/bant/ - International/Random

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Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 20:29:58 No.2530428 View View Reply Original Report

Quoted By: >>2530526 >>2530576 >>2530968 >>2531026

“imaginary” numbers thread.
what's your favourite fact about them?
and the least favourite?

Anonymous

Anonymous ID:YGOjgeRS Sun 15 Oct 2017 20:30:54 No.2530438 Report

Quoted By: >>2530448 >>2530528 >>2530555 >>2530572 >>2530594

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.

Anonymous

Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 20:32:40 No.2530448 Report

Quoted By: >>2531861

>>2530438
imaginary numbers are as real as negative numbers or 0

Anonymous

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Anonymous ID:iTHDh8XT Sun 15 Oct 2017 20:42:54 No.2530519 Report

Quoted By:

They give rise to fractals, and they are at the core of quantum mechanics. These numbers have some heavy galactic shit about them.

Anonymous

Anonymous ID:nFOUkEpt Sun 15 Oct 2017 20:43:25 No.2530526 Report

Quoted By: >>2530530

>>2530428
squareroute of (-4)

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 20:44:05 No.2530528 Report

Quoted By: >>2530572 >>2530594 >>2531861

>>2530438
I love you so much right now.

Anonymous

Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 20:44:09 No.2530530 Report

Quoted By:

>>2530526
2i

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 20:46:19 No.2530541 Report

Quoted By: >>2530555

Favorite:
They can be made somewhat intuitive by displaying them on a bidimensional plane

Least favorite:
Function display requires 4 dimensions

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 20:47:23 No.2530555 Report

Quoted By: >>2530580 >>2530594 >>2531861

>>2530541
>>2530438 - I'll defer you to the above post

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 20:49:32 No.2530572 Report

Quoted By: >>2531861

>>2530438
>>2530528
>the absolute state of /bant/ education

Anonymous

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Anonymous ID:PuL1cHYg Sun 15 Oct 2017 20:50:16 No.2530576 Report

Quoted By: >>2530599 >>2530616 >>2530618

>>2530428
Imaginary numbers are pretty fucking cool. Two things that blew me away

> If an imaginary function is differentiable, it's automatically analytic
> If you know only a small part of an imaginary differentiable function, you can immediately predict what the rest will look like

I mean especially that last one completely blew my mind

Anonymous

Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 20:50:33 No.2530580 Report

Quoted By:

>>2530555
imaginary numbers are real
prove me wrong
>but the name...
its a shitty name i know but that's not an argument

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 20:52:10 No.2530594 Report

Quoted By: >>2530814 >>2531861

>>2530438
>>2530528
>>2530555
Funnily enough, that probably was the same reaction people got about negative numbers, fractions and irrationals.
Solve this equation without using any number that doesn't fit this one standard: the solution has to exist in the natural numbers list
10x = 5
What's the value of x?

Anonymous

Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 20:52:56 No.2530599 Report

Quoted By: >>2530606

>>2530576
i think that's how you extend the riemann function right?

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 20:54:21 No.2530606 Report

Quoted By:

>>2530599
Yes. It's how you extend literally any function, that's the point. As soon as you know a very small part of a function, it's completely uniquely defined

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 20:55:36 No.2530616 Report

Quoted By: >>2530649 >>2530652

>>2530576
>If you know only a small part of an imaginary differentiable function, you can immediately predict what the rest will look like
How come? All imaginary differentiable functions are polynomials or something?

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 20:55:42 No.2530618 Report

Quoted By: >>2530633 >>2530637 >>2530652

>>2530576
Would you speak English please? And I've just had bad experiences with math, this abstract shit is useless unless you are planning to become a mathematician, physicist or something - so why jam it down my throat? Why not focus on the fact the education system is going to collapse any day now?

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 20:57:13 No.2530633 Report

Quoted By:

>>2530618
>Why not focus on the fact the education system is going to collapse any day now?
Why will it collapse?

