why did god make e^(i*pi) = -1 ? is there some message hidden in it?

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Anonymous Sat Jan 14 11:54:34 2012 No.4253889 [Reply] [Original]

why did god make e^(i*pi) = -1 ?

is there some message hidden in it?

>>	Anonymous Sat Jan 14 11:58:06 2012 No.4253901 "God made the natural numbers; all else is the work of man." -Leopold Kronecker

>>	GL !Bgpe2HycPk Sat Jan 14 12:03:38 2012 No.4253908 Seriously, I don't get it. Why are kids so fascinated by Euler's identity? When I saw it for the first time I thought something like "cool, a useful formula" and then I read on without being excessively impressed.

>>	Anonymous Sat Jan 14 12:11:22 2012 No.4253925 >>4253908 This formula combines different branches of mathematics with great simplicity, using the better known constants, however, people who say they like it are mostly pretends

>>	Anonymous Sat Jan 14 12:12:22 2012 No.4253928 It's God's way of telling you your a faggot.

Anonymous Sat Jan 14 12:14:22 2012 No.4253935

>Seriously, I don't get it. Why are kids so fascinated by Euler's identity?

Richard Feynman called Euler's formula "our jewel" and "one of the most remarkable, almost astounding, formulas in all of mathematics."

It's not impressive that you weren't impressed. If anything it shows that you're a dumbass and can't think deeply about math.

>>	Anonymous Sat Jan 14 12:15:22 2012 No.4253936 >>4253889 It's a product of Euler's wizardry and arcane manipulation of math. I'm astounded by his genius, not by the possibility of some hidden message

>>	Anonymous Sat Jan 14 12:15:22 2012 No.4253938 >>4253935 >I am the most fucking DEEP intellectual on this planet because I just took high school philosophy

>>	Anonymous Sat Jan 14 12:17:22 2012 No.4253940 >>4253935 here's another good formula that combines more useful math concepts 0e^(ipi) = -1*0

>>	GL !Bgpe2HycPk Sat Jan 14 12:17:22 2012 No.4253945 >>4253935 But that's like saying 1+1=2 is the most beautiful equation of math. Sure Euler's identity is useful, but there's nothing deep in an equation that's trivial and easy to prove.

>>	Anonymous Sat Jan 14 12:20:22 2012 No.4253955 >>4253945 sorry to hear about your aspergers

>>	GL !Bgpe2HycPk Sat Jan 14 12:23:22 2012 No.4253960 File: 16 KB, 243x246, 1318777787098.png [View same] [iqdb] [saucenao] [google] >>4253955 Wat?

>>	Anonymous Sat Jan 14 12:27:22 2012 No.4253965 it means if you rotate (1,0) by pi you get (-1, 0)

Anonymous Sat Jan 14 12:30:22 2012 No.4253976

>>4253945
>there's nothing deep about Euler's identity
No.
Euler's formula in full, <span class="math">\text{e}^{\text{i}\phi} = \cos\phi + \text{i}\sin\phi[/spoiler] is a very deep result, establishes a connection between algebra/analysis and geometry. Don't say something isn't deep if you don't understand it.

>>	GL !Bgpe2HycPk Sat Jan 14 12:32:22 2012 No.4253982 >>4253976 Can you explain what makes one formula "deeper" than another?

>>	Anonymous Sat Jan 14 12:34:22 2012 No.4253988 >>4253976 *<span class="math">\mathrm{e}^{\mathrm{i}\phi} = \cos\phi + \mathrm{i}\sin\phi[/spoiler]

>>	Anonymous Sat Jan 14 12:37:22 2012 No.4253995 >>4253982 Where else have you seen e, pi, i, 0 and 1 come together so elegantly? Learn to appreciate the beauty along with the utility

Anonymous Sat Jan 14 12:38:22 2012 No.4253997

>>4253982
One way (not the only way) a result can be 'deep' is if it connects two or more seemingly unrelated ideas. A result like, say, <span class="math">\sin(2a) = 2\sina\cosa[/spoiler] wouldn't qualify as deep in this sense, because, although useful, it doesn't broaden our understanding of math.

>>	Anonymous Sat Jan 14 12:41:22 2012 No.4254003 >>4253997 Good Lord and Savior Jesus Christ, I can't into TeX *<span class="math">\sin{2a} = 2\sin a \cos a[/spoiler]

>>	Anonymous Sat Jan 14 12:41:22 2012 No.4254004 >>4253940 Look I can make it deeper: <span class="math">x\cdot e^{i\pi}=x\cdot-1[\math][/spoiler]

>>	GL !Bgpe2HycPk Sat Jan 14 12:42:22 2012 No.4254006 >>4253995 It's elegant, no doubt. But is it deep? >>4253997 Then it can't be deep anymore once you know the proof. Because then you know why the "seemingly unrelated" ideas are related.

>>	cyriak Sat Jan 14 12:43:22 2012 No.4254010 Can someone explain why <span class="math">e[/spoiler] is incorporated?

>>	Anonymous Sat Jan 14 12:45:22 2012 No.4254020 >>4254010 We define for all real x, exp(ix) as cos(x) + isin(x). When x = Pi, you have exp(i*Pi) = -1. Simple as that.

>>	Anonymous Sat Jan 14 12:46:22 2012 No.4254021 >>4254006 >Because then you know why the "seemingly unrelated" ideas are related. Exactly. After seeing the result and proof for Euler's identity, you know that algebra is connected deeply with geometry. Hence it's a deep result.

>>	GL !Bgpe2HycPk Sat Jan 14 12:48:22 2012 No.4254026 >>4254020 We don't need to define, we can prove: http://en.wikipedia.org/wiki/Euler%27s_formula#Proofs >>4254021 You still didn't explain what you mean by "deep".

