/sci/ - Science & Math

Probably as many TREE(TREE(TREE..... as you can fit and ! at the end to fill up the final digits.

>>10266863
I don't know if I made it clear, but you can apply functions with powers.
So you could do something like TREE^(some huge number)!!!....

>>10266858
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

a(n)=TREE(n)
b(n)=a(a(a(a(a(n)))))
c(n)=b(b(b(b(b(n)))))
d(n)=c(c(c(c(c(n)))))
e(n)=d(d(d(d(d(n)))))
f(n)=e(e(e(e(e(n)))))
g(n)=f(f(f(f(f(n)))))
h(n)=g(g(g(g(g(n)))))
i(n)=h(h(h(h(h(n)))))
j(n)=i(i(i(i(i(n)))))
k(n)=j(j(j(j(j(n)))))
l(n)=k(k(k(k(k(n)))))
m(n)=l(l(l(l(l(n)))))
m(m(m(m(m(9)))))

>>10267067
TREE^[5^13](9)
lots more space for bigger numbers.
such as:

a(n)=TREE^[n^n!](A(n,n))
b(n)=a^[a(TREE(n))](n!!!)
c(n)=b^[b(TREE(n))](n!!!)
d(n)=c^[c(TREE(n))](n!!!)
e(n)=d^[d(TREE(n))](n!!!)
f(n)=e^[e(TREE(n))](n!!!)
g(n)=f^[f(TREE(n))](n!!!)
h(n)=g^[g(TREE(n))](n!!!)
i(n)=h^[h(TREE(n))](n!!!)
j(n)=i^[i(TREE(n))](n!!!)
k(n)=j^[j(TREE(n))](n!!!)
k(999)

>>10267102
You didn't talk about any of this notation in the OP...

Are you saying that for example f^[6](3) = f(f(f(f(f(f(3)))))) ?
Is that what that exponentiation sign means?

1+a
a=1+a

>>10267123
yes, sorry.
it can also be used like 3^^3 = 3^3^3 = ~7 trillion

>>10266858
"The largest number expressible in a Tweet, other than this number, plus one."

>>10267126
last time I checked aleph null isn't a natural number.
>>10267140
well played. you have lots more characters for making this one even larger.
plus, I kind of this sort of stuff when I first had the idea. Like a special TR() function where TR(n) is the largest number with n levels of recursion.

>>10267140
this number plus 2

>>10267123
>>10267132
Okay, in that case, I think this is pretty good:

a(n)=TREE^[n](n)
b(n)=a^[a(n)](n)
c(n)=b^[b(n)](n)
d(n)=c^[c(n)](n)
e(n)=d^[d(n)](n)
f(n)=e^[e(n)](n)
g(n)=f^[f(n)](n)
h(n)=g^[g(n)](n)
i(n)=h^[h(n)](n)
j(n)=i^[i(n)](n)
j^[j^[j(9!!)](9)](9)

>>10267123
>>10267132
Okay, in that case, I think this is pretty good:

a(n)=TREE^[n](n)
b(n)=a^[a(n)](n)
c(n)=b^[b(n)](n)
d(n)=c^[c(n)](n)
e(n)=d^[d(n)](n)
f(n)=e^[e(n)](n)
g(n)=f^[f(n)](n)
h(n)=g^[g(n)](n)
i(n)=h^[h(n)](n)
j(n)=i^[i(n)](n)
k(n)=j^[j(n)](n)
l(n)=k^[k(n)](n)
m(n)=l^[l(n)](n)
o(n)=m^[m(n)](n)
p(n)=o^[o(n)](n)
q(n)=p^[p(n)](n)
r(n)=q^[q(n)](n)
r^[9](9)

>>10267189
>>10267218
very nice, very nice.
but i just had a new idea: self contained recursion.
it's like this:
a_0=3^77
a_n=TREE^[(a_n-1)!](a_n-1)
a_(a_0)
i don't know, maybe it's too similar to iterated functions.

>>10266858
infinity minus 1

>>10267218
>>10267231
Twitter counts unicode as single character so you can use larger numerical characters than 9, like 極.

