User blog comment:KthulhuHimself/Terminal array notation./@comment-25601061-20151021181658/@comment-27014275-20151022062219

It's undefined. You probably mean: <0,<2>>, or <0<1>2>. Make sure that when you get to writing an array, the parentheses will only match at the very end of it.

<0,<2>>, However, is equal to: <0,0,0,...,0,1,<1>> And to solve this, you first need to define f(n) and n. So suppose that f(n)=n!, and n=3, <0,<2>> = <0,0,0,1<1>> = <0,0,3<1>>

Now suppose that 3!!!...!!! is a structure called x, then:

3    3     .    3

\/    \/     .   \/

x    x    . x

\/     \/    .   \/

x     x    . x

...  < ... <    ... < 3

\/     \/     .    \/

x      x    . x

is <0,0,1>. Now suppose that we call the structure above x, and put the new x in the structure above (only that now we refer to levels of recursion rather than recursion itself), you now have <0,0,2>. Repeat.

Now as a reminder, <0,<1>> = <0,0,0,...,0,1> (n entries),

and <1,<1>> = <0,0,0,...,0,1> (<0,0,0,...,0,1> (n entries) entries)

or essentially, for >

We just replace the original structure x (3!!!...!!!), with <0,0,0,...,0,1>

And there you have it, <0,<2>>