>>	Anonymous Sat Jan 14 12:50:22 2012 No.4254037 >>4254020 Dead wrong. Euler's identity isn't a definition. Rather, for <span class="math">z\in\mathbb{C}, \ \mathrm{e}^z := \lim_{N \rightarrow \infty} \left(1 + \frac{z}{N}\right)^N[/spoiler]. From this, Euler's identity can be proved.

>>	Anonymous Sat Jan 14 12:51:22 2012 No.4254042 >>4254026 Yes I did, see >>4253997

>>	Anonymous Sat Jan 14 12:51:22 2012 No.4254044 Sure is autism in here.

>>	Anonymous Sat Jan 14 12:52:22 2012 No.4254045 >>4254006 Nah. Not really. The series expansions of e^(x), cos(x), and i*sin(x) aren't "obvious". They just happen to be the same.

>>	GL !Bgpe2HycPk Sat Jan 14 12:54:22 2012 No.4254054 >>4254042 Now we're going in circles. The post you referenced doesn't explain what it means that geometry and algebra are "deeply" related.

>>	Anonymous Sat Jan 14 12:57:22 2012 No.4254066 >>4254037 >>4254026 Well you CAN define exp as in >>4254020 and from that prove everything else. Please stop being obnoxious smartasses.

>>	GL !Bgpe2HycPk Sat Jan 14 12:57:22 2012 No.4254067 >>4254045 >They just happen to be the same. Sounds like derp. 2+2 and 1+3 also just "happen to be the same". Fact is you can prove it and the idea needed for the proof is simple enough to expect first year students to see it.

Anonymous Sat Jan 14 12:57:22 2012 No.4254068

>>4254054
I didn't say they were 'deeply' related, I said they were related. They're related because the sinusoidal functions are just the exponential function in disguise, and because angles are just phases, an algebraic idea. This is captured in Euler's identity.

>>	GL !Bgpe2HycPk Sat Jan 14 12:59:22 2012 No.4254072 >>4254068 Then I have mistaken you with >>4254021 who said "connected deeply". It's hard to identify the posts of Anonymous.

Anonymous Sat Jan 14 12:59:22 2012 No.4254073

>>4254066
You can do whatever the hell you want, but there are better approaches than others. Defining exp(z) as in >>4254020 is stupid (although I concede that you *can* do it) because the definition has no obvious relation to the real valued exponential.

>>	Anonymous Sat Jan 14 13:00:22 2012 No.4254075 >>4254072 Ah I see, fair enough.

>>	Anonymous Sat Jan 14 13:03:22 2012 No.4254087 >>4254067 >>4254054 >>4254026 >>4254006 >>4253982 >>4253960 >>4253945 >>4253908 Obvious troll is obvious.

>>	GL !Bgpe2HycPk Sat Jan 14 13:04:22 2012 No.4254095 >>4254087 Pardon? I wasn't trolling. It was a serious discussion.

>>	Anonymous Sat Jan 14 13:07:22 2012 No.4254112 It is cool and interesting. It takes three crazy ass math values and puts them all in the same place.

>>	Anonymous Sat Jan 14 13:13:22 2012 No.4254133 >>4253908 I find it sad when people see equations like this as nothing more than a useful identity. A true mathematician sees its aesthetic qualities and admires it.

>>	GL !Bgpe2HycPk Sat Jan 14 13:15:22 2012 No.4254139 >>4254133 I prefer to see the beauty in theorems rather than in simple formulas. And I keep in mind that calling something "beautiful" or "deep" is nothing more than my individual opinion.

>>	Anonymous Sat Jan 14 13:18:22 2012 No.4254146 >>4254139 You're missing out then.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:22:22 2012 No.4254162 Pi? I think you mean tau/2.

>>	Anonymous Sat Jan 14 13:23:22 2012 No.4254164 >>4254162 Ewww! That makes it look ugly. :p

>>	Anonymous Sat Jan 14 13:25:22 2012 No.4254169 File: 9 KB, 180x128, 41704_100001529886192_6699_n.jpg [View same] [iqdb] [saucenao] [google] >>4254162 Tau/2? You mean <span class="math">\int_{-\infty }^{+\infty }\frac{1}{1+t^{2}}dt[/spoiler].

>>	Anonymous Sat Jan 14 13:26:22 2012 No.4254170 ITT, hipster math majors claim to be unimpressed by Euler's identity because it's commonly known. >hurrr durrr I prefer more practical equations, not concise, mind boggling relationships between some of the most important numbers

>>	Anonymous Sat Jan 14 13:27:22 2012 No.4254174 >>4254170 Only autists care about how formulas look.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:27:22 2012 No.4254175 >>4254170 >math >equations I'm gonna have a lot of work to do educating the people of this board.

>>	Anonymous Sat Jan 14 13:28:22 2012 No.4254176 >>4254162 oh fuck off, we're already using Tau for a ton of other things (RC time constants, torque, sheer stress etc.)

>>	Anonymous Sat Jan 14 13:29:22 2012 No.4254180 >>4254175 nobody cares

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:31:22 2012 No.4254185 >>4254176 We are also using "one" for a lot of things, like "one cookie" or "one finger". The fact that our symbols are limited while the objects of our reality are unlimited doesn't change the practicability of Tau.

>>	Anonymous Sat Jan 14 13:35:22 2012 No.4254194 >>4254185 That's because the English language is retarded.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:36:22 2012 No.4254197 >>4254194 At least math is not retarded.

