>>5950296
No pasta ITT. This is the original thread.

>>5950295
Notation is very important. Without consistent notation nobody will understand you.

>>5950295
>P.S. Mathmos tend to call it j.

Who is Mathmos?

>>5877689
autism/10

Fuckin idiot....

>>5955372
Why would you say that?

>>5955372
OP is inventing mah on her own. That means she's definitely smarter than you.

>>5955372
I bet you didn't even understand the math in OP.

>>5950296
I've never seen this pasta before.