>>10266858
Let graham's number=g
g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g^g

>>10267126
[math]\omega \not\in \mathbb{N}[/math]

>>10267252
I believe that simplifies to g^^204

>>10267140
>"The largest number expressible in a Tweet, other than this number, plus one."
Can you read?
>No linguistic self-references

>>10267248
seems interesting. using 京 for 10 quadrillion would create some true monsters.
>>10267252
graham's number has an external definition tho, plus you can create things way bigger with arrow notation
>>10267262
actually g^^205, the base counts too
>>10267263
I gave that a semi-pass because it figured out how to not directly reference itself. Still, I was looking for pure mathematical expressions.

>>10267276
That was already specified in the OP
>pure mathematical definition

>>10267175
That doesnt work you brainlet

>>10266858
>Numberphile
Terence Tao: Get mad pussy with your math skills

>>10267532 >>10267349 >>10267276 >>10267263 >>10267262 >>10267260 >>10267252

>>10267126
a wouldnt be a natural number

TREE(TREE(TREE(TREE... ...(9!!!... ...!!)
use as many TREEs as can be fit, then fill up the rest with factorials

>>10267552
that view to like ratio is statistically negligible and almost 100% of all the viewers wouldn't like

>>10267640
>he doesn't realize you can only like a video once but can watch it as many times as you want
Everyone who has watched has liked it immediately then gone on to watch it again (3 * G64) / 5,000,000,000 times.

>>10267552
>Numberphile
>Terence Tao: Get mad pussy with your math skills
nah

>>10267610
Why use factorials when you can throw a G64 in there?

>>10267610
>>10267680
TREE( is 5 characters, and at the end of the tweet you would need another series of close brackets which are only 1 character for each TREE(. [With 280 characters you can use exactly 56 TREE('s.]

With close brackets for each TREE(, this brings down the number of TREE('s to 46 without going over the limit. With this limit we have 4 more characters to use inside all of the TREE functions.
Insert the highest number we can obtain from 4 characters into the function.

TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE([huge number made from 4 characters]))))))))))))))))))))))))))))))))))))))))))))))

>>10267722
>Insert the highest number we can obtain from 4 characters into the function.
G64!
Or Graham's number factorial. Definitely bigger than 9!!!.

1. Describe a function, say F(x)
Function as follows where x is a natural number.
1. Take TREE(x). Let this equal to a number q.
2. Take TREE^^...(TREE(q) amount of arrows)...^^!!!..(TREE(q) amount of factorials)...!!! of (TREE(q)). Let this equal to a number w.
3. Take TREE^^...(TREE(w) amount of arrows)...^^!!!..(TREE(w) amount of factorials)...!!! of (TREE(w)). Let this equal to a number r.
4. e.t.c. with these steps. stop when the step number to the left has reached the number TREE(G64!).

2. Describe a new function, Z(x)
Function as follows where x is a natural number.
1. Take F(x). Let this equal to a number q.
2. Take F^^...(F(q) amount of arrows)...^^!!!..(F(q) amount of factorials)...!!! of (F(q)). Let this equal to a number w.
3. Take F^^...(F(w) amount of arrows)...^^!!!..(F(w) amount of factorials)...!!! of (F(w)). Let this equal to a number r.
4. e.t.c. with these steps. stop when the step number to the left has reached the number F(G64!).

3. Keep describing new functions, over and over again until the step number to the left, has reached the F(x)th new function.

Call this grand function, L(x).

Now in the tweet take L(L(L(L(.... ...(L(G64!))))))))... where L will fill up each of the 280 character spots.

>>10267762
this blew my mind but surely you can still get bigger than it

New variant:
-all forms of numbers allowed
-all computable functions from [http://googology.wikia.com/wiki/List_of_functions] allowed

Something I propose is:
d=D^[D(京)](TREE(京))
x={d^^d,d^^d,d^^d}
z(n)=H^[A(n,n)](n!!!)
p_0=z^[z(x)](x)
p_n=(z^[z(p_n-1)](p_n-1))!
r=TREE^[D(京!)](p_京)
f_0=p_(D(r)^京!!)
f_n=p_(D(f_n-1)^((京+n)!!))
b_0=f_r->f_r->f_r->f_r
b_n=b_n-1->b_n-1->b_n-1->b_n-1
a=b_D^[b_D^[b_D^[r](r)](r)](r!!)
TREE^[TREE(a!^^^(a!))](TREE(z(b_a)))

>>10267610
>>10267722
>putting the factorials in the parenthesis