/sci/ - Science & Math

[Anonymous No.6658589]

Alright, /sci/.
I want to know which one of you can think of the biggest number. Whoever has the biggest will receive a 30% off coupon for a smug sense of superiority. The rules are as follows:
1: Your number must be finite and real.
2: Your number must be computable and well defined. Even if you're using notation or part of a definition that was already posted in this thread, you must define it again in your post.
3: Your number must be defined in one post only (no two-parters).
4: The definition of your number must not involve any posts to come after yours.

I'll start with 0.

[Anonymous No.6658593]

I'll try 6

[Anonymous No.6658594]

Googolplex:
10^10^100

[Anonymous No.6658595]

>>6658589
I'll try graham's number.

[Anonymous No.6658598]

>>6658594
If this is deemed illegitimate then:

18

[Anonymous No.6658600]

>>6658589
exp(exp(exp(exp(exp(googolplex)))))

[Anonymous No.6658601]

>>6658589
Question about rule 2:

Graham's number is rather hard to compute and defined by use but not exact digits

[Anonymous No.6658603]

>>6658600
>no base

what exactly are you exponentiating?

[Anonymous No.6658604]

>>6658601
Is it too hard for you? If so, don't use Graham's number. If not, go ahead.

[Anonymous No.6658606]

>>6658601
graham's number is theoretically computable and well defined. and i already called it.

[Anonymous No.6658611]

>>6658589
let x = googleplex = 10^(10^100)

let y = x^(x^(x^(x^(x^(x^(x^(x^(x^(x^(x^(x^x))))))))))))

my number: y^(y^(y^(y^y^(y^(y^(y^y^(y^(y^(y^y^(y^(y^(y^))))))))))))

[Anonymous No.6658612]

>>6658611
your number << graham's number

[Anonymous No.6658615]

>>6658612
ok then.

let x = graham's number

let y = x^(x^(x^(x^(x^(x^(x^(x^(x^(x^(x^(x^x))))))))))))

my number: y^(y^(y^(y^y^(y^(y^(y^y^(y^(y^(y^y^(y^(y^(y^))))))))))))


:)

[Anonymous No.6658616]

>>6658606
But anybody can still call (graham's number + 1) or (graham's number to the power of graham's number). It's stupid game.

[Anonymous No.6658620]

"largest number" is a pointless exercise

"largest number used for some other practical purpose" is a much better metric

[Anonymous No.6658621]

>>6658603
base for unbased is e

[Anonymous No.6658623]

>>6658615

let your number = z

my number = z^graham's number

checkmate and check these dubs

[Anonymous No.6658627]

>>6658616
actually, if you replace the 3's in the formula for Grahams number using knuths up arrow notation, with grahams number, and you lift it grahams number of times instead of just 64, thats the graham'th root of my number.

[Anonymous No.6658628]

>>6658620
But that's why it's fun.

[Anonymous No.6658630]

>>6658623
let your number = a

my number = a^graham's number.


in my abstract algebra course a year ago our professor asked us all to write down the largest number we know in 10 seconds

>mfw some people wrote down as many 9's as they could in 10 seconds

[Anonymous No.6658634]

>>6658630
>not rounding that up to 10000......

[Anonymous No.6658636]

>>6658627
You get the idea.
I don't know nearly enough math to escalate this much further than you did.
But, still... let your number equal v, and my number = 2^v

[Anonymous No.6658656]

>>6658636
you are still 1 less than my number

[Anonymous No.6658660]

is anybody writing this down? we need to keep track/score of the biggest number.

[Anonymous No.6658662]

>>6658660
My computer has it written on the screen. What did you use to post with?

[Anonymous No.6658666]

>>6658595
> you must define it in your post

good luck with that arrow-shit

[Anonymous No.6658689]

>>6658627
This is the highest number as of now.
>>6658636
>>6658656
You didn't redefine in your posts (see rule 2)

[Anonymous No.6658720]

Shit nigger, this is the thread I was born for! Throughout my first semester at university I told people about big numbers and got called a moronic retard! Finally I meet likeminded people!

For the sake of easier notation I'll treat sequences as mappings from the natural numbers to them selfs, denote sequences as f(n) and composition really just by writing stuff after each other fg(n):=f(g(n)).

Alrighto! Let t be a choice function on the power set of the set of sequences (of natural numbers).

Let f_1,1 be the Ackermann-sequence (f_1(n)=A(n,n)).
Let f_i+1,j:=t{g|g(n)>f_i*...*f_1(n) for all n}
Let f_1,j+1 be the diagonal sequence f_1,j+1(n):=f_n,j(n)

Let g(n):=f_n,n(n)

My number is g(10).

(Yeah, I could have added stuff like ! or some could have raised some powers, but I'm still pretty confident my number is bigger than any of those posted until now. Except for those smart fuckers using other peoples numbers in their definition of course.)

[Anonymous No.6658725]

>>6658627
Oh didn't read that before posting >>6658720
Hm, yeah, maybe yours is bigger, not sure. I tried avoiding using big numbers in my definition. Alright let's try again.

[Anonymous No.6658732]

>>6658627
>graham'th root
Fun fact, the last 3 digits of Graham's number are 387. So we know for sure that "th" is the appropriate suffix for Graham's number (like "eighty seventh").

[Anonymous No.6658739]

>>6658720
>Let f_1,1 be the Ackermann-sequence (f_1(n)=A(n,n)).
>Let f_i+1,j:=t{g|g(n)>f_i,j*...*f_1,j(n) for all n}
>Let f_1,j+1 be the diagonal sequence f_1,j+1(n):=f_n,j(n)

Let g_1,1(n):=f_(n,f_n,n(n))(n)
Let g_i+1,j(n):=g_i,j*...*g_1,j(n)
Let g_1,j+1(n):=g_(g_n,n(n),j)(n)

Let h(n):=g_n,n(n)

Okay, now h(10) is bigger than anything posted so far.

[Anonymous No.6658760]

>>6658739
h(10) plus one

[Anonymous No.6658768]

>>6658589
Infinity minus one. I don't even know what that number would be called though. Maybe it's a googleplex raised to a googleplex.

