/sci/ - Science & Math

Every pattern conceivable exists within the digits of pi, and all other transcendental numbers.
It's not that no pattern exists, it's that all patterns exist, and therefore it's the same result as no pattern.

>>6367332
Does that mean that pi contains all the knowledge of the universe?

>>6367341
Yes, assuming you know how to extract it.
PROTIP: Trying to do so is not possible, and will drive you mad.

>>6367341
You could say it contains all possible statements, true and false alike.

>"pi = circumference divided by diameter,"

so I suppose you could just write it down and work it out yourself.

>>6367350
>work out a non-terminating, non-repeating decimal

Shouldn't we square the circle first?

>>6367332
Hold on. Is it proven for irrational, non-transcendental numbers, that certain patterns will never exist in the decimal representation's string of numbers? Like pi could contain a trillion digits of root 2 or e at some point, but root 2 will never contain pi, or any other sequence?

It's not even a widespread thought in mathematical community. Google normal numbers.

>>6367354
>infinite sequence
>doesn't contain X or Y
Yea, nah.

>>6367356
Root 2 has patterns though, as continued fraction, unlike pi. I mean, while root 2 is random, it's not as random enough to contain every sequence possible, is it?

>>6367359
>non-transcendental numbers
>transcendental numbers

One of these is unlike the other.
We're not talking about non-transcendental numbers, we're talking about pi.

>>6367328
LMWTFY
http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational

>>6367361
>implying the subject of matter is strictly regulated to the OP
>4chan
I'm bringing up a point about non-transcendental numbers, in >>6367354.

>>6367364
Which has fuck all to do with the nature of transcendental numbers.

>Do oranges X
>Well apples Y

>>6367332
Whoa wait, so you say you can mathematically prove with certainty that something as seemingly simple as all the even numbers in order from 2 to 200 exist in pi?

>>6367356
I don't understand are you saying that if something is infinite it has to have every possible sequence?
Like if you take the infinite set of all even numbers, you will eventually find all the odd numbers in it?

>>6367368
The infinite set of all even numbers is not transcendental.

>>6367365
Holy fuck if you can't answer the question that's fine. Don't need to get all buttblasted. God forbid I go off topic in your thread.

>>6367373
Ok, let's answer your little question.
No, root 2 does not contain every possible pattern, BECAUSE IT IS NOT TRANSCENDENTAL.
There, now can we move on to something remotely related to the OP?

>>6367376
>answers the question after the fourth reply

Good now where's the proof or what's the source?

>>6367380
>For example, the square root of 2 is irrational and not transcendental (because it is a solution of the polynomial equation x2 − 2 = 0). The same is true for the square root of other non-perfect squares.

>http://en.wikipedia.org/wiki/Transcendental_number

>>6367382

>>6367383
No, the root of 2 is still non-transcendental, regardless of my motive here.
Likewise, pi is still transcendental, regardless of my motive here.

>>6367385
Okay you replied so you must be actually retarded. Prove that root 2 does not contain every sequence possible, unlike pi.

There. If you can't into reading comprehension this time, I wonder how long it'll take you to walk into a fire following directions to exit the building.

>>6367388
root 2 is non-transcendental.
QED.

>>6367390
You're smart in this field right? Clearly smarter than me if you spout out an answer that confidently. Where is the proof to non-transcendental, irrational numbers, i.e., root 2, i.e., a random sequence of digits -> does not contain every sequence possible, i.e., pi, i.e., a random sequence of digits.

I literally have nothing better to do even if I just sit here replying to a ruseman. That's why I'm on /sci/.

>>6367397
*unlike pi

>>6367390
Where is the mathematical proof that transcendental numbers contain infinite finite patterns?

>>6367404
>infinite finite patterns
So, we're just making up terms now?

>>6367404
There is none. Not all transcendental number contains infinite finite patterns. For example the Liouville constant is transcendental and only consists of 1s and 0s. I think more will come out of proving >>6367388 instead though.

>>6367406
Well saying that is essentially saying "every existing pattern," which was already stated in this thread.

>>6367412
>essentially
By what metric is "essentially" the same as "exactly"?

>>6367413
It's fundamentally the same...