Anonymous

Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 20:57:45 No.2530637 Report

Quoted By: >>2530656

>>2530618
have you read the name of the thread?
does it say “education thread”?
no?
then stfu

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 20:59:25 No.2530649 Report

Quoted By: >>2530692

>>2530616
Welcome to Taylor Series 101
No brainlets allowed
No girls allowed
Ascension proof required for entry

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 20:59:39 No.2530652 Report

Quoted By: >>2530692

>>2530616
Technically yes! Every function defined in the complex numbers can be written in (infinite) polynomial form. As long as it's differentiable. Or, to be more accurate, something that's extremely similar to differentiability.

>>2530618
You're right. Nobody needs complex numbers except academics and certain electronics related fields. But I study math so, allow me to sperg out

Anonymous

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Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:00:25 No.2530656 Report

Quoted By: >>2530678

>>2530637

Anonymous

Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 21:02:44 No.2530678 Report

Quoted By: >>2530703

>>2530656
you're trying to derail the thread, what do you want me to do?

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:03:45 No.2530692 Report

Quoted By: >>2530725

>>2530649
Chill Juan

>>2530652
That's really cool, I wonder what the consequences of that are

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:05:05 No.2530703 Report

Quoted By: >>2530788

>>2530678
You're passionate about math and you come to 4chan, where is the logic in that?

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:06:57 No.2530725 Report

Quoted By: >>2530745 >>2530760

>>2530692
It's mindblowing. The obvious consequences are that they're really easy to perform calculations with, since polynomials are by far the easiest things to manipulate. However most "real" applications still go way above my head desu. I know they're used in a lot of theorems about prime numbers for instance, and this is ofcourse ridiculously important for encryption

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:08:22 No.2530745 Report

Quoted By: >>2530765

>>2530725
The consequences are the wearing out of my patience ergo an impending act of violence

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:09:30 No.2530760 Report

Quoted By: >>2530790 >>2530797 >>2530855 >>2530865

>>2530725
Do you have any idea of why complex numbers give rise to fractals? I mean, the rules that generate the Mandelbrot set are as simple as it gets, yet that thing has an infinite amount of nontrivial information in it

Anonymous

Anonymous ID:qAz0ceR1 Sun 15 Oct 2017 21:10:01 No.2530765 Report

Quoted By: >>2530825

>>2530745
but why?

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 21:12:47 No.2530788 Report

Quoted By:

>>2530703
Alright, what do you want us to talk about on this russian musical watching website?

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:12:55 No.2530790 Report

Quoted By:

>>2530760
I don't, sorry. That's still beyond me. I've had a very small introduction to the concept of fractal dimensions but it was just a little bit of interesting theory, nothing solid

Anonymous

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Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:13:41 No.2530797 Report

Quoted By: >>2530824

>>2530760
Did someone say "have?"

Anonymous

Anonymous ID:+IxnSSxM Sun 15 Oct 2017 21:15:25 No.2530814 Report

Quoted By: >>2530839

>>2530594
10x = 5
x = 5/10 = 0 remainder 5

Anonymous

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Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:16:07 No.2530824 Report

Quoted By: >>2530839 >>2532760

>>2530797
fractals indeed reside in our dreams

Anonymous

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Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:16:10 No.2530825 Report

Quoted By: >>2530852

>>2530765
I'll refer you to this absolutely sensical graph

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 21:17:29 No.2530839 Report

Quoted By:

>>2530814
And 0 reminder 5 is... What number again?

>>2530824
>tfw my dream girl is a fractal
>tfw i wouldn't understand her, her life is too complex and detailed

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 21:18:45 No.2530852 Report

Quoted By: >>2530863

>>2530825
Whatever your red function is, it has 2 different values at x = O
Very poorly made graph

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:18:55 No.2530855 Report

Quoted By: >>2530876

>>2530760
As far as I know, it's more so the recursive functions that lead to fractures. Doing something over and over again forever can define shapes that never smooth out as you zoom in on them. The concept of fractals were thought up to describe the jaggedness of coastlines, which is a real-world application, so fractals don't strictly need to exist in C.