[Anonymous No.6658777]

>>6658627
Hm . . . grahams number is really fucking big. Now that I think about it, maybe it's still bigger . . . fuck this shit:

>>Let f_1,1 be the Ackermann-sequence (f_1(n)=A(n,n)).
>>Let f_i+1,j:=t{g|g(n)>f_i,j*...*f_1,j(n) for all n}
>>Let f_1,j+1 be the diagonal sequence f_1,j+1(n):=f_n,j(n)
>Let g_1,1(n):=f_(n,f_n,n(n))(n)
>Let g_i+1,j(n):=g_i,j*...*g_1,j(n)
>Let g_1,j+1(n):=g_(g_n,n(n),j)(n)
>Let h(n):=g_n,n(n)

Let g:=(f_i) be a sequence of sequences.
Define: P_0(g)=identity on the natural numbers
P_i+1(g)=f_i+1*P_i(g) sequences.

Let h_1(n):=h(n)
Let h_i' be the constant sequence with h_i
Let h_i+1(n):=P_(h_i(n))(h_i')(n)
Let H(n):=h_n(n)

Okay, now I'm confident! Maybe! A bit at least!

[Anonymous No.6658778]

>>6658768
Infinite isn't a number

[Anonymous No.6658782]

>>6658768
Infinity -1 is infinity, stupid.

[Anonymous No.6658786]

>>6658778
>>6658782
It's not infinity retards. I subtracted one from it. How the hell can two numbers be equal to infinity? Go back to middle school.

[Anonymous No.6658791]

>>6658768
>>6658778
>>6658782
>>6658786

I hope I fell for some samefagging baitboat.

[Anonymous No.6658793]

>>6658786

epik torl

At least I fucking hope you're a troll.

Please.

[Anonymous No.6658798]

>>6658793
Are you kidding me? I though /sci/ was supposed to be math orientated. Alright let's consider proving it. Suppose infinity equals some huge number, say 10000000000000. We can keep subtracting one from that an infinite number of times until we get a number like five. Does five equal infinity? You're a moron.

[Anonymous No.6658801]

>>6658798
Hm, maybe I could copy that for times I feel the need to shitpost. I don't think I could come up with something that retarded without a lot of effort.

[Anonymous No.6658814]

>>6658798
∞=∞
∞+1=∞
1=0

[Anonymous No.6658821]

>>6658798

Infinity is an immeasurable concept.

/b/ is leaking, God save us.

[Anonymous No.6658845]

>>6658589
A post have a finite length and the number of words/symbols are also finite, sothere is only a finite numbers of possible posts.

Some of these posts are defining an integer following the rules you stated. So there IS a biggest one (a finite subset of the integers always have a biggest element) . which is well defined.

Now you should see where this is going, i can define in one post this number +1,(there, i just did it) and so i can define in one post a bigger number than the biggest i was supposedly able to make.

do i win something ?

[Anonymous No.6658852]

>>6658845
>bigger number than the biggest i was supposedly able to make
>supposedly
You supposed it, but that doesn't make it meaningful.
My number = the largest number that I'm "supposed" to be able to make +2.

[Anonymous No.6658853]

>>6658845

A sense of superiority.

On /sci/, that's about the best thing we cab give you.

[Anonymous No.6658855]

>>6658845
That's clever.

Well, let's assume we could agree on semantics totally and fix a function f that maps every post to a natural number. Well, obviously what you posted can't be mapped to the maximum of f +1, as this would be contradictory as you pointed out, so whenever we agree on semantics your shitty post doesn't mean what one might think it does.

>do i win something ?

Yeah, +1 internet you missleading shithead.

[Anonymous No.6658864]

>>6658666

It's easy:

f(x) = 2 ^x 3

G = f^12(7)

[Anonymous No.6658868]

>>6658720
>>6658725
>>6658739
>>6658777
you sound (and probably look) like a complete fucking faggot

[Anonymous No.6658893]

>>6658868
Yeah, I'm pretty gay! People don't like me and insult me whenever I post online, instead of politely avoiding me like in real life, but I thought people in this thread like big numbers, so maybe we can have fun talking about big numbers? Well, maybe I should go back to lurking.

[Anonymous No.6658901]

>>6658893
holy shit take your autism back to reddit for the love of christ

[Anonymous No.6658916]

Ready

(I'm assuming that "computable" means "computable with infinite computation power, but the program must halt")

given an integer N, the function F computes F(N) as follows:
enumerate all character strings of length less than N, and for each one, check whether it is a valid formal proof within ZFC (i.e., whether it is a valid sequence of lines, each line being either an axiom of ZFC or an immediate consequence of earlier lines by a rule of pure logic: all of this can be done with bounded checks), and, if it is, whether its conclusion is of the form "the Turing machine <T> terminates when run on an empty tape",
each time a proof of "<T> terminates" has been found, simulate the execution of T until it halts, and count the number of steps,
return the sum of the numbers in question.

Aaaaaand with that definition, I submit the number F(F(F(F(F(101000))))).

Bite me

[Anonymous No.6658918]

>>6658901
I'll try to be less annoying! Well, anyone else to propose a big number? Or fast growing sequence? I think the best ways to get a big number are fast growing sequences or defining them as the zero of a function that falls really slow.

[Anonymous No.6658921]

>>6658918
>using exclamation points

[Anonymous No.6658929]

>>6658916
I'm not convinced this is bigger than
>>6658777

[Anonymous No.6658936]

>>6658929
Aha, because the termination of any of the functions mentioned in this thread are all provable within ZFC in a reasonable amount of space (certainly far less than 101000 symbols, even after formalization), so the enumeration of all proofs of length less than 101000 will encounter a proof of termination of the corresponding program (translated to a Turing machine), which will then be executed in the computation of F(101000), so the latter is greater. More generally, the number F(101000) is (by construction) greater than any number whose termination can be proved in ZFC, hence, in orthodox mathematics, within in a reasonable size. So, one might say with a grain of salt: anyone who proposed a Turing machine to compute a large number and proved, within the standard framework of mathematics, and in a reasonable size, that it terminates, will have computed a number less than this program.

Of course, then I looped it a few times, just for good measure.

I've had to explain this several times, in case you can't tell.

[Anonymous No.6658941]

>>6658916
I guess that's the biggest number I've seen ever so far!

[Anonymous No.6658947]

>>6658929
Yeah, I think so as well.

[Anonymous No.6658953]

>>6658941
Of course, for all my best efforts, it's still as far from infinity as any other number ...

For the record, every time it says "101000" it's really supposed to be "10^1000". The formatting just didn't carry over when I c/ped.

Muchas gracias to
>>6658929
for giving me an excuse to ramble.

[Anonymous No.6658972]

I think it depends on the choice function t. For any reasonable choice function, there is a turing machine that computates the number given by H and the proof that it does is smaller than 10100 characters. However of course, you could choose a t that gives you f_2,1:=F^n(101000) or some shit, so I guess it's not clear wich is bigger. Mine is dependend on the choice function t while his is dependend on the implicit goedelization, so yeah, I guess there is no way to tell without fixing the t and the goedelization.