>>6367406
>>6367413

Well someone said that not every infinite pattern was in transcendental numbers, so I assume when you said all patterns exist in transcendental number you mean all finite patterns and all in this case must mean an infinite amount since "all patterns" is uncountably infinite, so what is the problem with the arrangement of the words to convey a logical message and why are you stalling and distracting instead of providing evidence for your claims?

>>6367414
And 0.999... is fundamentally 1.
Your point is?

>>6367332
That's only a conjecture. This property is related to "normal numbers". It's actually even stronger than normal numbers. And Pi isn't proven to be normal.

It is proven to be irrational and transcendental , yes, but for now we don't even know if there isn't a point after which Pi's decimals in base 10 stop having the "0" digit in them. For all we know, it is possible that there is only a finite number of 0's in Pi's decimal expansion. We just know that it won't end up with an infinitely repeated sequence.

>>6367415
>someone said that not every infinite pattern was in trascendental numbers
Where?
Please point out the post that makes this claim.

>>6367416
"Essentially" is fundamentally the same as "exactly".

>>6367418
Cool.
Let's see a proof.

>>6367420
Oh, ok.
So you won't have any problem if I replace all integers with N-0.000...1, right?
I mean, they're essentially the same.

>>6367332
>Every pattern conceivable exists within the digits of pi
There is zero evidence supporting that. You're just making that assumption based on the fact that it's an irrational number. Just because it's an irrational number doesn't make that true.

>>6367424
>doesn't repeat
>doesn't end
So, why should we think that it does not contain all patterns again?

>>6367421
Of what? Of the fact that we have no proof in either direction? Yeah of course I can prove that, just give me a minute and I'll deliver. Retard.

>>6367422
But they're not exactly the same.

>>6367332
>Every pattern conceivable ALMOST certainly exists within the digits of pi, as far as we know
FTFY

>>6367426
Because 3.1401001000100001000001000000100000001 doesn't repeat , doesn't end, and doesn't contain the pattern "2". Dumbass.

>>6367426
Think about it retard. There are an infinite number of combinations of digits. You could easily skip an infinite amount of them of them and still continue on infinitely.

>>6367431
That's no pi.

>>6367432
>infinite number of combinations of digits
How is that not all patterns, again?

>>6367433
>That's no pi.
It doesn't matter. It's evidence supporting the idea that an irrational number can exist without covering every single possible combination of digits. So unless you can provide evidence that pi specifically does, you shouldn't make claims about it.

>>6367426
>doesn't repeat
>doesn't end

That also describes positive real numbers, but again it doesn't mean the infinite set of positive real numbers contains negative complex numbers.

>>6367428
But you just said "essentially" is fundamentally the same as "exactly."

>>6367434
You've yet to prove that the number you gave is irrational...

>>6367429
The decimals of Pi are not a stochastic process. You cannot pull "almost surely" here and hope it'll work. The only way I can think of to formalize your statement into one that makes sense would be that the measure of the set of patterns that don't occur in Pi is 0, but that implies having a measure on the set of patterns, and even if you had that it would still be an unproven statement.

>>6367433
>All patterns
>you skipped an infinite amount of patterns

>>6367436
Which has fuck all to do with pi.
Pi will also never be greater than 4.

>>6367438
... if you really need us to prove that for you, you don't deserve to partake in this discussion. Sorry. It's like high-school level.

>>6367438
wasn't me who gave the number, but by definition it was irrational since it continues forever and doesn't repeat.

>>6367441
Then pi does not contain the pattern greater than 4.

>>6367440
>skipped an infinite amount of patterns
>in an infinite sequence
So, none?

>>6367444
indeterminate
unless you can show me your proof that inf - inf is none

>>6367442
Does it?
Cool, prove it.

>>6367443
>contain the pattern greater than 4
This means what in english?

>>6367437
Oh yes but "fundamentally" is only substantially the same as "essentially."

>>6367445
this is math nigger, proof or get wrekt.

>>6367444
Usually I'd think you're a troll, but I don't know, something tells me you might actually be serious, and it scares me. Are you really this dumb? Do you really need a proper explanation on why an infinite sequence doesn't necessarily contain all patterns? Even when an example has already been posted in the thread?

Nah you must be trolling.