>>	Anonymous Sat Jan 14 13:36:22 2012 No.4254198 >>4253889 all equations are just tautologies saying e^(i*pi) = -1 is just a boring way of saying A=A

>>	Anonymous Sat Jan 14 13:37:22 2012 No.4254200 File: 8 KB, 190x266, 1314123072981.jpg [View same] [iqdb] [saucenao] [google] >>4254185 >insert: [shitty argument/discussion about variables and numbers that is recursive and pointless]

Anonymous Sat Jan 14 13:39:22 2012 No.4254208

>>4254197
I think it's time for you to stop posting.
http://archive.installgentoo.net/sci/?task=search2&ghost=&search_text=&search_username=m
athgenius&search_tripcode=&search_media_hash=&search_del=dontcare&search_int=dontcar
e&search_ord=new
Please take a look back at your previous post and name a single one that isn't utter shit.

>>	Anonymous Sat Jan 14 13:41:22 2012 No.4254215 >>4254197 Look, if we're going to use a Greek letter, we might as well consult the Greeks as to its meaning, hence Tau is actually 300.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:41:22 2012 No.4254216 >>4254208 You call it shit, because your inferior mind can't grasp the intellectual deepness and the meta-level implications of my posts. A simple mind like yours will never see the truth.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:43:22 2012 No.4254220 >>4254215 You are playing with words, but you don't change the underlying truth.

Anonymous Sat Jan 14 13:47:22 2012 No.4254239

>>4254220

I was going to argue, but then I looked in my textbook and it still says <span class="math">\pi[/spoiler]. I win.

You can claim victory when everyone starts using Tau instead of pi, which, should it ever actually occur, will only do so after a great deal of time from now.

In the meantime you may wallow in your dribble and advocate such irrelevant things as changing A to B and B to A etc.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:48:22 2012 No.4254246 >>4254239 I always win. For me it is enough to know the truth.

Anonymous Sat Jan 14 13:51:22 2012 No.4254254
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>>4254246

go back to your maths them faggot. Oh no you want human interaction but are too much of an autist to talk to actual people. You will never be happy because humans are social creatures and you are a dick.

>>	Anonymous Sat Jan 14 13:52:22 2012 No.4254256 >>4254254 reported for normalfag

>>	Anonymous Sat Jan 14 13:52:22 2012 No.4254259 >>4254216 Oh great, now we have a new Quentin in /sci/.

mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:55:22 2012 No.4254269 [DELETED]

>>4254254
You cannot troll a genius. I had more interaction with humans than you will ever have. My genius intelligence allows me to arbitrarily manipulate random people. This was some mental stages before the one I'm currenlty in. Now banalities like social life have become pointless.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:56:31 2012 No.4254275 >>4254259 I don't know the person you are calling Quentin. Was he a genius like me?

>>	Anonymous Sat Jan 14 13:58:39 2012 No.4254284 >>4254246 "The use of the Greek letter π to denote the ratio of a circle's circumference to its diameter was also popularized by Euler, although it did not originate with him" You seriously want to argue with Euler?

>>	Anonymous Sat Jan 14 13:59:47 2012 No.4254288 File: 50 KB, 440x360, 1298497598014.jpg [View same] [iqdb] [saucenao] [google] >>4254275 >>4254275 pic related

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 13:59:47 2012 No.4254289 >>4254284 >argument by authority You cannot fool a genius.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 14:00:55 2012 No.4254291 >>4254288 Your pic shows coolface. I don't see how it is related to this thread.

>>	Anonymous Sat Jan 14 14:06:34 2012 No.4254304 File: 179 KB, 589x564, At least you tried.jpg [View same] [iqdb] [saucenao] [google] >>4254291

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 14:10:06 2012 No.4254317 >>4254304 Now you are posting random pictures.

>>	Anonymous Sat Jan 14 14:32:39 2012 No.4254395 BRING BACK EK THIS NEW TRIPFAG IS SHIT

>>	EK !EKFQOBUFnQ Sat Jan 14 14:35:03 2012 No.4254401 >>4254395 sup

>>	Anonymous Sat Jan 14 14:37:19 2012 No.4254412 well the universe is made out of numbers, you just cant see them. also god is like super clever, he made physics.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 14:41:42 2012 No.4254421 >>4254395 Your envy is showing. That's a natural reaction to being confronted with a superhuman.

>>	Anonymous Sat Jan 14 14:45:14 2012 No.4254429 >>4254421 EK would kill you in 4 posts.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 14:49:38 2012 No.4254446 >>4254429 EK is not capable of keeping up a debate due to her emotional instability. She would give up before seeing the truth in my posts.

>>	Anonymous Sat Jan 14 14:51:55 2012 No.4254451 >>4254421 >>4254446 Lol wow you're fucking stupid. Goddamned 12-year-olds. Get off the internet. "Hurrr I'm a superhuman. Durrr I'm a genius. Hurr durr herpty derpty blarrrgh."

>>	Anonymous Sat Jan 14 14:52:02 2012 No.4254457 >>4253889 >god >numbers 0/10

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 14:52:02 2012 No.4254458 >>4254451 Your post is pointless. I am untrollable. Stop wasting your time and start learning from me.

>>	Anonymous Sat Jan 14 14:56:27 2012 No.4254469 The true formula: <span class="math">e^{i\tau}-1=0[/spoiler]

>>	Anonymous Sat Jan 14 14:56:27 2012 No.4254473 >>4254458 "I am untrollable." Nice cover. Fucking 'tard.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 14:57:42 2012 No.4254478 >>4254473 What is there to cover? My high intellect? My deep insights in the nature of things? I will forgive you the ad hominem attacks.

>>	Anonymous Sat Jan 14 14:58:42 2012 No.4254480 >>4254458 I'm sick of you fucking idiots acting like big shit. You have no idea how little you actually know. Fucking Good Will Hunting wannabe faggot. captcha: profoundly rincelop

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 14:59:51 2012 No.4254483 >>4254480 Your aggressions are natural. They won't annoy me.