[Anonymous No.6658983]

>>6658953
>Of course, for all my best efforts, it's still as far from infinity as any other number ...

Yeah, but I like your idea a lot. I envy you for it. The only thing not beautifull about it in my opinion, is that you need to start off with 10^1000, but well, for most goedelizations F will return 0 for numbers smaller than 1000 I guess.

[Anonymous No.6658993]

>>6658983
Yes, unfortunately true. I have one way in mind to defeat my described F(N), in this game, but I'm not sure I want to share .....

[Anonymous No.6659013]

420

[Anonymous No.6659034]

>>6658993
I guess the trick here is to define recursive a lot and that's best done using language. So I'd define G(n) to be the maximum over all the numbers whose proof of existence is smaller than n, I guess that's faster than F also we don't need all the features of ZFC, so maybe we could cut something there.

[Anonymous No.6659051]

>>6659034
Mmmm, but unfortunately incomputable.

Let ZFC stand for ZFC to which some large cardinal axiom has been added. So far I'll remain vague on what the axiom in question is, but an inaccessible cardinal will do.

Now, within ZFC, the consistency of ZFC, and even its arithmetical soundness, is a theorem: it is a theorem of ZFC that every Turing machine whose termination ZFC proves does, indeed, terminate. (This is a consequence of the fact that ZFC constructs a "transitive model" of ZFC, which has the same natural numbers as the Universe, and proves that the axioms of ZFC are true in that model, so all the theorems of ZFC are true in the natural numbers.) In particular, within ZFC, the proof of termination of the program computing F(101000) is fairly short, certainly not as long the more than 101000 symbols it requires within ZFC: this is an example of proof speed-up.

But now if we define F to be the same function as F but enumerating the proofs within ZFC instead of ZFC, the above paragraph shows that F(101000) is far, far, larger than F(101000) or even F(F(⋯(F(101000)))) with F(101000) iterations of F, or anything naïvely constructed along those lines: indeed, since ZFC proves (uniformly and in a fairly short space) that the function F is well-defined (i.e., that the Turing machine computing it always terminates), it proves that all these constructions can be computed. This explains that:

Replacing the system ZFC in the definition of the program by one (ZFC) obtained by adding strong axioms of infinity makes the number much larger, considerably more so than trying to iterate the function or any such naïve construct. Furthermore, using a stronger axiom of infinity provides a similar largeness above a weaker axiom: the larger cardinal axioms indeed give you much larger integers than smaller ones!

Now as for what axiom of infinity you want to accept, that's up to you ...

[Anonymous No.6659074]

Nono, F doesn't ennumerate proofs, but gives out the largest number that can be proven to exist with a proof with less than n symbols. Since there are finite proofs, with less than n symbols, this is welldefined. Or I use some goedelization, or something, I'm sure something like that works.

Maybe it's faster using a function that gives the order of the largest finite group where n gives you some restrictions for generators and relations, like "n" generators and "n^2" symbols for relations or something.

[Anonymous No.6659085]

>>6658634

>Not replacing every decimal with 9...

[Anonymous No.6659140]

I think I can beat all these. There's an enormous number called TREE(3), far bigger than Graham's number. http://en.wikipedia.org/wiki/Kruskal's_tree_theorem
Define x = TREE(...(TREE(3)...) where the nesting happens TREE(3) times.
Then define y = x [x up arrows] x using Knuth's up-arrow notation. http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation
Take that.

[Anonymous No.6659144]

>>6659140
Actually >>6658916 might win. Not sure.

[Anonymous No.6659162]

>>6659144
Yup, >>6658916 is definitely the reigning champion.

[Anonymous No.6659170]

Okay, round 2.
Take the number y I defined in >>6659140.
Take F(n) from >>6658916.
Take z = F(...(F(y))...) where the nesting happens F(y) times. (1)
Take a = z [F(y) up arrows] z. (2)
Now alternate (1) and (2) a times where a is character limit of this thread.
Call that number b. Define b = g(y).
Take g(g(g(g(g(y*9001))))).
/out

[Anonymous No.6659185]

http://mathoverflow.net/questions/32891/finding-the-largest-integer-describable-with-a-string-of-symbols-of-predefined-l
Case closed.

[Anonymous No.6659201]

Let x be the sum of the absolute value of all numbers posted in this thread.

Let y be the sum of the absolute value of all numbers that are going to be posted from now on.

My number is x + y.

[Anonymous No.6659206]

>>6659201
"Let y be the sum of the absolute value of all numbers that are going to be posted from now on."
Not computable

[Anonymous No.6659216]

>>6659013
swag

[Anonymous No.6659219]

>>6659201
my number is Graham's Number ^ (x*(x+y))

Check mate atheists

[Anonymous No.6659223]

You're all fucking idiots:

According to Don Page, physicist at the University of Alberta, Canada, the longest finite time that has so far been explicitly calculated by any physicist is

Google it

[Anonymous No.6659225]

Inb4 it's too difficult to figure out which number is largest.

[Anonymous No.6659310]

>>6658589
pi

[Anonymous No.6659331]

>>6659310

HAHAHAHAHAAHAHAHAHAH 14 year old detected

[Anonymous No.6659344]

>>6659331
explain it then.

[Anonymous No.6659345]

>>6659344
<span class="math"> \pi < 4 [/spoiler]

[Anonymous No.6659348]

>>6659345
read the parameters of the OP, please.

[Anonymous No.6659358]

THE SUM OF ALL OTHER (POSITIVE) NUMBERS IN THIS THREAD. INCLUDING FUTURE ONES.

I WIN.

[Anonymous No.6659360]

>>6659170
I see what you did, and I'm ready to rumble.

Remember my function F(N)? We're using F#(N), now. Instead of ZFC, F#(N) uses ZFC+I0.

My new submission is F#(F#(F#(F#(F#(10^1000))))).

Yes, it dwarfs yours, per >>6659051. I <3 axioms

>Can we please not allow submissions that rely on previous ones? That just bugs me, since it would eventually fall into a loop of +1, +1, +1 …

>>6659358
Uncomputational

[Poo to you. No.6659363]

>>6658589
>I'll start with 0.

>implying 0 is a number
>implying 0 has value

Come on. Its a Googleplexianth. 1 over a googleplexian, which is a 1 followed by a googol of zeros.

[Anonymous No.6659366]

>>6659360
NO IT'S NOT. YOU'RE JUST A SORE LOSER.

