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This blog post is for my notation in the xkcd forum game "My Number is Bigger!" It's the latest one, just so you know. Participants are encouraged to put their notations on blog posts. Note that you have to have a registered account to create a post.

Note: In addition, it is recommended to have examples of your notation and how it solves rather than just a formal definition (though definitions are also encouraged.

=Extension 0: Basic Notation

n|() = n^n

n|()X = n|X|X|...|X|X for X times

Special limit case:

n|(()) = n|()()...()() for n ()'s

Examples:

2|()() = 2|()|() = 4|() = 256

2|()()() = 2|()()|()() = 256|()() > 10^^257 = Mega

3|()() = 3|()|()|() = 27|()|() ~ 10^10^40

4|()()() = 4|()()|()()|()()|()() ~ 10^^^10^^^10^^^10^^10^^10^^10^10^10^619

3|(()) = 3|()()() = 3|()()|()()|()() ~ 10^^10^^10^10^40

...

Analysis

n|() = n^n ~ f_2(n)

n|()() = n|()()...()() for n times, so it has growth f_3(n)

n|()()() iterates ()(), so it has growth rate f_4(n)

n|()()...()() for m ()'s, in general, has growth rate f_m+1(n)

n|(()) = n|()()...()() for n times, so it has growth f_w(n)

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