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:19:43 No.2530863 Report

Quoted By:

>>2530852
Considering it took 3 minutes on MS Paint and was meant as a joke, I'd say absolutely

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:19:48 No.2530865 Report

Quoted By: >>2530876 >>2530877 >>2530878

>>2530760
I do have a "free" book about complex numbers from Princeton (in pdf). It's what we used in class, pretty comprehensive but you need a decent background in calculus

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:20:57 No.2530876 Report

Quoted By: >>2530891

>>2530855
Still, you could multiply over and over without anything interesting appearing. The fact is that interesting things do appear, and it's not clear why

>>2530865
If you have the link, I'd be interested

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:21:03 No.2530877 Report

Quoted By: >>2530912 >>2530919 >>2530934

>>2530865
Can I just stick it up my ass?

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:21:05 No.2530878 Report

Quoted By: >>2530891

>>2530865
go for it

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:22:30 No.2530891 Report

Quoted By: >>2530917 >>2530938 >>2531043 >>2531063

>>2530876
>>2530878

http://kryakin.org/am2/Stein-Shakarchi-2-Complex%20analysis.pdf

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 21:23:14 No.2530912 Report

Quoted By: >>2530915

>>2530877
Do it and take pictures.
Sharpie and timestamp is required in order to fit this board's standards as well

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 21:23:44 No.2530915 Report

Quoted By:

>>2530912
are*

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:23:53 No.2530917 Report

Quoted By: >>2530936 >>2530944

>>2530891
Stein Shakarchi? A Japanese-German mathematician?

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:24:06 No.2530919 Report

Quoted By: >>2530945

>>2530877
dude, he literally just said it's a PDF

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:24:48 No.2530934 Report

Quoted By:

>>2530877
400 pages. I hope you have a big fuckin ass, son

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 21:25:32 No.2530936 Report

Quoted By:

>>2530917
https://google.com/stein%20shakarchi

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:25:54 No.2530938 Report

Quoted By:

>>2530891
Thanks PuL

Anonymous

Anonymous ID:Q1vNnYom Sun 15 Oct 2017 21:26:26 No.2530944 Report

Quoted By: >>2530991

>>2530917
https://google.com/search?q=stein%20shakarchi
messed up the url

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:26:29 No.2530945 Report

Quoted By: >>2530959

>>2530919
I'll print it out

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:27:24 No.2530959 Report

Quoted By:

>>2530945
It would be easier to download it to your palm-pilot

Anonymous

Anonymous ID:RJdE+vk6 Sun 15 Oct 2017 21:28:02 No.2530968 Report

Quoted By:

>>2530428
It's great to use as an electrical engineer, and they work.

They're imaginary.

Anonymous

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Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:29:20 No.2530991 Report

Quoted By:

>>2530944
Here you go, as requested, I've extrapolated the date based on Adolf Tamagochi's Frankentoulious Principle

Anonymous

Anonymous ID:lxcIONn4 Sun 15 Oct 2017 21:29:35 No.2530998 Report

Quoted By: >>2531015 >>2531037 >>2531043

They are above negative and positive infinity. They are like a different dimension and they actually have real life uses. I wish I could learn more

Anonymous

Anonymous ID:lxcIONn4 Sun 15 Oct 2017 21:30:19 No.2531015 Report

Quoted By:

>>2530998
about them

Anonymous

Anonymous ID:RJdE+vk6 Sun 15 Oct 2017 21:31:09 No.2531026 Report

Quoted By: >>2531035 >>2531054

>>2530428
I can use them to describe my girlfriend, she's the square root of 100

Anonymous

Anonymous ID:RJdE+vk6 Sun 15 Oct 2017 21:31:44 No.2531035 Report

Quoted By: >>2531047 >>2531054

>>2531026
Square root of -100

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:31:58 No.2531037 Report

Quoted By:

>>2530998
But what is today but yesterday's tomorrow?