[Anonymous No.6659369]

>>6659360
>Uncomputational

Not if you add them up

[Anonymous No.6659371]

>>6658845
This is similar to: http://en.wikipedia.org/wiki/Richard%27s_paradox
The problem is that you cannot make sense of what it means for a post to define a specific number (one could say you haven't defined the word "define", if one wanted to sound like a twat), so you cannot say something like "the biggest number possibly thus defined, plus one".

Anyway OP, define <span class="math">TREE(n)[/spoiler] to be the length of the longest sequence of n-labelled trees, <span class="math"> \left \{ T_i \right \}_{i \in I}[/spoiler], such that for each i, <span class="math">|V(T_i)| \leqslant i[/spoiler], and no <span class="math">T_i[/spoiler] embeds into any <span class="math">T_j[/spoiler] for j > i.
This function is massive for n > 2. Much, much more so than anything you could make out of Graham's number, or Friedman's n function, or Ackermann's function, or anything else like that. It also grows faster than just about any function you could calculate.

[Anonymous No.6659374]

a
u
t
i
s
m

[Anonymous No.6659375]

>>6659374

Found the Engineer

[Anonymous No.6659376]

>>6659363
His number plus 1

[Anonymous No.6659382]

>>6659376

Your number squared in chess board sequence for every post this thread has and will get

[Anonymous No.6659390]

>>6659382
>will get
"The definition of your number must not involve any posts to come after yours."
>has
"Even if you're using notation or part of a definition that was already posted in this thread, you must define it again in your post."
The rules are there for a reason.

[Anonymous No.6659393]

is this what not masturbating does to people

[Anonymous No.6659402]

>>6659393


shut up loser, we're making Mathematics.

[newt !!tbq4mzzlMHI No.6659405]

hur Ackermann's function where all the arguments are a googleplex^googleplex^googplex... until the character limit.

how silly
or just define another function in terms of the Ackermann function that's even bigger

[Anonymous No.6659409]

>>6659405

The Ackermann function, +1.

[Anonymous No.6659435]

>>6658916
Okay, an idea based on this one. Compute G(n) by:
enumerate all strings of characters of length less than n, and check whether each one is a proof in "NBG + Reinhardt - Choice" of the form "this Diophantine equation has a solution". Then, for each such proof, calculate the solution by checking each possibility, starting at 0 (i.e if the equation is in X and Y, try X = 0 Y = 0, then X = 1 Y = 0, etc. until the solution is found). Then G(n) is the number of steps taken to brute force the solution to each such proof.
Then I define my function as <span class="math">G^{G(10^{1000000})}(10^{1000000})[/spoiler].
I believe this should work for the same reason - a general Diophantine equation is algorithmically unsolvable, just like the halting problem.

[Anonymous No.6659440]

>>6659435
That should read "...G(n) is the PRODUCT of the steps..."

[Anonymous No.6659442]

>>6659435

This +1

I can just let these people do all the hard work. Its amazing.

[Anonymous No.6659448]

>>6659442
>Even if you're using notation or part of a definition that was already posted in this thread, you must define it again in your post.

[Anonymous No.6659453]

>>6659448

>even though you're a faggot, I forgive you.

Fuck OP's rules, and fuck you. DOUBLE your post now, nigger.

[Anonymous No.6659460]

>>6659453
You're right; we don't need rules.
My number is higher than any number that you'll even consider submitting for the rest of your life. I don't even need to define it.

[Anonymous No.6659497]

π^-10

[anee !IGmmcgCsNE No.6659509]

π^-10

[Anonymous No.6659515]

>>6659497
>>6659509

lol

[anee !IGmmcgCsNE No.6659523]

>>6659515

why is this funny?

[Anonymous No.6659526]

>>6659523
Watching idiots embarrass themselves is fun to anybody.

[anne !IGmmcgCsNE No.6659532]

>>6659526

no, but what is exactly so funny?

[Anonymous No.6659548]

>>6658589

> all that small numers

I will definely win this shit:

( 999999999999999999999999999999999999999999999999999999 ^ 9999999999999999999999999999999999999999999999999999999999999999999999 ^ 9999999999999999999999999999999999999999999999999999999999999 ^ 9999999999999999999999999999999999999999999999999999999999 ^ 9999999999999999999999999999999999999999999999999999999999999999999999999999 ^ 9999999999999999999999999999999999 ) !

[Anonymous No.6659552]

>>6659548
not even close

[Anonymous No.6659554]

>>6658916

What about ( [your answer] ^ [your answer] ) !

[Anonymous No.6659555]

>>6659554
>if you're using notation or part of a definition that was already posted in this thread, you must define it again in your post.

[Anonymous No.6659558]

>>6659554
dwarfed by
>>6659360

[Anonymous No.6659564]

>>6659552

Well, at least my number is bigger than the number of atoms on the universe, r... right?

[Anonymous No.6659585]

<span class="math">^graham's number graham's number<span class="math">
in case I fucked up my latex, it's graham's number tetrated to graham's number[/spoiler][/spoiler]

[Anonymous No.6659590]

>>6659585
wow that's 10 levels of fucked up
<span class="math"> ^{graham's number} graham's number[/spoiler]

[Anonymous No.6659591]

A power tower of tree(3) tree(3) times.

[Anonymous No.6659592]

>>6659548
I know that a lot of the higher end math here can be hard to grasp, but you could at least try.
9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[Anonymous No.6659597]

>>6659591
Do I win this yet? I can't latex, I hope you understand what I mean, this is a tetration.

[Anonymous No.6659601]

>>6659564
Correct. The number of atoms in the universe is only 81 digits long; just your expression of your number is longer than that. But it could have been better expressed as
9999999999999999999999999999999999999999999999999999999999999999999999 ^^ 6

>>6659585
Graham's number is actually the 64th in a sequence. To get the next number, you take 3^^^...3, with as many up-arrows as the previous number in the sequence. For instance, G(65) is 3^^^...3 with Graham's number of up-arrows. This already dwarfs your tetration by over ... wait for it ... Graham's number orders of magnitude.

>>6659592
>>6659591
Insignificant.

The reigning champ is (still) >>6659360.

[Anonymous No.6659611]

>>6659601
Didn't notice the thread went on for this long. Thoguht noone would come up with tree(3) but people already manipulated it.

[Anonymous No.6659612]

>>6659360
>Remember my function F(N)?
>Even if you're using notation or part of a definition that was already posted in this thread, you must define it again in your post.

