Let us, for the sake of convenience, call G(1, G(1)) A. Your number, obviously, is less than (A) ^A^A^A^ (A * (A ^A^A^A^A) ). That number is less than A^A^A^A^A^A^A^A^A^A, which is less than Ack(A, 11, 4).
Now let us take G(1, G(1)+1), as opposed to Ack(G(1, G(1)), 11, 4). G(1, G(1)+1) is equal to G(G(1), G(1)), so we are comparing G(A) and Ack(A, 11, 4). I shouldn't have to explain why G(x) grows faster than Ack(x, 11, 4).
Okay, so that's (G(G(1, G(1)+2)^100^100^100^100))*((G(1, G(1)+2)^100^100^100^100)^2). 100^100^100^100 is 100^100^10^200, which is equal to 100^10^(2*(10^200)), which is less than 100^10^10^201, which is 10^(2*(10^10^201)), which is less than 10^10^10^202. And (10^10^10^202)^2 is 10^(2*(10^10^202)), which is less than 10^10^10^203, so your number is less than (G(G(1, G(1)+2)^10^10^10^203))*(G(1, G(1)+2)^10^10^10^203). Since G(1, G(1)+3) is massively greater than G(1, G(1)+2), your number is less than G(G(1, G(1)+3))*G(1, G(1)+3). Since G(G(x, y)) is really just G(x, y+1), your number is less than G(1, G(1)+4)*G(1, G(1)+3), which is less than G(1, G(1)+5).
Say something silly, Laugh 'til it hurts, Take a risk, Sing out loud, Rock the boat, Shake things up, Flirt with disaster, Buy something frivolous, Color outside the lines, Cause a scene, Order dessert, Make waves, Get carried away, Have a great day!
This is dufhugth20's substitute account. On two out of three computers in my house, I've been locked out of my main account, which is the reason why I've made this account in the first place. See me as the same guy, or "dufhugth20". Anybody who makes accounts and claims to be me are lying, unless I say that I have to make another account.
Well, well, well. You have finally forced me to activate Project DAOT.
(Note: In this, we assume that 0 does not count as a positive integer.)
In which a,b, and c must be positive integers, X is shorthand for at least 3 positive integers, and Y is shorthand for at least 1 positive integer.
DN(a) = a
DN(a,1) = DN(a+1)
DN(a,b) = DN(a+1,b-1)
DN(a,b,1) = DN(a,b)
DN(a,1,c) = DN(a)
DN(a,b,c) = DN(a,DN(a,b-1,c),c-1)
As you can see, DN(a,b,c)=Ack(a,b,c).
DN( X ,1) = DN( X )
DN(1, X ) = DN( X )
DN( X ,1, Y) = DN( X , Y )
DN( Y ,a,b,c) = DN( Y ,a,DN( Y , b-1,c),c-1)
As you can see, DN(10,10,10,x,2)>G(x) because DN(10, 10, 10, DN(10, 10, x-1, 2), 1) > Ack(10,10,G(x-1)) because DN(10,10,10,y)>Ack(10,10,y) and because DN(10,10,10,1,2)>Ack(10,10,10).
As you can see, DN(10,10,10,x,3)>G(x,x) because DN(10,10,10,DN(10,10,x-1,3),2)>G(G(x,x-1)) because DN(10,10,10,x,2)>G(x) and because DN(10,10,10,1,3)>G(1,1).
Now, let’s take a look at that monstrous salad number of yours. Long story short, it is less than G(G(Googleplex^1000), G(Googleplex^1000)). Far less than I was expecting. Therefore, my number is:
[Status] "I tried to save you... but instead I got you killed."
Very important news below.
I have forgotten my passwords to my other two accounts. Since the power went out yesterday, two of the computers I use have logged me out, and I have forgotten my names to those Twitch accounts as well. So, from now on, this will be my main account. Thank you for reading.
Say something silly, Laugh 'til it hurts, Take a risk, Sing out loud, Rock the boat, Shake things up, Flirt with disaster, Buy something frivolous, Color outside the lines, Cause a scene, Order dessert, Make waves, Get carried away, Have a great day!
[Status] "I tried to save you... but instead I got you killed."
Very important news below.
I have forgotten my passwords to my other two accounts. Since the power went out yesterday, two of the computers I use have logged me out, and I have forgotten my names to those Twitch accounts as well. So, from now on, this will be my main account. Thank you for reading.
That number is not defined. You can't just spew out random characters and expect it to be a number. I will, however, graciously define it for you. Also, please stop creating meaningless salad numbers and actually invent new functions.
In which a is a positive integer, b is a positive integer strictly less than a, X is shorthand for any amount of positive integers possibly separated by any separators up to and including aD-separators, and Y is shorthand for any amount of positive integers possibly separated by any separators up to but not including aD-separators.