>>6367448

for all x greater than 0 but less than infinity, y = x + 4

>>6367448
>Cool, prove it.
Are you literally retarded? Look at the number again dumbass. It starts off as 3.14 and then adds a single 0 and then a 1, then two 0s and then a 1, and so on and so forth with an ever increasing number of zeros.

That will cover an infinite number of combinations of digits if you continue, but it certainly won't cover every single combination of digits that can exist.

>>6367447
>1-1=0
>2-2=0
>10000000000-10000000000 = 0
>inf-inf = 0

Any number minus itself is 0, regardless of it's size.

>>6367451
If it's so trivial you shouldn't have any problem presenting such a proof.
If it's clear to retards it should be even more clear to you.

>>6367455
So what you're saying is, it repeats?

>>6367457
true, but you're forgetting that infinity isn't a number.

>/sci/ in charge of knowing math

>>6367450
You have to understand how math works in the real world. When a property is trivial enough so that any mathematician that may be interested in the rest of your results visualizes a sketch of the proof within 10 seconds of reading the property, and could write down the proof in a few minutes if he wanted afterward, then you don't write that proof, and you focus on more interesting ones.

I understand that it's not how it works for your high-school teacher, but he's just teaching you, he's not discussing math with you. Get the difference?

>>6367460
>isn't a number
[citation needed]

>>6367462
No. It never repeats itself. You're obviously trolling and I'm not having this conversation any more. This is the last time I visit /sci/. You guys are fucking stupid.

>>6367462
And what you're saying is, your hobby is pretending that you're a retard on the Internet.

>>6367463
So you don't actually have a proof?
Nice to know.

>>6367464
Don't let the door hit you on the ass on your way out.

>>6367467
>muh ad hom
Can you or can you not produce the simple proof that even a retard like me couldn't refute?

I think the enormous amount of troll activity here is run by two guys...

And I don't just mean this thread. I mean all of /sci/.

>hurr durr what are infinite sets?
>hurr durr there can't possibly be more than one infinite set

This whole thread

>>6367469
Shhhh.
We're having fun.

>>6367471
Can you prove that?

>>6367468
>So you don't actually have a proof?

No, what I'm saying is that if a sketch a the proof doesn't pop in your head when thinking about it for 10 seconds, and if you can't formally write down a complete proof in a few minutes, then I don't want to discuss this with you because you don't have the math knowledge or the intelligence to understand the discussion anyway.

>>6367474
All I'm hearing is a big fat "no".
Again, if it's SO trivial, you could have typed it 20 times over in the time you spent typing all that ad hom.

>>6367470
Alright. So you're saying that it repeats. Of course here, we mean infinitely, otherwise it doesn't make it rational. So tell me: what is the sequence that infinitely repeats in the end of that number, the way 142857 repeats in the expansion of 1/7. Tell me what that sequence is, and I'll tell you why it doesn't.

>>6367479
No, that's not how proofs work.
You made a claim, you back it up.

>>6367481
>only contains 0 and 1
So, it's everything in binary?

>hurr durr what is Liouville's constant
>it certainly isn't an irrational number which only contains 0 and 1

>>6367477
I could have, but why would I spend time doing that for you when you can't provide anything valuable to me? If you call me "Mr Anon" and politely ask me to educate you, I will give you a formal proof out of altruism. If you keep thinking of yourself as an equal, you don't deserve my generosity.

>>6367483
nope. It's not even every binary number. Why don't you fucking google it and learn how infinite sets work you retard.

>>6367484
>don't want to spend time on trivial proofs
>spend a greater amount of time telling me how much better you are than me

Maybe I'm just not smart enough to comprehend it, but your logic seems a little off here...

>>6367485
Why don't you back up your claims once in a while?

>>6367475
/sci/'s Theorem shows that for any number people on the board /sci/, there is exist such a number of people who aren't trolls that x-y=2, where x equals the number of people currently in the board and y equals the current number of people who aren't trolling.

>>6367487
Considering that you're a troll, if I use "1+1=2" at some point in my proof you'll ask me to prove that too, so I think I'm spending less time trolling back than actually writing down a proof that goes back to Peano's axioms.