[Anonymous No.6659614]

>>6658593
>>6658594
>>6658595
>>6658598
>>6658600
>>6658601
>>6658603
>>6658604
>>6658606
>>6658611
>>6658612
>>6658615
>>6658616
>>6658620
>>6658621
>>6658621
>>6658623
>>6658627
>>6658628
>>6658630
>>6658634
>>6658636
>>6658656
>>6658660
>>6658666
>>6658720
>>6658739
>>6658768
>>6658782
>>6658791
>>6658793
>>6658801
>>6658821
>>6658845
>>6658852
>>6658853
>>6658855
>>6658864
>>6658868
>>6658921
>>6658929
>>6658936
>>6659162
>>6659170
>>6659185
>>6659201
>>6659051
>>6658936
>>6659366
>>6659369
>>6659371
>>6659374
>>6659375
>>6659390
>>6659393
>>6659402
>>6659405
>>6659409
>>6659435
>>6659440
>>6659442
>>6659448
>>6659453
>>6659460
>>6659509
>>6659523
>>6659526
>>6659532
>>6659548
>>6659552
>>6659564
>>6659585
>>6659590
>>6659591
>>6659592

x = (sum of all numbers of this thread)^(sum of all numbers of this thread

Biggest number:

(x!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)

This number is already bigger than infinite.

[Anonymous No.6659620]

>>6659614
>bigger than infinite
You have nooo idea what that means, buddy. But if you say soo ....
>>6658589: 1: Your number must be finite.

[Anonymous No.6659621]

>>6659614
>Even if you're using notation or part of a definition that was already posted in this thread, you must define it again in your post.

[Anonymous No.6659668]

827492386423904603294028975062394623094623956320956329056329856209861235612956739563948563409561439531453563415035894631509346543563459836453456347856315836539456305634564398596939408565349864395864318956347560348757634583564750453561438561485763583476538475653451345614385

rekt

[Anonymous No.6659682]

>>6659668
>laughingrecursivefunctions.jpg

[Anonymous No.6659692]

Largest useful number? Grahms number. I win.

Largest number? I take your answer and square it. I win

[Anonymous No.6659718]

It's a circlejerk thread, that said I propose 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^1110^10^10^10^10^10^10^10

[Anonymous No.6659723]

>>6658760

h(10) plus two

[Anonymous No.6659735]

>>6659360
F#(F#(F#(F#(F#(F#(F#(F#(F#(F#(F#(F#(F#(100000000!^10000)))))))))))))

[Anonymous No.6659736]

10^0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

[Anonymous No.6659739]

>>6659736
forgot the 1 lel

[Anonymous No.6659753]

<span class="math">9^(infinity x graham's number)[\math][/spoiler]

[Anonymous No.6659755]

>>6659753
its so big it broke latexs

[Anonymous No.6659760]

my dick^your mom's mouth

[Anonymous No.6659766]

-1/12

[Anonymous No.6659781]

Note: I am a former tachyonic being who traveled from the end of time to the beginning of time, then decayed into ordinary matter and have lived normally since. From my perspective, all points in time, including the future, are in the past.
Therefore, all posts after this one actually came before this post, from my perspective. But the posts before this one also came before.

With that in consideration, I declare my number to be the largest number in this thread (excluding this one) plus one.
Note that this includes all following posts, since those posts actually have come before my post from my perspective.

[Anonymous No.6659782]

What makes a number big? Its size can only be determined if you put the number in a discrete context. For example, 1 unit is smaller than 2 units, or 5 atoms is a larger quantity than 3 atoms.

In that case, how would you determine the "bigness" of a number like -5? What is the size of -5 apples, or -5 atoms?

[Anonymous No.6659784]

>>6659766
winrar

[Anonymous No.6659790]

>>6659782
Magnitude (i.e. distance from zero).

-5 has the same "bigness" as 5.

That's not relevant anyways, since I don't think anyone has submitted a negative answer aside from >>6659766.

[Anonymous No.6659791]

>>6658589
>computable
get out
>>>/g/

[Anonymous No.6659795]

>>6659766
Is that supposed to be the sum of all numbers? It is only calculable with something like the Riemann Zeta function since it is a divergent series.

I don't know if that counts.

>>6659790
A negative number isn't really a thing outside of a context, right? You can't have really have -5 apples.

[Anonymous No.6659798]

>>6659791
Ironically, the reason that I added that rule was because I don't know shit about math or computers. I heard something about non-computable "busy beavers", but I couldn't be bothered to look up how they worked, so I just banned them.

[Anonymous No.6659801]

>>6659795
Sure you can. You needed five apples. You borrowed five apples from Nancy. You ate the five apples. Now, since you owe five apples to Nancy, you can be said to have five less than zero apples – that is, -5 apples.

Also, negative velocity.

>>6659798
Busy beavers are the best though! Do you want a ELI5 explanation?

[Not him No.6659803]

>>6659801
> Do you want a ELI5 explanation?
yes

[Anonymous No.6659804]

>>6659801
>Do you want a ELI5 explanation?
Sure, if it's not too much trouble.

[Anonymous No.6659808]

>>6659801
That's why I said without a context. You can't have -5 apples without previously having 5 or more apples. What I mean, which I am having a difficult time putting to words, is that there are not actually quantities below zero.

[Anonymous No.6659809]

>>6659808
Sure! Most of mathematics wouldn't reflect the real world without "context". I could go into how maths is a language for models, which are part of map, versus territory, and Platonism and engineering and instrumentalism … but I've got a Busy Beaver explanation to write.

>>6659803
>>6659804
Gimme 10

[Anonymous No.6659820]

>>6659808
You can't have 5 apples without having received apples.

That requires context, therefore 5 is not a quantity.

[Anonymous No.6659823]

>>6659809
Sounds like Gödelian Model Theory. Alright, I don't think I need to ask anything else (even though I was stating rather than asking).

[Anonymous No.6659824]

>>6659809
Ahhh planning fallacy just hang tight guys

[Anonymous No.6659828]

>>6659820
Let's just say that 5 apples exist, rather than having someone own or receive those 5 apples. At this point, it is entirely semantic... Anyway, I agree; numbers are just representations of things, not actually containing any weight outside of an application.

[Busy Beaver Function 101: A No.6659858]

>>6659824
Once upon a time, there was this cool guy named Turing – there's a movie coming out about him soon – and he helped crack the ENIGMA code in WWII. As such, he was a pioneer of early computing … and the mathematical theory thereof. He developed a concept called the Turing machine, which is a simple model that can be used to simulate any possible computer program, just by following rules about moving along a strip and changing values. I won't waste too much time explaining this.