>>	Anonymous Sat Jan 14 14:59:51 2012 No.4254484 >>4254469 gtfo

>>	Anonymous Sat Jan 14 15:00:58 2012 No.4254485 >>4254480 >mfw he posts on /sci/ and isn't a Good will hunting genius >mfw he posts on /sci/ and isn't a schizophrenic math Nash genius. why do you even come here

Anonymous Sat Jan 14 15:00:58 2012 No.4254487

>>4254478
>high intellect
>deep insights "in the nature" of things
Nice grammar dumbass. And they aren't ad hominem attacks. They are completely related to everything in this thread. Nobody's going to listen to some idiot who thinks he's better than everyone else. Anyone with half a brain is accomplishing things in the real world, not wasting their time on /sci/ with the low-tier math and science discussions.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 15:02:14 2012 No.4254496 >>4254487 Due to my brilliancy I alread solved all real world problems long time ago. Now I have plenty of time to help this board learn what I learned.

>>	Anonymous Sat Jan 14 15:06:46 2012 No.4254509 >>4254496 Do you feel sorry for the earths population because so few can live in the USA?

>>	Anonymous Sat Jan 14 15:07:46 2012 No.4254510 >>4254496 >solved all real world problems Almost had me going for a second there.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 15:09:02 2012 No.4254514 >>4254509 >>4254510 Is this what simple minds refer to as "problems"? Trivial issues of economy? The problem I am dealing with are located on meta-layers way beyond your imagination.

>>	Aquila !!gAQL6Rry0wi Sat Jan 14 15:22:38 2012 No.4254546 File: 47 KB, 300x300, meh.ro3568.jpg [View same] [iqdb] [saucenao] [google] >autism everywhere

Anonymous Sat Jan 14 15:40:39 2012 No.4254627
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>>4253935

Stop being such a pompous faggot.
Depending on what area of mathematics you're interested in, you'll rarely get in touch with complex numbers, let alone this identity, so there'd be no reason to get riled up about it.

>>4253976
It may be fascinating/important/astounding to most people (including me, by the way), but it's not "deep".
Grothendieck-Hirzebruch-Riemann-Roch is deep, or the Galois correspondence. Something you learn in your first semester definitely isn't.

pic unrelated

>>	Anonymous Sat Jan 14 15:42:55 2012 No.4254636 >>4254627 >pic unrelated ... but as interesting as your post

>>	Mathematician Racist Sat Jan 14 15:47:27 2012 No.4254656 >Have no empirical counter-argument. Therefore blame the thesis-founder for autism. Good luck on disputing trough a Phd exam.

>>	Anonymous Sat Jan 14 15:58:55 2012 No.4254715 Ok, I need to reinstall a filter, what does everyone use nowadays, 4chan x or 4chan plus?

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:01:12 2012 No.4254723 >>4254715 A filter? Do you want to exclusively read my comments without the noise of Anonymous between them?

>>	Anonymous Sat Jan 14 16:05:35 2012 No.4254742 >>4254723 With that remark, I genuinely believe you are a virgin and either underaged or severely socially retarded.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:06:42 2012 No.4254747 >>4254742 Keep em going. I don't mind you insulting me.

>>	Anonymous Sat Jan 14 16:06:50 2012 No.4254748 >>4254185 that's awfully retarded

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:09:06 2012 No.4254760 >>4254748 Is it? Who are you to call a genius retarded?

Anonymous Sat Jan 14 16:17:03 2012 No.4254796
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When the fuck did this board turn to shit? Where's Josef, by the way?
Fuck, as if those "atheist vs religion" threads weren't bad enough, everything else seems having to end in a flame war.
>o shit, I'm participating

>>4254636
Glad you like it, have another one

>>	Anonymous Sat Jan 14 16:19:19 2012 No.4254810 >>4254796 What do you expect from a shit thread?

>>	Anonymous Sat Jan 14 16:22:35 2012 No.4254825 >>4254796 >implying Josef isn't also a troll >implying he wouldn't immediately start shitposting ITT

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:23:51 2012 No.4254830 >>4254796 >Josef Do you mean this guy who insists that 0.999... = 1 although I proved him wrong? It's hard to tell whether he's trolling or just retarded.

Anonymous Sat Jan 14 16:27:15 2012 No.4254843
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>>4254810

My mistake, I admittedly didn't read OPs post, >>4253935 was the first thing that caught my attention.
Agreed, it's hilariously bad and bound to invoke a shitstorm.

>>	Anonymous Sat Jan 14 16:36:18 2012 No.4254876 >>4254830 0.999... = 1 is true

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:37:18 2012 No.4254877 >>4254876 No, it's not. We had three threads last week and every time I proved why it's wrong.

>>	Anonymous Sat Jan 14 16:37:26 2012 No.4254880 >>4254877 You admitted to trolling (and evidenced by your name). Try again.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:38:34 2012 No.4254882 >>4254880 Nonetheless my point still stands and you can't disprove me while I can disprove any fallacious pseudo-proof you post.

>>	Anonymous Sat Jan 14 16:39:34 2012 No.4254885 >>4254877 prove it again. I have seen proof that it is true but not that it isn't.

>>	Anonymous Sat Jan 14 16:39:43 2012 No.4254888 >>4254882 Hmm. I was madder the first time. Step up your game. I'm getting bored.

>>	Anonymous Sat Jan 14 16:41:50 2012 No.4254894 >>4254882 >2012 >can't evaluate 1-(1-.9999999...)^2 ISHYGDDT

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:41:50 2012 No.4254895 >>4254885 Did you read the last threads on this issuee? The proof was poasted there. http://archive.installgentoo.net/sci/thread/4213228#p4213309

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:42:58 2012 No.4254898 >>4254888 You are not supposed to be mad. You are supposed to see that I'm right. >>4254894 Indeed, this expression cannot be evaluated.

