my number is bigger!

The rules are simple:

• no infinity
• no uncomputable functions
• no directly referencing the previous number
  We'll start with 9 instead of 9,999.

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

f₉(9)

f₉(9)^^f₉(9) (i hope this isnt uncomputable)

f₉(f₉(9)^^f₉(9))

f₉(f₉(9)^^f₉(9)) uu f₉(f₉(9)^^f₉(9))

I'm using the Ultrex formula thingamajig. Check the Wiki page on the Googology page.

f_{ψ₀(Ω_Ω)}(9)

f_lim(BMS) + psi(W_w)_(9)

f_{lim(MMS)+Y(1,3)+ψ(Ω_Ω)}(9999)

f_lim(BMS) + psi(W__w)^^w+1(9) where W__w means the limit of bucholz function

Not even close. MMS means Mutant Matrix System.

I don't know what any of these mean so I guess I'll just combine the last 2 together
(f_lim(BMS) + psi(W__w)^^w+1(9))^^^(f_{lim(MMS)+Y(1,3)+ψ(Ω_Ω)}(9999))

d^5(99)
Loader's number

Okay. I might be doing a salad notation here, but I have an idea.
1: Define an array fx(x,x2,x3...).
2: Define f1(x,x2,x3...) to be equal to a power tower of each of its terms. Example: f1(1,2,3) -> 1^2^3
3: Now, define f(x,x2,x3...) to have its last 2 terms replaced with a subarray of itself minus its first digit and the main array's f-number subtracted by one if it's longer than 3 terms. Example: f2(1,2,3) -> f1(1,f2[2,3)),
4: Now if it's a 2-length array with an f number above one, then reduce its f number and increment each of its terms by one until the f number is one, also incrementing the f-number of the outer arrays.
Example: f5(1,2,3,4) -> f4(1,2,f5(2,3,4)) -> f4(1,2,f4(2,f5(3,4))) -> f9(1,2,f9(2,f1(7,8))) -> f9(1,2,f9(2,5764801)) -> f17(1,2,f1(11,5764809)) -> f17(1,2,f1(11,5764809)) -> f17(1,2,11^5764809)) -> f16(1,f17(2,11^5764809)) -> f32(1,f1(18,11^5764809)) -> f32(1,18^[11^5764809]) -> f1(33,18^[11^5764809]) -> roughly 22^18^11^5764809.
5: Now, recurse arrays like this. f[fx(x,x2,x3...)].(x,x2,x3...)., which ill shorten to f^2x(x,x2,x3...), and now, if you do that iteration x times, you call it f^wx(x,x2,x3...).
6: Now, that w is an ordinal, which can be swapped out for any ordinal you like.
What is f^[e_e_0]10(10,10,10,10,10,10...[ f^[e_e_0]10(10,10,10)times]...10,10,10). I'll call it Baileyboy's Number.