Shit, this might be harder than I thought. It's got serious implications with axioms and Tarski and Gödel and aaahhh

Okay. Turing machines "halt" when they reach the end of a program. Maybe you made a program to calculate the product of two and three; in this case, it would halt when it gets its answer (six). However, there are also programs that never halt: for instance, the program

>n=1
>while True:
>>n=n+1

(written in Python. I don't yet speak Turing machine, unfortunately)

[Busy Beaver Function 101: B No.6659862]

>>6659858
These are obvious examples, but, the trickier a program gets, the harder it is to tell if it will ever halt. Will Minecraft ever halt? Umm … good question. Unfortunately, there's NO WAY to find out. Turing proved the existence of the "halting problem", which states that you'll never be able to prove whether a program is just taking a long time to run … or if it's never going to end.

This has got to do with things like Tarski and axioms not being able to prove their own consistency, but I'll skip that for simplicity's sake. Maybe if I do a better job tomorrow, I'll post it. Keep an eye out.

The Busy Beaver function – I'll call it E(n) – defines the maximum number of steps a Turing machine can take before a halting program of length n halts. So … take the set of all programs of length n. Now, throw out the ones that don't halt. And then run the rest, and see which one runs the longest. Count how many steps the machine takes to complete the problem, and you have the Busy Beaver number of n. Doesn't sound too bad, right?

[Busy Beaver Function 101: C No.6659867]

>>6659862
Except for the halting problem. We can't tell the difference between a program that's just running for a REALLY long time, and a program that will never halt. We can't throw out the nonhalting programs, so we just run all of length n … and then what? After most of them have halted, how do we know whether to keep waiting for the remainders to halt, or just stop because they'll never do it?

In fact, if we had a way to calculate the Busy Beaver numbers, we'd solve the halting problem right there. All we have to do to test a program of length n, to see if it halts or not, is to run it until it hits E(n) steps, and then if it hasn't stopped, it's nonhalting. The Busy Beaver numbers are INHERENTLY INCALCULABLE by Turing machines – which, you'll remember, includes every computer.

[Busy Beaver Function 101: Fina(...) No.6659872]

>>6659867
But that doesn't explain why they're fun. They're fun because they get huge, really, really quickly. Now, we don't have any way to find the numbers besides brute-forcing it, so we only have a few numbers and a few guesses. IIRC, E(1) is around 6, and E(5) has a lower bound of 47,176,870, and E(6) has one of 10^36534. Can you see how quickly this grows? Faster, in fact, than Knuth up-arrow notation or the Ackermann function. E(12) is already bigger than g(1). At LEAST.

So yeah. That's about it for now. Hope you guys learned something! :D And that I haven't suffered from a complete misunderstanding of the topic! D:

*goes to sleep*

[Anonymous No.6659879]

>>6659862
>axioms not being able to prove their own consistency

Incompleteness theorem?

[Anonymous No.6659882]

>>6659872
Based beaver.
Thanks a lot. I think I might understand now.

[Anonymous No.6659894]

Haha no sleep yet

>>6659879
Bingo! There are some clever analogues between how axioms can't prove their own consistency, and how halting is uncomputable.

>>6659882
Glad I could help!

Understanding of the Beaver should help with understanding my currently-unchallenged answers to OP's question:
Pt1 >>6658916
Pt2 >>6659360

[Anonymous No.6660087]

NUMBER OF PLANCK SCALES SINCE GOD WAS CREATED.

I WIN

[Anonymous No.6660091]

Biggest number that is possible to describe while obeying all the rules in the OP.

[Anonymous No.6660160]

>>6658589
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

[Anonymous No.6660188]

Infinity + 1

[Anonymous No.6660198]

The number of years until OP gets laid.

[Anonymous No.6660258]

>>6660198
*finite* numbers, goofball

[Anonymous No.6660677]

>>6658589
x=Graham's number
a(x)=(x↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑x)!
b(a)=(a↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑a)!
c(b)=(b↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑b)!
...
z(y)=(y↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑y)!
aa(z)=(z↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑z)!
ab(aa)=(aa↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑aa)!
ac(ab)=(ab↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑ab)!
...
My number = zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz (zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzy)

[Anonymous No.6660685]

>>6660677
That's a pretty big number.

[Anonymous No.6660691]

>>6658621
e is based base

[Anonymous No.6660696]

>>6658720
nice

[Anonymous No.6660780]

>>6660677
... reasonably sure >>6658916 is still bigger

[Anonymous No.6660832]

all in the universe made into a symbolic set numbers is the "biggest" number if it equals the same number like all 1's in as a state as a function. all the 0's or 1's are combined into one big assed 1 or 0 state, 0=could be heat death but heat death is something so somthing can combine into a 1, so it equals a giant big assed 1 thing, 1 time as one big assed thing as well..

[Anonymous No.6660862]

>>6660780
>>6658916 is still bigger than the other answers in this thread that follow the rules because of >>6658936 and >>6659051. It's a clever construction that'll beat any attempt to use things like Graham's number or TREE(n).

[Anonymous No.6660900]

I win and I dub a 0.

[Anonymous No.6661161]

>>6658589
Lol that was easy to win:


> my number's name is "leNumba"
> leNumba is huge
> if you sum all number of this thread, it would still be massively less than 0,000000000000000000000000000000...???...9% of leNumba
> humans can't comprehend leNumba
> leNumba is very huge

[Anonymous No.6661169]

>>6661161
>> humans can't comprehend leNumba
>not computable and well-defined

[Anonymous No.6661179]

>>6661169

What the fuck did you just fuckimg say about leNumba, you little bitch? You are nothing to leNumba, but just another target.

[Anonymous No.6661192]

>>6661179
But I've got leNumba^2.

[Anonymous No.6661212]

The product of all the digits of Pi.

[Anonymous No.6661219]

>>6661161
Lenumba is this some kind of joke

[Anonymous No.6661222]

>>6661212
> finite and real

[Anonymous No.6661227]

>>6661222
It is finite and real. But the product of all the digits of pi is zero, so he still loses.

[Anonymous No.6661232]

>>6661192

I just forgot to tell you, you can't do any operation with lenumba, because it is so huge that the current universe does not support this kind of logic.