>>	Anonymous Sat Jan 14 16:43:07 2012 No.4254899 >>4254895 You posted to an old thred with no evidence last time. Your act is getting old. Troll us with something original.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:43:07 2012 No.4254901 >>4254899 The proof is in there. I'm not trolling. Read it and realize it's rigorous and correct.

>>	Anonymous Sat Jan 14 16:45:16 2012 No.4254905 >>4254898 > Indeed, this expression cannot be evaluated. o rly? A better troll would be able to do this one

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:46:30 2012 No.4254912 >>4254905 The expression is semantically invalid. You are not allowed to square a number with infinite decimals.

>>	Anonymous Sat Jan 14 16:47:38 2012 No.4254916 >>4254901 Hmmm. Really, I got madder with you last time. I want you to bring your A-game. C'mon, big guy, I know you can. Show us your true trolling powers.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:48:38 2012 No.4254920 >>4254916 I'm not here for trolling. I'm here for helping you learn.

>>	Anonymous Sat Jan 14 16:48:38 2012 No.4254921 >>4254912 > You are not allowed to square a number with infinite decimals. What's stopping us?

>>	Anonymous Sat Jan 14 16:49:47 2012 No.4254923 >>4254920 Man, every new turn is just a bit weaker. C'mon, make me rage. Do I have to say pretty please?

>>	Anonymous Sat Jan 14 16:49:47 2012 No.4254926 >>4254912 >implying <span class="math">\sqrt{2}^2≠2[/spoiler] Try a more unique troll

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:49:47 2012 No.4254928 >>4254921 It's not defined. If you did it, you'd violate the rules of mathematics.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:51:03 2012 No.4254934 >>4254923 Maybe you can rage from seeing me not making you rage. >>4254926 sqrt(2) is sqrt(2) with 2 being a number without infinite decimals.

>>	Anonymous Sat Jan 14 16:51:03 2012 No.4254937 File: 23 KB, 225x329, 1274278685853.jpg [View same] [iqdb] [saucenao] [google] >>4253889 >god LMFAO

>>	Anonymous Sat Jan 14 16:52:10 2012 No.4254939 >>4254934 C'mon. Everyone knows that approximations don't equal the actual values. I need you to troll with all your might! Troll for us! Trooooooooll!

Anonymous Sat Jan 14 16:53:19 2012 No.4254941

>>4254037
exactly, that's my problem with Euler's formula, when someone asks you to define complex powers as soon as you give that definition Euler's formula follows. That's why I don't find it that impressive. Such definition is not natural, yet the resulting Euler's formula is easily foreseeable with such a definition.

I know that we don't have much choice defining complex powers and now mountains of science rest on those definitions, that doesn't make it more intuitive or natural though. So I would agree with Kronecker here, this is work of man.

>>	Anonymous Sat Jan 14 16:54:19 2012 No.4254942 >>4254934 false 2 = 2.000000000....

Anonymous Sat Jan 14 16:54:19 2012 No.4254943
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>>4254901

Properties of a sequence of numbers (or other objects like functions) need not to hold when passing on to the limit, albeit you might need to know an explicit construction of the reals (hence, an understanding of what "two numbers are identical" means) in order to understand this. Using equivalence classes of cauchy sequences, you will in fact see that 0.999..=1

oh why the hell do I even bother, your trolling is way too obvious and I'm probably just wasting time.

mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 16:57:43 2012 No.4254950 [DELETED]

>>4254939
I'm not going to troll. Trolling has to be kept to /b/.

>>4254942
Poor troll attempt. Infinite decimals means at least one non-zero digit.

>>4254943
The proof present to sequences and both converge to different limits. One sequence converges to 0.999... while the other converges to 1.

Anonymous Sat Jan 14 16:59:59 2012 No.4254955

>>4254943

> your trolling is way too obvious and I'm probably just wasting time.
Yes, but don't you want him to show you, with all his might, that he is indeed the greatest troll, ever? Don't you wish to stand, in rapt attention, seething with rage and fury, so that you might once again feel alive? Would it wonderful to look upon this exaggerated form of a person, beckoning you with insults upon insults, and defeat his irrational (yes, it's a pun) numerology with logic?

>>	Anonymous Sat Jan 14 17:00:07 2012 No.4254957 >>4254950 >2012 >Infinite decimals means at least one non-zero digit. >mfw

>>	Anonymous Sat Jan 14 17:01:14 2012 No.4254962 >>4254950 mathgenius (not trolling) !!Ceavr+zDPUk, I am the dissappoint. You simply can't enrage me like before.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:03:30 2012 No.4254967 >>4254955 >>4254962 It's good to see you not being enraged. Now you can calmly admit that I was right. >>4254957 Did you never learn any math in school?

>>	Anonymous Sat Jan 14 17:03:30 2012 No.4254970 File: 86 KB, 768x1024, toygirls9.jpg [View same] [iqdb] [saucenao] [google] >>4254955 lol'd. I kinda do, but since my exams are ahead, I better spend my time studying instead of explaining the definition of convergence to some troll.

>>	Anonymous Sat Jan 14 17:04:30 2012 No.4254972 >>4253935 Parrotting somebody wise doesn't make you wise, it just makes you a parrot. If YOU can't appreciate for yourself why it's impressive, then you're no more astute than the OP or myself. The difference is that we admit that we don't get it.

>>	Anonymous Sat Jan 14 17:06:47 2012 No.4254980 >>4254967 > It's good to see you not being enraged. Now you can calmly admit that I was right. About...?