DN( X |^a Y) = DN( Z ), where Z is shorthand for DN(DN( Y ),a,3) copies of DN( X ) in parentheses, separated by commas and every DN(DN( Y ),b,3) copies by a bD-separator for all b between 1 and a-1 inclusive.
In which a and b are positive integers, and Y is shorthand for at least 2 positive integers, call the number of integers in Y c.
<a,b> = DN( X ), where X is shorthand for b copies of a.
< Y , a> = DN( Z ), where Z is shorthand for a copies of < Y > separated by (c-1)D-separators.
(
Ack(a, b, 1) = a+b
Ack(a, 1, c) = a
Ack(a, b, c) = Ack(a, Ack(a, b-1, c), c-1)
G(1) = Ack(10, 10, 10)
G(a) = Ack(10, 10, G(a-1))
G(a, 1) = G(a)
G(a, b ) = G(G(a), b-1)
)
G(1, G(1))^100^100^100^100 * G(1, G(1))^100^100^100^100
Alright... let's put in some more parentheses. (This is being favorable with the grouping, by the way)
(G(1, G(1))) ^100^100^100^ (100 * (G(1, G(1)) ^100^100^100^100) )
Let us, for the sake of convenience, call G(1, G(1)) A. Your number, obviously, is less than (A) ^A^A^A^ (A * (A ^A^A^A^A) ). That number is less than A^A^A^A^A^A^A^A^A^A, which is less than Ack(A, 11, 4).
Now let us take G(1, G(1)+1), as opposed to Ack(G(1, G(1)), 11, 4). G(1, G(1)+1) is equal to G(G(1), G(1)), so we are comparing G(A) and Ack(A, 11, 4). I shouldn't have to explain why G(x) grows faster than Ack(x, 11, 4).
G(1, G(1)+2)
Fabastic!
(
Ack(a, b, 1) = a+b
Ack(a, 1, c) = a
Ack(a, b, c) = Ack(a, Ack(a, b-1, c), c-1)
G(1) = Ack(10, 10, 10)
G(a) = Ack(10, 10, G(a-1))
G(a, 1) = G(a)
G(a, b ) = G(G(a), b-1)
)
Okay, so that's (G(G(1, G(1)+2)^100^100^100^100))*((G(1, G(1)+2)^100^100^100^100)^2). 100^100^100^100 is 100^100^10^200, which is equal to 100^10^(2*(10^200)), which is less than 100^10^10^201, which is 10^(2*(10^10^201)), which is less than 10^10^10^202. And (10^10^10^202)^2 is 10^(2*(10^10^202)), which is less than 10^10^10^203, so your number is less than (G(G(1, G(1)+2)^10^10^10^203))*(G(1, G(1)+2)^10^10^10^203). Since G(1, G(1)+3) is massively greater than G(1, G(1)+2), your number is less than G(G(1, G(1)+3))*G(1, G(1)+3). Since G(G(x, y)) is really just G(x, y+1), your number is less than G(1, G(1)+4)*G(1, G(1)+3), which is less than G(1, G(1)+5).
G(1, G(2))
Not really, it takes me less time than you might think.
(
Ack(a, b, 1) = a+b
Ack(a, 1, c) = a
Ack(a, b, c) = Ack(a, Ack(a, b-1, c), c-1)
G(1) = Ack(10, 10, 10)
G(a) = Ack(10, 10, G(a-1))
G(a, 1) = G(a)
G(a, b ) = G(G(a), b-1)
)
G(1, G(3))
Word of advice: Raising numbers to some teeny tiny power is pretty much useless if you just slap it on.
1e+99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
(
Ack(a, b, 1) = a+b
Ack(a, 1, c) = a
Ack(a, b, c) = Ack(a, Ack(a, b-1, c), c-1)
G(1) = Ack(10, 10, 10)
G(a) = Ack(10, 10, G(a-1))
G(a, 1) = G(a)
G(a, b ) = G(G(a), b-1)
)
Dude. If you don't understand the current number, don't embarrass yourself. Your number was beaten last page.
G(1, G(3)+2)[/b]
Nope. No infinite numbers allowed. It's even discussed in the video.
G(1, G(3)+3)
G(1, G(Googleplex)+Googleplex)
(Still one-upping, if possible.)
G(2, G(Googleplex)+(Googleplex)+Googleplex)
Read the text below.
This is dufhugth20's substitute account. On two out of three computers in my house, I've been locked out of my main account, which is the reason why I've made this account in the first place. See me as the same guy, or "dufhugth20". Anybody who makes accounts and claims to be me are lying, unless I say that I have to make another account.
Bazinga!
G(((((((((((2, G(Googleplex)+(Googleplex)+Googleplex)*(tree(3)*999999999999999999999999999999999999999999999999999999)^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^3))*99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999)googolplex)^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^K ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^K)^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^(Grahams number!*2)*K!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^K)
Well, well, well. You have finally forced me to activate Project DAOT.