[Anonymous No.6661235]

>>6661227

> zero

I kek'd

[Anonymous No.6661242]

>>6661235
The 33rd digit of <span class="math">\pi[\math] is 0. Thus, every partial product for the digits of pi for <span class="math">n\geq 32[/spoiler] is zero. Thus, the infinite product of the digits of <span class="math">\pi[\math] converges to zero.[/spoiler][/spoiler]

[Anonymous No.6661244]

>>6661235
>>6661235
The 33rd digit of <span class="math">$\pi$[\math] is 0. Thus, every partial product for the digits of pi for <span class="math">$n\geq 32$[/spoiler] is zero. Thus, the infinite product of the digits of <span class="math">$\pi$[\math] converges to zero.[/spoiler][/spoiler]

[Anonymous No.6661245]

>>6661227
lel

[Anonymous No.6661250]

>>6661235
The 33rd digit of <span class="math">$\pi$[/spoiler] is 0. Thus, every partial product for the digits of pi for <span class="math">$n\geq 32$[/spoiler] is zero. Thus, the infinite product of the digits of <span class="math">$\pi$[/spoiler] converges to zero. If he had said sum instead of product, this would be different.

[Anonymous No.6661254]

>>6661245
>>6661235
Nevermind, you guys are right. Forgot that you can't converge to 0; the product just diverges. I'm an algebraist, not an analyst, so I hope you'll excuse this retardation.

[Anonymous No.6661279]

>>6661254

So that means that leNumba wins, r...right?

[Anonymous No.6661301]

Everything here
>Even if you're using notation or part of a definition that was already posted in this thread, you must define it again in your post. 3: Your number must be defined in one post only (no two-parters). 4: The definition of your number must not involve any posts to come after yours.
Made this a counting thread.
Fuck off, OP.

[Anonymous No.6661502]

>>6661301
Counting is math, and it's more difficult than you might expect.

[Anonymous No.6661504]

>>6661502
check skype

[Anonymous No.6661514]

>>6658798
>Suppose infinity equals some huge number

Theres your problem.

[Anonymous No.6663010]

I buy it

[Anonymous No.6663017]

So, no one has posted this yet, huh?

"Who Can Name the Bigger Number?"
by Scott Aaronson

http://www.scottaaronson.com/writings/bignumbers.html

[Anonymous No.6663081]

>>6663017
>But for each fixed whole number N, just as there are only finitely many distinct words with N letters, so too are there only finitely many distinct machines with N rules.

Likely I'm misunderstanding what "rules" are in the context of Turing Machines, but couldn't a rule be "After encountering x symbols of type t_1, print a symbol of type t_2", and these x, t_1, and t_2 have infinite potential values, leading to infinite Turing Machines with N rules?

[Anonymous No.6663091]

My number is the largest number ITT plus 1.

[Anonymous No.6663119]

>>6663091
That's infinite, you retard.

>lrn2self-reference

[Anonymous No.6663138]

>>6658589
x

x = The biggest computable real number ever well defined outside of this thread + 1

I am correct. You know I am. I want my 30% coupon now.

[Anonymous No.6663143]

>>6659739
top kek

[Anonymous No.6663159]

>>6658916
F(F(F(F(F(F(F(F(F(F(101000)))))))))).

haha nigger

[not going to grad school No.6663488]

>>6663138
ok ill play this game.
this guy's number plus 1

[Anonymous No.6663660]

>>6660691
thank you based e

[Anonymous No.6665514]

>>6658589
10 to the whatever the fuck power.
That's a 1 with whatever the fuck zeroes next to it.

[Anonymous No.6665560]

>>6658589
>dat fish
Lol, I have one of those.

[Anonymous No.6665772]

f1_1(x) = x+1, f1_n(x) = f1_n-1^x(x)
fk_1(x) = f(k-1)_x(x), fk_n(x) = fk_n-1^x(x)

fn_n(n) for n=2 is already bigger than anything anyone has posted yet. The process of recursively defining functions and iterations of them would be tedious, so instead my submission is this program for constructing the largest possible number in a finite character space. Now some other /sci/ jackoff can actually construct the winner.

[Anonymous No.6665784]

>>6665772

Actually, let's just go

g(n) = fn_n(n)

My number is then g^x(x) for x = gamma[g(3)].

[Anonymous No.6665806]

>>6658589
I bet OP just read this
http://www.scottaaronson.com/writings/bignumbers.html


Anyway, I win.
lets define a recursive series of recursive functions
f_1(x,0) = x
f_1(x,n) = f_1(x^x, n-1)

f_2(x,0) = f_1(x,x)
f_2(x,n) = f_2( f_1(x,x), n-1 )

f_k(x,0) = f_[k-1](x,x)
f_k(x,n) = f_[k-1]( f_[k-1](x,x), n-1 )

f_G(G,G); G=graham number

[Anonymous No.6665809]

>>6659614
>syntax error: mismatching brackets

[Anonymous No.6665811]

X

Where X = y+1

Where y is the highest value posted in this thread which satisfies OP's criteria

[Anonymous No.6665822]

OP mum's weight in kilos

[Anonymous No.6665834]

>>6665811
Your doesn't satisfy the criteria because it's recursive and goes to infinity

[Anonymous No.6665883]

function ackermann( $m , $n )
{
if ( $m==0 )
{
return $n + 1;
}
elseif ( $n==0 )
{
return ackermann( $m-1 , 1 );
}
return ackermann( $m-1, ackermann( $m , $n-1 ) );
}

define G=Grahams number

echo ackermann( ackermann(G,G), ackermann(G,G));

[Anonymous No.6666023]

3^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^3

[Anonymous No.6666050]

9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^...to the end of the character limit.

This sequence is the most efficient use of characters to specify a very large number.

[Anonymous No.6666068]

>>6666050

Prove it.

> disclaimer: your statement is false

[Anonymous No.6666075]

>>6666050
9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[Anonymous No.6666081]

>>6665883
That would be a... big number.

[Anonymous No.6666110]

>>6666023
That notation doesn't even mean anything.

[Anonymous No.6666112]

>>6666110
Oh wait, you're probably using those as Knuth up arrows.
Nevermind.

Learn LaTeX, bro.

[Anonymous No.6666137]

The smallest number bigger than any finite number named by an expression in the language of set theory with a googol symbols or less.

[Anonymous No.6666144]

>>6658589
biggest how?

100/3
that's pretty big, depending on your definition

[Anonymous No.6666145]

>>6666144
Name a definition of "big"-ness whereby your number has any chance of winning.

[Anonymous No.6666146]

>>6666145
Length

33.3... goes on forever
I'll take my medal in gold

[Anonymous No.6666153]

>>6666137
Pretty sure I won guys.

[Anonymous No.6666158]

>>6666153
<span class="math">That number + 1[/math[/spoiler]

[Anonymous No.6666163]

>>6666158
lol the rules say finite and real. This is infinity.