>>	Anonymous Sat Jan 14 17:07:54 2012 No.4254982 >>4254967 yes, and last time I checked, 2 = 2 2.0 = 2 ... ... ... 2.00000000... = 2

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:07:54 2012 No.4254983 >>4254970 No need to explain any definitions. I know them better than you. >>4254980 About the topic of the discussion.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:08:02 2012 No.4254987 >>4254982 Your point being what?

>>	Anonymous Sat Jan 14 17:08:02 2012 No.4254989 >>4254983 That e^(i*pi) = -1 ?

>>	Anonymous Sat Jan 14 17:09:11 2012 No.4254990 >>4254987 2 = 2.00000000... which is an infinite decimal

>>	Anonymous Sat Jan 14 17:09:11 2012 No.4254991 >>4254983 > No need to explain any definitions. Weren't you here to teach and prove yourself right? I don't understand!

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:09:11 2012 No.4254992 >>4254989 The e^(i*pi) =/= 0.999...

>>	Anonymous Sat Jan 14 17:10:19 2012 No.4254995 >>4254992 That is the discussion?

>>	Anonymous Sat Jan 14 17:10:19 2012 No.4254997 >>4254992 No one is claiming that e^(i*pi) = 0.999...

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:10:19 2012 No.4254999 >>4254990 No, it's not. They are all zero. >>4254991 Right, I'm here to teach you. But I don't need him to explain definitions to me which I know better.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:11:26 2012 No.4255003 >>4254997 Sorry, I meant e^(i*pi) =/= -0.999...

>>	Anonymous Sat Jan 14 17:12:26 2012 No.4255005 >>4254999 2 ≠ 0 try again

>>	Anonymous Sat Jan 14 17:12:26 2012 No.4255008 >>4254999 > Right, I'm here to teach you. Then please, teach us your trolling methods!

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:12:36 2012 No.4255010 >>4255005 2 is the digit before the decimal point. Your turn.

Anonymous Sat Jan 14 17:12:36 2012 No.4255012
File: 117 KB, 768x1024, 1311109233032.jpg [View same] [iqdb] [saucenao] [google]

>>4254983

Okay, then I pass the ball to you.
Enlighten me, what's the definition, and how do we derive from it that the limit of 0.9, 0.99, 0.999, ... is indeed not 1 like you claimed? (see >>4254950)

>>	Anonymous Sat Jan 14 17:12:36 2012 No.4255014 >>4255003 You can't divide equals signs. They aren't numbers.

>>	Anonymous Sat Jan 14 17:13:42 2012 No.4255016 >expand the maclaurin series of the natural exponential function. (e^(x)) >now let x = itheta >combine like terms. >find out that e^(itheta) is just a trig function in disguise (cos(theta) + sin(theta)) >plug in pi > get -1

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:14:42 2012 No.4255017 >>4255008 You are already proficient in trolling. >>4255012 >shifting the burden of proof I made a proof. Now it's your turn to show way it's wrong.

>>	Anonymous Sat Jan 14 17:15:51 2012 No.4255020 >>4255010 so what? There are an infinite number of zeros after the point. You can't just say that 0 is excluded from being repeated. There is no basis for doing so.

>>	Anonymous Sat Jan 14 17:15:51 2012 No.4255021 >>4255017 Irrational numbers are only approximations, and do not actually equal the decimal number thay are represented with.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:16:59 2012 No.4255025 >>4255020 There is a basis. It's called a definition. Your lack of math knowledge makes it really hard to explain stuff to you. >>4255014 Keep trolling out. This is a serious thread.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:17:06 2012 No.4255027 >>4255021 Yes. Your comment is unrelated.

>>	Anonymous Sat Jan 14 17:17:06 2012 No.4255032 >>4255025 yes, but once you have a definition, you have to prove that repeating decimals can't be squared. Which you have not done.

>>	Anonymous Sat Jan 14 17:18:15 2012 No.4255033 >>4255027 If you say so. > Irrational number is a decimal number that repeats forever without a pattern. Now, number with repeating patterns, on the other hand... > ...like 0.999 repeating...

>>	Anonymous Sat Jan 14 17:18:15 2012 No.4255038 >>4255025 > Keep trolling out. This is a serious thread. seriously, <span class="math">\frac{=}{=}[/spoiler] is not evaluatable

mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:20:30 2012 No.4255046 [DELETED]

>>4255032
It follows from the fact that we're dealing with infinity here.
Take your nonsensical expression from above:
>1-(1-.9999999...)^2
If we were allowed to do what you suggest, it would evaluate to
>1-(0.000...0001)^2
>1-0.000...000...0001 (with infinity^2 zeros)
>0.999...
Which is obviously not true since we subtracted less than the difference between 1 and 0.999...

>>	Anonymous Sat Jan 14 17:20:30 2012 No.4255047 >>4255038 dude, thats cool <span class="math">\frac{\frac{=}{=}}{\frac{=}{=}}[/spoiler] Also so much trololololololololing

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:22:38 2012 No.4255052 >>4255033 Your post is incoherent. >>4255038 >>4255047 Keep trolling to /b/. We are discussing real math here.

Anonymous Sat Jan 14 17:22:38 2012 No.4255053

>>4255017

Amazing mind hier reporting in this troll thread.

Knowing concepts doesn't make you a genius... genius make new concepts like Euler or Einstein. What concepts have you created sir? T
o me you are not much different than a soulless forum-fan that spend all his day reading what others post, and at the end of the day claim to be a expert on the subject.

Yes 1=/=0.999...