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:32:30 No.2531043 Report

Quoted By:

>>2530998
>>2530891
Well then it's your lucky day! This Belgian is giving away free textbooks

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:33:02 No.2531047 Report

Quoted By:

>>2531035
ha, good one

Anonymous

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Anonymous ID:gpWqN1yU Sun 15 Oct 2017 21:33:41 No.2531054 Report

Quoted By: >>2531083

>>2531026
>>2531035
10i
i don't ged id :DDD

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:34:15 No.2531063 Report

Quoted By: >>2531080 >>2531107 >>2531113 >>2531146 >>2531177

>>2530891
I was taking a look at the part on conformal mappings, and apparently you can't map the entire complex plane into the unit circle. That's interesting, in the real line you can map the entire thing to the interval [0, 1].

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:34:59 No.2531080 Report

Quoted By:

>>2531063
Are these the same people that said the world was flat?

Anonymous

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Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:35:08 No.2531083 Report

Quoted By:

>>2531054
His girlfriend is Interstate Highway 10.

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:36:35 No.2531107 Report

Quoted By: >>2531126

>>2531063
You can with a purely surjective function, maybe not a homeomorphic function.

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:36:54 No.2531113 Report

Quoted By: >>2531152 >>2531212 >>2531225

>>2531063
What you're talking about is the Riemann sphere. Basically you need to add 1 extra point to the complex numbers (i.e. infinity) and then you can

https://en.wikipedia.org/wiki/Riemann_sphere

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:37:35 No.2531126 Report

Quoted By:

>>2531107
Oh, I'll show you homoerotic function alright....

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:38:54 No.2531146 Report

Quoted By: >>2531182 >>2531207

>>2531063
And yeah now that you mention it complex numbers also have a LOT of applications in the whole business of geometry, defining shapes, counting all their holes and all that shit

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:39:25 No.2531152 Report

Quoted By:

>>2531113
I was watching a lecture by Roger Penrose on spinors, and he was talking about this sphere. Holy shit. Thanks.

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:41:35 No.2531177 Report

Quoted By: >>2531225

>>2531063
Okay so,
C is topologicaly equivalent to RxR.
RxR\{(0,0) is a connected set.
Connectivity is a topological invariance.
R\{(0)} is a disconnected set.
Therefore C is not topologiacly equivalent to R. QED

I believe you (what's a conformal mapping?)

Anonymous

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Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:42:25 No.2531182 Report

Quoted By:

>>2531146
Seriously burger? You're not gonna make a joke about counting holes? I left it there especially for you

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:44:21 No.2531207 Report

Quoted By:

>>2531146
>Oh look at those holes! That doughnut and that coffee mug each have one of them! Woah!

Anonymous

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Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:44:29 No.2531212 Report

Quoted By: >>2531363

>>2531113
And by the way, visited the page, very informative.

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:45:25 No.2531225 Report

Quoted By: >>2531240 >>2531254 >>2531328 >>2531371

>>2531113
Why do you need to add the infinity?

>>2531177
What is \{(0,0)? That's not proper latex senpai

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:46:15 No.2531240 Report

Quoted By:

>>2531225
Latex Senpai? Sounds kinky....

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:46:58 No.2531254 Report

Quoted By: >>2531273

>>2531225
I write my proofs by hand because I'm a real boy.

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:48:31 No.2531273 Report

Quoted By: >>2531282

>>2531254
What happened to the Belgian? I have his wikipedia page edited

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:49:12 No.2531282 Report

Quoted By: >>2531340

>>2531273
Someone will see it. You have done good.

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:50:47 No.2531328 Report

Quoted By: >>2531363 >>2531412

>>2531225
Why? That's a good question. I'm not sure if I can give a convincing argument, but I can try. Basically, if you don't have that one "closing point" at the end, the complex plane just keeps stretching on infinitely. So if you were to wrap it around a sphere, it would get closer and closer to a single point, but it would never actually cover it. Does that make sense?

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:51:21 No.2531340 Report

Quoted By:

>>2531282
Thank you, sir.

Anonymous

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Anonymous ID:dtRWYC4M Sun 15 Oct 2017 21:52:09 No.2531358 Report

Quoted By:

the average are dumb stupid and lie shit
and enslave you equaly

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:52:16 No.2531363 Report

Quoted By: >>2531407

>>2531328
>>2531212 - Made sense to me after this.

