No.3342
Using letters, symbols and numbers write the largest number you can in 100 characters or fewer.
No infinity/s and if you make up a symbol/operation/etc you must be able to define it with in the 200 characters.
I'll start with a relatively small number to get the ball rolling.
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
pic unrelated
No.3343
A pointless challenge, since each successive post can outdo the previous post with the following:
"The sum of every natural number smaller than the number >>3342 posted"
(replace post number as appropriate).
It's short and guaranteed to be larger.
No.3344
9.9 x 10^9999999999999
Weird thread.
No.3345
>>3343
oh yeah. well lets say then you can't refer to what other posts have said. it has to be self contained.
>>3344
9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
No.3346
No.3348
Busy Beaver Number 9999999999999999999999999999999999999 state 99999999999999999999999999999 symbols
// get fucking rekt
No.3349
>>3345
9^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^9
see https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
No.3351
>>3348
BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(BB(TREE(3))))))))))))))))))))))))
No.3352
Here's a number I made up, symbolized by ¶.
¶ - the sum of all numbers that have been thought
No.3353
>>3351
you got me
>>3352
not bad
No.3396
ε0
Def:
- ω1 is the smallest infinite ordinal
- ε0 = sup {ω, ω^ω, ω^(ω^ω), ω^(ω^(ω^ω)), …}
/end thread
No.3400
No.3401
>>3396
you can use Knuth's up-arrow notation though; >>3349
ε₀ = ω^^ω
No.3403
>>3401
>>3400
ε0 is the upper limit of the largest countable ordinal. You can reach it with knuth's notation, but ultimately ε0 is what is reached before you get to uncountable ordinals.
No.3411
>nobody's written Graham's Number yet
wew
No.3418
>>3411
other anons have already give much larger numbers than grahams number.
>>3403
>>3401
>>3400
>>3396
woah woah woah.. you can't use infinite ordinals because infinities are not allowed, especially not on their own as that's just (an) infinite. you might be able to get away with using it to construct a function from the fast growing hierarchy, as that would out-put a finite number but you'd still be using the properties of an infinite to get it, so i don't know if that would still be against the rules.
No.3425
>>3349
Expanding on up-arrow notation, using the n-arrow operator ↑^n:
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)9)9)9)9)9
No.3427
x
x is defined as largest number less than infinity
No.3428
would "the sum of all numbers" count as an infinity?
No.3430
>>3427
>>3428
I can prove that your numbers don't exist as their existence would cause a paradox
No.3444
No.3448
>>3444
okay
>>3427
your number plus one cannot exist
the relation "being bigger" is defined through plus one operation
therefore your number isn't a natural number as you can always add one to a natural number
>>3428
similar to >>3428 except that here I try to define sum of all numbers plus itself
No.3462
>>3448
ok how is this: the sum of all numbers except for that sum itself
No.3464
9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^99
No.3465
>>3462
yeah no
every natural number n has it's successor, n+1.
the sum of all numbers except for that sum itself plus one is greater than the sum of all numbers except for that sum itself, but it's not that sum itself, therefore it must be included in the sum.
but, the sum of all numbers except for that sum itself is lesser than the sum of all numbers except for that sum itself plus one, therefore it cannot include the sum of all numbers except for that sum itself plus one in the sum, which is a paradox.
therefore the sum of all numbers except for that sum itself, if it exists, isn't a natural number.
No.3480
>>3465
>therefore the sum of all numbers except for that sum itself, if it exists, isn't a natural number
OP didnt say it has to be a natural number
No.3481
>>3352
I'm changing the symbol to this:
🍆
No.3483
>>3480
okay so I have to get to a contradiction
so in >>3465 I proved that your number cannot be a natural number. however, a sum of natural numbers is always a natural number (since you can break summation down into iterated successor relation, which is the relation that defines natural numbers as a set).
so we can see that your number is a natural number, yet cannot be a natural number, therefore your number cannot exist.
No.3590
G64↑^(G64↑^(G64↑^(G64↑^(9↑^(9↑^(9↑^(9↑^(9↑^(9↑^(9↑^(9↑^(G64↑^(9↑^(9↑^(9↑^(9↑↑9)9)9)9)9)9)9)9)9)9)9)9)9)9)9)9)G64
I peppered some grahams numbers into the arrow notation post
No.3594
♪(x) is x with the decimal point removed. ♪(pi)
#ITried
No.3595
>>3351
this is still winning by far m8s
No.3596
>>3351
>>3595
Hmm.
BB!(x)=BB(BB(x)).
BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(BB!(TREE(3))))))))))))))))
No.3597
>>3590
Also, why limit yourself to G64? Why not make that G99?
No.3599
>>3596
TREE(3)=t
n'=n+1
D(0)=t
D(n')=BB(D(n))
E(0)=t
E(n')=D(E(n))
F(0)=t
F(n')=E(F(n))
G(0)=t
G(n')=F(G(n))
G(G(t))
No.3600
>>3599
TREE(3)=t
n'=n+1
M(0,0)=t
M(0,n')=BB(M(0,n))
M(n',m)=M(n,M(n,m))
N(0)=t
N(n')=M(N(n),N(n))
N(t)
No.3602
>>3600
>89 chars, if I counted correctly
TREE(3)=t
n'=n+1
M(0,0)=t
M(0,n')=BB(M(0,n))
M(n',m)=M(n,M(n,m))
N(0)=t
N(n')=M(N(n),N(n))
N(N(N(N(t))))
No.3612
>>3602
>It was actually 88
TREE(3)=t
n'=n+1
M(0,0)=t
M(0,n')=BB(M(0,n))
M(n',m)=M(n,M(n,m))
N(0)=t
N(n')=M(N(n),N(n))
N(N(N(N(N(t)))))
No.3629
>>3612
TREE(n) is proved finite by Kruskal's tree theorem.
TREE(9)=t
n'=n+1
M(0,0)=t
M(0,n')=BB(M(0,n))
M(n',m)=M(n,M(n,m))
N(0)=t
N(n')=M(N(n),N(n))
N(N(N(N(N(t)))))
No.3630
99!E+9!^9!^9!^9!^9!^9!^9!^9!^9!^9!^9!^99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!
looks big enough
No.3635
>>3630
This doesn't even beat g64, let alone >>3351
No.3643
I define # to be the amount of electrons in the universe
Using the n-arrow operator ↑^n:
#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑^(#↑↑#)#)#)#)#)#)#)#)#)#)#)#)#)#)#)#)#
No.3644
>>3643
>the amount of electrons in the universe
but electrons are a grand canonical ensemble
No.3859
>>3643
>I define # to be the amount of electrons in the universe
One?
No.3860
hey niggas
Can someone explain TREE in VERY, very, very, very layman terms
No.3861
>>3481
I define "ß", as absolute value of the sum of all numbers that have been thought.
ß
No.3886
>>3861
I define ":^)" as value of the sum of all numbers that have Not been thought of.
:^)