Yes Intellectuals =/= Genius

In fact i believe you enjoy being the attention whore in /sci/

>>	Anonymous Sat Jan 14 17:23:47 2012 No.4255058 >>4255053 ouch.jpg

>>	Anonymous Sat Jan 14 17:23:47 2012 No.4255059 >>4255046 >assuming 1≠.999999... to disprove 1=.99999... >mfw

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:24:54 2012 No.4255063 >>4255053 The concepts I developped are way too high to explain them on this board. It would take thousands of pages to explain them and I'm sure you wouldn't understand even 1% of it.

Anonymous Sat Jan 14 17:24:54 2012 No.4255064

>>4255046

> dealing with infinity
An irrational number is not infinity. It's is a number that cannot be represented by a ratio.
A rational number is not infinity. It's is a number that can be represented by a ratio.

Ratio, in this case, is better known as a fraction.

1/3 = 0.3 repeating.

0.3 repeating + 0.3 repeating + 0.3 repeating = ?
1/3 + 1/3 + 1/3 = ?

>>	Anonymous Sat Jan 14 17:25:03 2012 No.4255068 >>4255063 > them and You need a comma here, stud. > Assuming you can write a thousand pages.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:25:03 2012 No.4255070 >>4255059 This was not the proof of 0.999...=/= 1. It was the proof that you cannot square numbers with infinite decimals, requested by another poster. >>4255064 >1/3 = 0.3 repeating. This is wrong.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:26:10 2012 No.4255073 >>4255068 "And" doesn't require a comma.

>>	Anonymous Sat Jan 14 17:26:10 2012 No.4255074 >>4255064 > 0.3 repeating + 0.3 repeating + 0.3 repeating = ? > 1/3 + 1/3 + 1/3 = ? 0.3 rep. + 0.3 rep. + 0.3 rep. = 0.9 rep. 1/3 + 1/3 + 1/3 = 3/3 = 1 0.9 rep. = 1. Sounds legit.

>>	Anonymous Sat Jan 14 17:27:10 2012 No.4255077 >>4255070 > square numbers with infinite decimals You mean square approximations.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:27:19 2012 No.4255078 >>4255074 0.333... cannot be represented as a fraction.

>>	Anonymous Sat Jan 14 17:27:19 2012 No.4255079 >>4255073 In the case of the conjunction of two complete scentences, then it does.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:28:27 2012 No.4255082 >>4255077 In this case I don't mean approximations. >>4255079 The comma is optional.

>>	Anonymous Sat Jan 14 17:28:27 2012 No.4255084 >>4255070 you assumed 1≠.9999999... in your "proof".

>>	Anonymous Sat Jan 14 17:28:27 2012 No.4255085 >>4255078 Yes it can, since it is not an irrational number. See? You can make me rage afterall! Don't stop! It feels good!

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:29:27 2012 No.4255088 >>4255084 I can do this. It was independently proved earlier.

>>	Anonymous Sat Jan 14 17:30:34 2012 No.4255091 >>4255082 > In this case I don't mean approximations. Yes you do. Oh, yeah. Now you're into it.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:30:34 2012 No.4255093 >>4255085 It can't. The proof is similar to the one for 0.999...=/= 1. You should be able to figure it out by yourself.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:31:43 2012 No.4255096 >>4255091 I don't.

>>	Anonymous Sat Jan 14 17:31:43 2012 No.4255097 >>4255088 No! Don't rehash old trolling methods! Be fresh! Show us, so that I can dwell on it and feed my anger!

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:32:50 2012 No.4255100 >>4255097 There is no trolling in what I posted. It's pure mathematical reasoning.

>>	Anonymous Sat Jan 14 17:32:50 2012 No.4255101 >>4255088 Are you crying? Attention/whore >I bet your family doesn't respect you

>>	Anonymous Sat Jan 14 17:32:50 2012 No.4255103 >>4255096 Then it doesn't equal the number it originated from. So you either have to approximate, or you have an inequality. That's right. I'll feed your trolling, as you feed my anger.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:32:50 2012 No.4255104 >>4255101 You cannot troll me. I am untrollable and I will always forgive you.

>>	Anonymous Sat Jan 14 17:33:59 2012 No.4255105 I'm only here for the toygirls<span class="math">\frac{\frac{\frac{=}{=}}{\frac{=}{=}}}{\frac{\frac{=}{=}}{\frac{=}{=}}}[/spoiler]

>>	Anonymous Sat Jan 14 17:33:59 2012 No.4255107 >>4255100 > There is no trolling in what I posted. C'mon. Don't be trite. Just quietly admit it to yourself and keep it up! Give us more to rage upon!

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:33:59 2012 No.4255109 >>4255103 >the number it originated from The only number it can originate from is the number itself.

>>	Anonymous Sat Jan 14 17:34:06 2012 No.4255111 >>4253889 http://tauday.com/#sec:euler_s_identity

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:34:06 2012 No.4255113 >>4255107 Can't you read my name? It says "not trolling".

>>	Anonymous Sat Jan 14 17:34:06 2012 No.4255114 >>4255104 So you are one of those pedophiles ponies users? Your mother should have punched her cunt for bring this temporary world an awful person like you.

Anonymous Sat Jan 14 17:35:15 2012 No.4255118

>>4255084
Assume:
.9999999... ∈ ℝ
1 ∈ ℝ

Then:
1-.9999999... ∈ ℝ since ℝ is closed under addition.
(1-.9999999...)*(1-.9999999...) ∈ ℝ since ℝ is closed under multiplication.
1 - (1-.9999999...)*(1-.9999999...) ∈ ℝ since ℝ is closed under addition.

So it can be evaluated.

>>	Anonymous Sat Jan 14 17:35:15 2012 No.4255119 >>4255104 Getting bored again... Show me some formulas that I know are wrong. Don't do recursive stuff, because that's just hipster.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:35:15 2012 No.4255120 >>4255114 You can continue. It won't annoy me. Maybe it will annoy other users or the mod, but not me.