>>6367488
It's not very hard to google.
http://mathworld.wolfram.com/LiouvillesConstant.html

I'm not holding your hand anymore. You're on your own.

>>6367490
And your method for determining who is and isn't trolling is... what?
Also, you're assuming discreet trolling.
have you considered fuzzy trolling?

>>6367493
>wahhh why should I have to provide evidence of my claims
>my iq is over 9000

>>6367498
>Asks for evidence
>Cannot click links and read
Hmm...

>>6367496
What is fuzzy trolling?

>>6367499
What is fuzzy logic?

>>6367499
To trolling what http://en.wikipedia.org/wiki/Fuzzy_logic is to logic. Based on the PhD thesis of Anon, 2008.

>>6367501
>ask for evidence
>takes 50 fucking posts to get any evidence, and it comes with the stench of indignation

>>6367501
I think it's just a heavy case of pic related. I kind of feel bad for him.

>>6367502
What >>6367503 said apparently.

>>6367505
And here we sit, 101 replies later.

>>6367504
>and it comes with the stench of indignation
What do you expect when you come in here making false claims and pretending like you know your shit and refusing to google anything we tell you?

You're a retard. Of course we're going to treat you as such.

>>6367504
His first fucking post mentioned Louville's constant. Does your dad hold your pee-pee when you go to the bathroom? Learn to fucking google.

To half of these posts.

>>6367508
>wahhhh why should I carry the burden of proof
>my iq is over 9000, just trust me

>>6367507
Well what actually happens is that saying "You are fucking retarded" to trolls over and over again is the most interesting thing to do on /sci/ when there isn't an interesting thread in sight, which is the case most of the times.

I miss Putnam threads. Trolls mostly left these alone because they couldn't understand the problems anyway.

>>6367509
>false claims
Such as?

>>6367511
>implying people who know how to use google have higher intelligence than people like you
Oh wait, actually that's probably true.

>>6367513
So, you couldn't possibly do anything that's not responding to obvious bait on /sci/?

>>6367514
Okay let me rephrase. You made unverified claims and presented them as fact.

>>6367516
>muh iq, 9000
You know no matter how many times you call me a retard, you're still not providing evidence of any of your claims, right?
It's almost as if... as if you can't actually prove them...

>>6367511
>Hurr durr
>Durr hurr hurr hurr
>Hurr durr durr hurr durr durr hurr
I guess if you keep trolling like that for long enough, you might get an infinite sequence that contains all patterns of hurrs and durrs. Go on anon, think of yourself as a monkey with a typewriter, and write us some Shakespeare. Oh and you might want to just press your keyboard randomly, it'll increase the chance that you ever write something valuable, compared to what will happen if you keep using the worthless piece of garbage that you call your brain.

>>6367518
What claims?
Where?
Please point them out.

>>6367519
I already provided you a link to a page that talks all about liouville's constant. If you cant click on it and read a little, then I don't care if you believe me or not.

>>6367521
>Every pattern conceivable exists within the digits of pi, and all other transcendental numbers.

>>6367522
Mmmmm.
I like you.
You just keep going and going.

>>6367517
Well, I have two options:
- I answer troll bait and keep posting here while waiting for something interesting to be posted, and then I can actually participate in an interesting discussion for a minute before the thread dies because no one cares anyway,
- Or I can just leave /sci/ for a long time, because why would I just f5 it every 5 minute just to see that there still isn't anything valuable?

I alternate between the two solutions.

>>6367517
Why does anyone like responding to obvious bait? It's like they get a sense of justice by defeating the "BIG OLD MONSTER."

>>6367524
>/sci/ is one person

>>6367525
NO WHY DID YOU STOP. DON'T SHOW YOUR TRUE COLORS. KEEP AT IT!

>>6367527
>>6367526
It's like you folks think you're just dinner.

>>6367519
Hey, I've got a rad idea. Formulate formally the claim you think that that anon has provided and not proven (or not given enough to get the proof of using a google search). Then we won't have to show you why you're wrong because you'll have trolled your way out of the discussion anyway.

>>6367534
Good god man, I don't want to drink the world dry in a single night.
Let's pace ourselves.

>>6367524
That's the very claim everyone has been saying is unproven since like the 10-th post here, dumbass. It wasn't posted by anybody still posting at the moment.

