User blog:Googleaarex/ASN Notation

Let a...[b] = aa...aa/w b a's. Then a....[b] = a...[a...[...[a...[a]]...]]/w b nested, a.....[b] = a....[a....[...[a....[a]]...]]/w b nested, etc.

Let a...[b,c] = a...{...}...[b] /w c+2 .'s, a....[b,c] = a...[b,a...[b,...[...[b,a...[b]]]...]]/w c nested, a...[b,c,d] = a...{...}...[b,c] /w d+2 .'s, etc.

Support a...[b[2]c] = a...[b,b...b,b]/w c b's, a...[b[2]c,d] = a...{...}...[b[2]c]/w d+2 .'s, a...[b[2]c[2]d] = a...[b[2]c,c...c,c]/w d c's, a...[b[3]c] = a...[b[2]b...b[2]b]/w c b's, etc.

Finally, we have a....[b[x]c] = a...[b[a...[b[...[a...[b[a...[b[x]c]]c]]...]c]]c]/w y nested, a...[b[x,y]c] = a...{...}...[b[x]c]/w y+2 .'s.

The limit is a...[a[a[...]a]a]/w a nested = AndSoOn(a).

GoogolASN = AndSoOn(Googol)

Example

 * 3...[3,3]
 * 3.....[3]
 * 3....[3....[3....[3]]]
 * 3....[3....[3...[3...[3...[3]]]]]
 * 3....[3....[3...[3...[333]]]]
 * 3....[3....[3...[333...333]]]/w 333 3's
 * 3....[3....[333...333]]/w 333...333 3's /w 333 3's
 * 3....[3...[3...[...[3...[3...[3]]]...]]]/w 333...333 nested /w 333...333 3's /w 333 3's
 * 3....[3...[3...[...[3...[333]]...]]]
 * 3....[3...[3...[...[333...333]...]]]/w 333 3's