>>	Anonymous Sat Jan 14 17:37:32 2012 No.4255128 >>4255120 Okay, I'll help you out. Please troll us with this... (pic provided).

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:37:32 2012 No.4255130 >>4255118 >0.999... ∈ ℝ Are you sure about this? >>4255119 Why should I post wrong formulas? Okay, here is one for you: 1=0.999...

>>	Anonymous Sat Jan 14 17:38:32 2012 No.4255133 File: 47 KB, 960x540, 0.9is1.png [View same] [iqdb] [saucenao] [google] >>4255128 And the pic...

Anonymous Sat Jan 14 17:38:32 2012 No.4255134 [DELETED]

<span class="math">\frac{\frac{\frac{\frac{\frac{\frac{=}{=}}{\frac{=}{=}}}{\frac{\frac{=}{=}}{\frac{=}{=}}}}{\frac{\fr
ac{\frac{=}{=}}{\frac{=}{=}}}{\frac{\frac{=}{=}}{\frac{=}{=}}}}}{\frac{\frac{\frac{\frac{=}{=}}{\fra
c{=}{=}}}{\frac{\frac{=}{=}}{\frac{=}{=}}}}{\frac{\frac{\frac{=}{=}}{\frac{=}{=}}}{\frac{\frac{=}{=}
}{\frac{=}{=}}}}}}{\frac{\frac{\frac{\frac{\frac{=}{=}}{\frac{=}{=}}}{\frac{\frac{=}{=}}{\frac{=}{=}
}}}{\frac{\frac{\frac{=}{=}}{\frac{=}{=}}}{\frac{\frac{=}{=}}{\frac{=}{=}}}}}{\frac{\frac{\frac{\fra
c{=}{=}}{\frac{=}{=}}}{\frac{\frac{=}{=}}{\frac{=}{=}}}}{\frac{\frac{\frac{=}{=}}{\frac{=}{=}}}{\fra
c{\frac{=}{=}}{\frac{=}{=}}}}}}[/spoiler]

WE MUST GO DEEPER

>>	Anonymous Sat Jan 14 17:38:33 2012 No.4255136 File: 205 KB, 494x710, 6fda7e6e75ad7496c9c4ab8eda99622b.jpg [View same] [iqdb] [saucenao] [google] >>4255120 Mods doesn't want you to be here too.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:38:39 2012 No.4255137 >>4255133 We had this argument several times. Wolfram uses approximations.

>>	mathgenius (not trolling) !!Ceavr+zDPUk Sat Jan 14 17:39:39 2012 No.4255142 >>4255136 I am posting math on the board for science and math.

>>	Anonymous Sat Jan 14 17:40:47 2012 No.4255146 File: 106 KB, 953x613, .99999 = 1.jpg [View same] [iqdb] [saucenao] [google] sage in all fields

Anonymous Sat Jan 14 17:41:55 2012 No.4255150 [DELETED]

File: 2 KB, 390x288, 3523a.gif [View same] [iqdb] [saucenao] [google]

sup /sci/

I have an exam for my Abstract Algebra class in two days and i haven't attended for 3/4th of the semester. How boned am I? considering just not going now and retaking the class next year.
Picture related.

>>	Anonymous Sat Jan 14 17:41:55 2012 No.4255152 >>4255142 Well, you had me for a little while, but unfortunately your routine is old. You quickly lost my attention. Please find something fresh to use. (That one where a rope the length of pi being infinitely long was pretty good.)

>>	Anonymous Sat Jan 14 17:42:03 2012 No.4255155 >>4255130 0.999... ∈ ℝ yes it is What field do you think it is a part of?

>>	Anonymous Sat Jan 14 17:47:34 2012 No.4255173 well mods finally banned him, what a troll

Anonymous Sat Jan 14 17:50:59 2012 No.4255182
File: 20 KB, 289x400, Robert_Solovay..jpg [View same] [iqdb] [saucenao] [google]

>>4255150

How advanced is that course? If you're mostly dealing with stuff like subgroup lattices as indicated in the picture (i.e. rather basic group theory), you should be fine, just work hard in the time that's left.
If the course is way beyond that (homological algebra....), you're fucked.

>>	Anonymous Sat Jan 14 17:58:54 2012 No.4255209 >>4254073 >implying that (ix)^n/n! has nothing in common with (ax)^n/n! for a in the reals Confirmed for retard mode

Anonymous Sat Jan 14 18:01:19 2012 No.4255225

I can't be bothered to read this whole thread but
"deep" in mathematics refers to something that connects multiple very different branches of math together.
e to the i theta is "deep".
It says something about reality as well, seeing as e, pi, i, sin, and cos are all naturally occurring. To link them all by equality, especially in such a simple statement, is an impressive statement about the nature of things, and the nature of Mathematics.

>>	Anonymous Sat Jan 14 18:08:06 2012 No.4255253 If 0.999... = 1 then 0.999... is a NATURAL NUMBER

>>	Anonymous Sat Jan 14 18:09:06 2012 No.4255257 >>4255253 No. It just means they are considered equivalent.

Anonymous Sat Jan 14 18:12:39 2012 No.4255277

Even though this degraded into a troll thread rather quickly, I'm going to make a legitimate post.

I'm a second year in EE taking a digital signal processing class. Within the first week, we've used Euler's identity extensively. It has many practical applications when dealing with sums or products of sinusoids with different frequencies and phases.

It's not just something that exists in the vacuum of pure mathematical knowledge -- there are many practical applications of it (especially in EE).

>>	Anonymous Sat Jan 14 18:25:07 2012 No.4255330 >>4255253 God, you're fucking retarded. They're the same number, faggot.

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/sci/ - Science & Math