zlacker

>>jeremy+(OP)
Now the contest for programmers: Write the biggest number in one line of code (80 characters, keywords count as 1 character, whitespace - 0) using computer language of choice(standard library with infinite integer type) that any reasonable programmer can prove that it is actually a finite number.

>>gglon+Hj
Mathematica has important whitespace for indicating multiplication, and it's not clear what counts as a keyword, so here are 80 copy-and-pasteable characters:

  u[n_][a_][b_]:=If[n==0,a b,Nest[u[n-1]@a,1,b]];Nest[u[#^#^#][#]@#&,9,u[99][9]@9]

u[n][a][b] gives a (Knuth's up arrow)^n b. The after-the-semicolon expression computes

  f(f(f(f(... u[99][9][9] fs total ... f(9) ... ))))

with the function f(n)=u[n^n^n][n][n]. This clearly results in a finite number, since it is just iterated iterated iterated iterated ... (finitely many "iterated"s) ... iterated exponentiation of finite numbers.

However, even when I try to compute (after $RecursionLimit=Infinity)

  Nest[u[#^#^#][#]@#&,2,u[2][2]@2]

my kernel crashes. This number is BIG.

There is one obvious way to make this number even bigger: make the base case yield a^b. However, then it's not Knuth's up arrow notation, so it's harder to debug by looking at the wikipedia page :). I used all my tricks (like using @) to get rid of extraneous characters, which gave me space to put #^#^# as the first argument of u. I still had 1 character remaining, so a 9 became 99. If you can squeeze a few more characters #^#^# and 99 should be substituted for u[#][#]@# and 9.

https://en.wikipedia.org/wiki/Knuth's_up-arrow_notation

>>evanb+7t
I just realized 99 should be replaced with "9!".