>>6367530
Well regardless of whether you're the person who made that statement, that is what we were arguing. So what you're telling me is that you were arguing a side without even knowing what you were arguing.

>>6367535
I've got a better idea, imagine as intensely as you can you cutting your wrists and bleeding into glowing silver goblets while standing in a midwestern cornfield.

>>6367541
I'm telling you it doesn't matter what side I'm arguing.
That's just a means to an end.

>>6367543
Done. Now what about those claims?

>>6367545
By the time we reach the statement that it doesn't matter which side someone argues anyway, it's time to call /thread.

...but NOT ON /SCI/! Let's the trolling continue.

>>6367536
Oh uh... I wasn't actually participating. I was just watching.

>>6367546
What about them?
I got what I was after.

>>6367551
you're assuming I was here to argue at all.
PROTIP: I'm not.

>>6367550
I'm glad to hear that. Does it mean you're leaving? Would you mind taking your friends with you and closing the door on your way out?

>>6367553
Nope, not until you're dry, and it looks like you ain't.

>>6367552
I'm definitely NOT assuming that. I'm assuming if anybody still posting in this thread is here to argue about anything at all, he's even more retarded than what people like >>6367440 pretend to be.

>>6367549
You're missing out.

>>6367558
You just don't get it.

>>6367555
There isn't really a post-limit anymore, is there? Man we're in for a long time. I should buy a 4chan pass, these captchas are starting to annoy me.

>>6367561
YOU are in it for a long time.

>>6367560
If you state something like that, you'd better prove it. Where is your evidence?

>>6367560
What if I told you that his posts were the bait?

>>6367565
>>6367564
What if I told you it doesn't matter what we say?

>>6367562
It's ok, I got junk food and a huge folder of bad movies.

>>6367565
The thing about this guy is, he doesn't realize that the only difference between us is that I know there is no difference between us.

>>6367567
Oh good, that means I've got some junk food.
Carry on.

>>6367569
(Oh and also that I can actually do math, but it's not relevant anymore)

>>6367567
If it doesn't have The Room in HD, it's not a big enough folder yet. (also, see "Jesus Christ Vampire Hunter)

>>6367572
It never was.

>>6367571
Yeah I didn't mean movies that bad that I can't actually watch them. I meant movies around the local maximum of http://imgs.xkcd.com/comics/so_bad_its_worse.png 's curve.

>>6367574
Fair enough.

>>6367511
You are the one making all the assertions who has the burden of proof who never bothers to address inconsistencies with their assertions to instead demand an infinite loop of evidence for the lack of evidence of consistency.

>>6367332
This is retarded.

No pattern involving 2s exists in an irrational made up of only 0s and 1s.

You should be ashamed.

>>6367328
>Can you prove that there isn't <whatever>
Can you prove a negative??
Can you Lrn2logic?

>>6367797
>Can you prove a negative??
Yes, it is pretty common.

For example it is easy to prove there isn't a largest number.

>>6367801
Okay I'd like to see you do that. Go ahead and try right now.

you can just count from 1 to infinity and you will find the same thing.

>>6367824
that's not proof. That's like saying "you can just calculate pi from digit one to infinity and find the same thing. Just take my word for it. it's infinite guys"

>>6367824
so somewhere in pi, there's the count from 1 to infinity and, somewhere in the count from 1 to infinity, there's pi
and somewhere inside the count from 1 to infinity inside pi there's another pi
and somewhere inside pi inside the count from 1 to infinity there's another count from 1 to infinity

fuck infinity

>>6367808
the successor function is an axiom of whole numbers

the proof is trivial given that you faggot

Perhaps you think the proof of Fermat's Last theorem is wrong? It does after all prove a negative.

>>6367797
In Mathematics negatives are proven all the time.

>>6367835
>so somewhere in pi, there's the count from 1 to infinity and, somewhere in the count from 1 to infinity, there's pi
No. If that were the case it'd be a repeating pattern which we know it isn't.

Goddamnit why is this thread still a thing.

>>6367846
Because the undereducated think they are knowledgeable.