(Note: In this, we assume that 0 does not count as a positive integer.)
In which a,b, and c must be positive integers, X is shorthand for at least 3 positive integers, and Y is shorthand for at least 1 positive integer.
DN(a) = a
DN(a,1) = DN(a+1)
DN(a,b) = DN(a+1,b-1)
DN(a,b,1) = DN(a,b)
DN(a,1,c) = DN(a)
DN(a,b,c) = DN(a,DN(a,b-1,c),c-1)
As you can see, DN(a,b,c)=Ack(a,b,c).
DN( X ,1) = DN( X )
DN(1, X ) = DN( X )
DN( X ,1, Y) = DN( X , Y )
DN( Y ,a,b,c) = DN( Y ,a,DN( Y , b-1,c),c-1)
As you can see, DN(10,10,10,x,2)>G(x) because DN(10, 10, 10, DN(10, 10, x-1, 2), 1) > Ack(10,10,G(x-1)) because DN(10,10,10,y)>Ack(10,10,y) and because DN(10,10,10,1,2)>Ack(10,10,10).
As you can see, DN(10,10,10,x,3)>G(x,x) because DN(10,10,10,DN(10,10,x-1,3),2)>G(G(x,x-1)) because DN(10,10,10,x,2)>G(x) and because DN(10,10,10,1,3)>G(1,1).
Now, let’s take a look at that monstrous salad number of yours. Long story short, it is less than G(G(Googleplex^1000), G(Googleplex^1000)). Far less than I was expecting. Therefore, my number is:
DN(10,10,10,DN(10,10,10,10^10^100^1000,2),3)
DN(10,10,10,DN(10,10,10,10^10^100^1000,2),3)
+ 9000
We're going back.
DN(10,10,10,DN(10,10,10,10^10^100^1000,2),3)+9002
Still trying to one-up. I can't one-up the complex numbers.
DN(20,20,20,20DN(20,20,20,20,20^200^2,000^20,000+3),4)+9999
[Avatar] David, from my cancelled RPG
[Status] "I tried to save you... but instead I got you killed."
Very important news below.
I have forgotten my passwords to my other two accounts. Since the power went out yesterday, two of the computers I use have logged me out, and I have forgotten my names to those Twitch accounts as well. So, from now on, this will be my main account. Thank you for reading.
In which a,b, and c must be positive integers, X is shorthand for at least 3 positive integers, and Y is shorthand for at least 1 positive integer.
DN(a) = a
DN(a,1) = DN(a+1)
DN(a,b) = DN(a+1,b-1)
DN(a,b,1) = DN(a,b)
DN(a,1,c) = DN(a)
DN(a,b,c) = DN(a,DN(a,b-1,c),c-1)
DN( X ,1) = DN( X )
DN(1, X ) = DN( X )
DN( X ,1, Y) = DN( X , Y )
DN( Y ,a,b,c) = DN( Y ,a,DN( Y , a,b-1,c),c-1)
<a,b> = DN( X ), where X is shorthand for b copies of a separated by commas.
My number: <10, 10>
<Googleplex, Googleplex>
<<Googolplex+1, Googolplex+1>, <Googolplex+1, Googolplex+1>>
<<Googolplex+1, Googolplex+1>, <Googolplex+1, Googolplex+2>>
<<<<Googolplex+1, Googolplex+1>, <Googolplex+1, Googolplex+2>>,4,5,6>>
<<<<Googolplex+2, Googolplex+2>, <Googolplex+2, Googolplex+3>>,7,8,9>>
[Avatar] David, from my cancelled RPG
[Status] "I tried to save you... but instead I got you killed."
Very important news below.
I have forgotten my passwords to my other two accounts. Since the power went out yesterday, two of the computers I use have logged me out, and I have forgotten my names to those Twitch accounts as well. So, from now on, this will be my main account. Thank you for reading.
That number is not defined. You can't just spew out random characters and expect it to be a number. I will, however, graciously define it for you. Also, please stop creating meaningless salad numbers and actually invent new functions.
In which a is a positive integer, b is a positive integer strictly less than a, X is shorthand for any amount of positive integers possibly separated by any separators up to and including aD-separators, and Y is shorthand for any amount of positive integers possibly separated by any separators up to but not including aD-separators.
DN( X |^a Y) = DN( Z ), where Z is shorthand for DN(DN( Y ),a,3) copies of DN( X ) in parentheses, separated by commas and every DN(DN( Y ),b,3) copies by a bD-separator for all b between 1 and a-1 inclusive.
In which a and b are positive integers, and Y is shorthand for at least 2 positive integers, call the number of integers in Y c.
<a,b> = DN( X ), where X is shorthand for b copies of a.
< Y , a> = DN( Z ), where Z is shorthand for a copies of < Y > separated by (c-1)D-separators.
<2,2,2,2,100>