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:52:40 No.2531371 Report

Quoted By:

>>2531225
I think C is homeomorphic to a bounded open square, which needs that extra point to close off it's open edge. once everything adheres to the closed point it can morph into a 2sphere.

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 21:54:17 No.2531407 Report

Quoted By: >>2531424

>>2531363
You done good son gave me a giggle 10/10 shitposting

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:54:38 No.2531412 Report

Quoted By: >>2531452 >>2531506

>>2531328
It makes sense. But I'm wondering, what if you made two functions A and B such that

A maps [0, 1] to [-infinity, infinity]
B maps [0, 1] to [0, 2pi]

and then you take the values of A to be the radius and the values of B to be the angles in a polar projection, can't you map the entire plane without adding the infinity point?

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 21:55:22 No.2531424 Report

Quoted By:

>>2531407
Coming from you, that means a lot!

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 21:56:51 No.2531452 Report

Quoted By: >>2531487 >>2531514

>>2531412
Look at A more closely.
R is not [,], it's (,).
Let C map (0,1) to R.

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 21:59:02 No.2531487 Report

Quoted By:

>>2531452
Oh yes, you are right. Even so, I'm mapping the entire plane in a region bounded by a square, am I not?

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 22:00:27 No.2531506 Report

Quoted By: >>2531533

>>2531412
That's a good idea. However then you get into the problem of continuity. You can map any open and closed intervals to ]-inf, inf[, but the twist is, you can't create a *continuous* function from a closed interval to ]-inf, inf[. So the order of your complex numbers would get completely messed up.

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 22:01:11 No.2531514 Report

Quoted By:

>>2531452
You need f: [0,2pi) to {unit circle} to be a homeomorphic function.
injective, surjective, continuous, and continuous in inverse

Anonymous

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Anonymous ID:iTHDh8XT Sun 15 Oct 2017 22:02:24 No.2531533 Report

Quoted By: >>2531571 >>2531620 >>2531641

>>2531506
What about this one? It's continuous (although only defined in an open interval, but is that a problem?)

Anonymous

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Anonymous ID:iTHDh8XT Sun 15 Oct 2017 22:05:02 No.2531567 Report

Quoted By:

Also this thing seems like a map from the unit circle from the whole of C, without needing the infinity point of the Riemann sphere. Is it not?

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 22:05:14 No.2531571 Report

Quoted By:

>>2531533
Ah yes that's exactly the problem. Your interval has no "endpoints", so again, looking at the sphere it would stretch infinitely closer to one point, but it would never quite touch it

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 22:08:03 No.2531620 Report

Quoted By: >>2531728

>>2531533
You can do something similar with the real numbers. If you try to map them to the unit circle, you would just get a circle with a tiny little hole on top. That hole on top is infinity

Anonymous

View Same Google ImgOps iqdb SauceNAO R.png, 16KiB, 700x814

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 22:09:25 No.2531641 Report

Quoted By: >>2531728

>>2531533
Here,
You can't map R to [0,1), only to (0,1).
You can't force the open ends together because they're open; they're defined as not including their own boundaries.
There's always a gap.

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 22:14:33 No.2531728 Report

Quoted By: >>2531760 >>2531765

>>2531620
>>2531641
I think I understand now

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 22:16:47 No.2531760 Report

Quoted By:

>>2531728
It pretty much just revolves around learning how open/closed sets work. I had the comfort of having them thrown in my face for a whole year straight

Anonymous

View Same Google ImgOps iqdb SauceNAO R.png, 9KiB, 700x814

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 22:17:07 No.2531765 Report

Quoted By: >>2531810

>>2531728
If you try to map C to a 2sphere you get an almost-a-sphere with an open hole (the hole itself is closed, but the sphere is open right there.)

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 22:19:35 No.2531810 Report

Quoted By: >>2531835 >>2531902

>>2531765
But what is the motivation for making a closed sphere, if the open one with the tiny hole contains all the actual points?