>>6367801
>Can you prove a negative??
>Yes, it is pretty common.
As a logical error, it is unfortunately very common. For example:
>it is easy to prove there isn't a largest number.
no.jpg
Lrn2negative

>>6367846
that's not how infinity works buddy
keep believing though

>>6367850
So you believe it's still unknown if N is finite or infinite?

>>6367850
The distinction between negative and positive truths is the logical error you are making.

>>6367850
>Not sure if troll or retard. Probably the latter.

>>6367865
>negative and positive truths
Now you're writing fiction.

>>6367867
Exactly.

Do you believe >>6367862 ?

>>6367866
>Probably
Lrn2probability, then tell us about it, retard.

>>6367328
http://www.youtube.com/watch?v=uKuG4qqtP1Q

>>6367871
>first i was srs, then i realised i was wrong, so then i was like, yeah i was trolling

>>6367842
>the proof of Fermat's Last theorem ... does after all prove a negative.
no.jpg
Lrn2Logic

>>6367885
Why is /sci/ suddenly so full of underaged trolls?

>>6367902
>Why is /sci/ suddenly so full of the logic-impaired?
... because Logic is undervalued in modern society, to its detriment.

(in base 64) we have a formula for every digit of pi

also if you take a transcendental and change every (say) 1 to 0, you still could a transcendental. so transcendental does not imply containing everything

>>6367962
>Logic is undervalued in modern society
Of that, there can be no doubt, Mister Holmes.

>>6367962
>still being a tryhard troll

>>6367875
>i was trolling
>>6367902
>trolls
>>6367997
>troll
A discernable pattern emerges.

Its easier to assume that, just like we assumed that we cannot travel faster than light because at present our perception of physics dosent allow us to even push to that limit.

>>6368008
>noticing references to trolling on 4chan

>>6368044
>more trolling
they get younger every summer

>>6368051
>summer
ausfag?

Somewhere inside pi you are having sex with your high school crush :3

>>6368066
Somewhere inside pi you are doing anal with your dead mom while Barbara Bush sits on your face.

>>6367843
>negatives are proven all the time
Disproof of an assertion is not the same as proof of its negative, Aristotle.

>>6368117
>denying the excluded middle
oh god, faggots everywhere

>>6368121
>excluded middle
Lrn2spectrum, Augustine

God damn, this thread is just embarrassing.

What is it about the denizens of /sci/ that makes them incapable of identifying trolls?

>>6367332
>>6367341
Pi contains all information in the universe in the same way a random string of digits contains all of the information in the universe in the same way that a monkey on a typewriter will type out shakespear.

Pi isn't completely random, so it won't contain every possible combination of numbers. For one thing, <span class="math">\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{{\pi}^{2}}{6}[/spoiler]
This seems pretty ordered, and it doesn't contain part of the sum of 1/3, so you would be missing some stuff there.
A number that would contain everything, is 0.1234567891011121314151617181920...

>ITT

>>6367328
>Niven, Ivan. A simple proof that π is irrational. Bulletin of the American Mathematical Society 53 (1947), no. 6, 509--509. http://projecteuclid.org/euclid.bams/1183510788..

>>6369028
Most people agree that it's irrational. The matter of the thread has become wether or not pi contains all possible combinations of digits.

>>6367332
transcendental numbers =/= Normal Numbers

Get the fuck out

>>6367354
Only applies to finite sequences for normal numbers.
We don't know whether π is algebraically independent from √2.

>>6367359
>Root 2 has patterns though, as continued fraction, unlike pi.

Never post here again.
https://en.wikipedia.org/wiki/Continued_fraction#Generalized_continued_fraction

>>6369072
>Never post here again.
I think I'll still hang around here, but thanks for the correction, friend.

>>6369072
A number being normal doesn't imply it has all possible finite patterns. (if you meant that)
The OP's question is actually pretty interesting, there's a lot of shitposting though.

>>6369309
>A number being normal doesn't imply it has all possible finite patterns. (if you meant that)

"Almost surely" does

https://en.wikipedia.org/wiki/Infinite_monkey_theorem#Correspondence_between_strings_and_numbers

>>6368599
>this thread is just embarrassing
Certainly your own contribution to it must be an embarrassment, Anon. Go seek forgiveness from your mother.