User blog comment:Googleaarex/Make an extension of the notation/@comment-25371339-20140923221002/@comment-25371339-20140924004948

Extension:

a-^'-b = a-^*(^*(^*(...(^*(^*(^*(^)*)*)*)...)*)*)*-a with b levels

a-^'^-b is next level.

We can have a-^'^^-b, a-^'^^^-b, etc.

Also a-^'^*-b, a-^'^**-b, etc.

Then:

a-^'^'-b = a-^'^*(^*(^*(...(^*(^*(^*(^)*)*)*)...)*)*)*-a with b levels

a-^'*-b = a^'^'^'...'^'^'^'-a with b levels

etc.

Then:

a-^''-b = a-^'*(^*(^*(...(^*(^*(^*(^)*)*)*)...)*)*)*-a with b levels

This makes a visible pattern.

Limit is a-^'(^'(^'(...(^'(^'(^')')')...)')')'-b