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 22:20:57 No.2531835 Report

Quoted By: >>2531891

>>2531810
Being open means it's missing the point there.

Anonymous

Anonymous ID:5ugDQ0gY Sun 15 Oct 2017 22:22:28 No.2531861 Report

Quoted By:

>>2530448
>>2530528
>>2530555
>>2530572
>>2530594
It's pasta you fucking morons.

Anonymous

Anonymous ID:5ugDQ0gY Sun 15 Oct 2017 22:23:50 No.2531882 Report

Quoted By: >>2531903

Fucking holomorphic functions are C^infinty, that's pretty fucking neat.

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 22:24:27 No.2531891 Report

Quoted By: >>2531991

>>2531835
b-but it's not an actual point, infinity is not a number

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 22:25:08 No.2531902 Report

Quoted By:

>>2531810
Because closed spheres are a mathematician's wet dream. You can just loop all your shitty functions around it in any direction and move them around all you want, you can still be sure they are neatly fitted on a nice surface that's equal all around. Lots of physics calculations become much easier when viewed in spherical models

Anonymous

Anonymous ID:f5K+l+Jr Sun 15 Oct 2017 22:25:17 No.2531903 Report

Quoted By:

>>2531882
Yep, Tupac Holograms

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 22:32:37 No.2531991 Report

Quoted By: >>2532019 >>2532091

>>2531891
You're right. Infinity is not a number in the set of real or complex numbers. That was why we had to say that we were dealing with open sets in the first place. However, the extra point is still necessary, and calling it the point at infinity is the best way to name it. Points don't need to come from somewhere if the whole reason we needed it was because it was missing.

Also, the points themselves aren't exactly the same as numbers; their names are numbers.

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 22:34:50 No.2532019 Report

Quoted By: >>2532091

>>2531991
Also once you expand your notation for like, the basic +* operations and the inequality signs, you can sort of treat it like one of the numbers anyways. If you're attentive with what you're doing

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 22:41:21 No.2532091 Report

Quoted By: >>2532255 >>2532344

>>2531991
>Also, the points themselves aren't exactly the same as numbers; their names are numbers.
How come? Isn't two always two?

>>2532019
That's nice, like being able to assert that 1/infinity = 0 without it being an abuse of notation

Anonymous

Anonymous ID:PuL1cHYg Sun 15 Oct 2017 22:42:12 No.2532255 Report

Quoted By:

>>2532091
Exactly

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 22:50:10 No.2532344 Report

Quoted By: >>2532377

>>2532091
You can move a square around RxR, and it will still be a square.
You can map C to a sphere\{point} in all sorts of ways, but no matter where the hole ends up, that's the point f(infinity). That happens no matter what the point's coordinates are. It can have whatever coordinates it might have, but it can always just be called " the point on the sphere which does not have a preimage in C."

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 22:52:44 No.2532377 Report

Quoted By: >>2532440 >>2532509

>>2532344
I understand what you just said, but I don't understand how that relates to what you said about points not being the same as numbers

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 22:57:48 No.2532440 Report

Quoted By:

>>2532377
The difference is subtle, and I don't know that it matters that much to what we're talking about.

the proof is left to the reader

Anonymous

Anonymous ID:9C6zvvBC Sun 15 Oct 2017 23:02:23 No.2532509 Report

Quoted By: >>2532650

>>2532377
to say that they're different is kind of hard to enplane, but it's useful for doing change of bases in linear algebra and when looking at finite groups mod some number

The numbers in R each have a point, but what about some other line that's not R? What if the line isn't even in R^n?

Anonymous

Anonymous ID:iTHDh8XT Sun 15 Oct 2017 23:09:21 No.2532650 Report

Quoted By:

>>2532509
that's beyond the things I've encountered so far, I'm just a pleb physics bachelor

Anonymous

View Same Google ImgOps iqdb SauceNAO copertina-660x330.jpg, 112KiB, 660x330

Anonymous ID:kbCVtqb/ Sun 15 Oct 2017 23:16:50 No.2532760 Report

Quoted By:

>>2530824
DMT experiences for example

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