[Anonymous No.6666169]

>>6659736
>>6659739
i laffed hard

[Anonymous No.6666173]

this is really just a test in fooling around with latex, but...

Let G be Graham's number, then define our number to be

<span class="math">\left.\begin{matrix}
{\stackrel{\stackrel{\stackrel{\underbrace{G\uparrow^{G\uparrow^{G\uparrow ...}}}}{
\underbrace{G\uparrow^{G\uparrow^{G\uparrow...}}}\text{times}}}{
\underbrace{G\uparrow^{G\uparrow^{G\uparrow...}}}\text{times}}}{\vdots}}
\end{matrix}\right\}\stackrel{{\underbrace{G\uparrow^{G\uparrow^{G\uparrow...}}}\text{times}}}{G\text{ times}}[/spoiler]

[Anonymous No.6666176]

>>6666173
Dang, latex didn't compile properly... well here's the pic of the number

Let G be Graham's number...

[Anonymous No.6666186]

>>6666176
ok i'm done fooling around, gnite m8's

[Anonymous No.6666187]

>>6666176
I dunno, >>6665883 still scares me more.

[Anonymous No.6666194]

>>6666187
ok i lied im still awake

true, the whispers of the ackermann function are truly terrifying

[Anonymous No.6666198]

>>6665883
Why the hell are you writing in what I believe is PHP?
This is /sci/ not /g/.
Hell even on /g/ you'd be ridiculed.

[Anonymous No.6666202]

>>6666187
here we go, quick solution

...

we have to go deeper...

[Anonymous No.6666206]

>>6666198
Not him, but you're just as bad as /g/ for ridiculing him for expressing his answer in code form.

[Anonymous No.6666213]

>>6666202
actually I'm not quite sure this is larger than his just to be safe (also fixed the error i just noticed with my use of the knuth up arrow notation)

[Anonymous No.6666229]

>>6666213
oh fug

[Anonymous No.6666236]

>>6665883
This reaches maximum recursion depth so fucking quickly.

[Anonymous No.6666238]

>>6666236
OP didn't say that the number had to be computable before the heat death of the universe

[Anonymous No.6666272]

The fibonacci sequence at the gth term, where g is grahams number

[Anonymous No.6666286]

>>6666272
That's still got nothing on my main man Allahu Ackermann.

That's just calculating (phi^G)/sqrt(5).

[Anonymous No.6666289]

&forall R {
{for any (coded) formula [ψ] and any variable assignment t
(R( [ψ],t) ↔
( ([ψ] = `x_i ∈ x_j' ∧ t(x_1) ∈ t(x_j)) ∨
([ψ] = `x_i = x_j' ∧ t(x_1) = t(x_j)) ∨
([ψ] = `(∼θ)' ∧ ∼R([θ],t)) ∨
([ψ] = `(θ∧ξ)' ∧ R([θ],t) ∧ R([ξ],t)) ∨
([ψ] = `∃x_i (&theta)' and, for some an xi-variant t' of t, R([θ],t'))
)} →
R([φ],s)}

[Anonymous No.6666291]

>>6666289
bro that's gross.

[Anonymous No.6666292]

>>6666289
i'm intrigued by this but too tired to parse this

care to explain?

[Anonymous No.6666293]

>>6666272
The Fibonacci sequence can be modeled by the function found here:
https://en.wikipedia.org/wiki/Fibonacci_sequence#Closed-form_expression
This means that the sequence grows (approximately) exponentially.
As n tends to infinity, <span class="math">\displaystyle F_n[/spoiler] is approximated better and better by <span class="math">\displaystyle \frac{\varphi^n}{\sqrt{5}}[/spoiler].
(The constants are defined in the link)
You would've done better even just using 2^G.

Though, still, that would've paled in comparison to other numbers here.

[Anonymous No.6666309]

>>6666292
The smallest number bigger than any finite number named by an expression in the language of set theory with a googol symbols or less.

[Anonymous No.6666340]

what's the smallest number you can come up with?

[Anonymous No.6666342]

>>6666340
define small

[Anonymous No.6666344]

>>6666342
the opposite of big

[Anonymous No.6666349]

>>6666340
0 has the lowest magnitude, I guess.

[Anonymous No.6666378]

>>6666340
obligatory:
length of your penis in millimeters

[Anonymous No.6666380]

>>6666378
plank lengths*

[Anonymous No.6666427]

Let Anon's number A be the largest known computable number at the time of this post.

A is not a constant. Every planck time, it grows at an exponential rate of (the number of possible configurations of the universe from the beginning to the the current moment)*(the number of shitposts ever made on 4 chan)^(the largest computable number at the new time). Then add one infinitesimal and a complex 1i because why the fuck not.

[Anonymous No.6666428]

>>6666427
Complex numbers are not ordered.

[Anonymous No.6666429]

>>6666428
Take the absolute value

[Anonymous No.6666482]

>>6658589
Here you go smartass, pic related.

[Anonymous No.6666501]

Over 9000!

[Anonymous No.6666553]

>>6666428
you can define an order relation on C.
It's just that it's not compatible with the field structure of it.

[Anonymous No.6666564]

>>6658589
-1/12

[Anonymous No.6666572]

Let x be the highest number in this thread.

define y as x+1.

[Anonymous No.6666576]

I've never understood the fascination with "large numbers," probably because no matter how big you imagine a number N to be, the next guy can just say, "lol N + 1."
As such, considering different orders of infinity is way cooler.

[Anonymous No.6666582]

>>6666572
xD

[Anonymous No.6666597]

>>6666576
True that, well only if you mean gayer.

[Anonymous No.6666717]

>>6666564
subtle

we have a winner, no matter what they're gonna say

[Anonymous No.6666743]

>>6666717

[Anonymous No.6666829]

>>6659360
There's pretty much no way to win after this post since any number you can define in a 4chan post will be definable in ZFC with that many symbols

Unless...

Define a new total order on R which is the standard order on R\{0} and x<0 is true for all x in R\{0}

0

I win fuck y'all

[Anonymous No.6666831]

>>6666829
*x <0 for all x in R\{0}

[Anonymous No.6666834]

>>6666829
>>6666831

Phone is breaking wtf

*x is less than 0 for all x in R\{0}

[Anonymous No.6666842]

>>6659375
To be quite honest, I would've said the same thing about people in this thread, and I am an engineer.

[Anonymous No.6666857]

>>6666829
>>6666831
>>6666834
> butthurt that nobody cares about my big number