User blog:Username5243/XKCD My Number is Bigger Notations

This blog post is for the notations 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 this post. Note that you have to have a registered account to edit this 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). Once we get really high in the thread you may want to split your notation into your own blog post. If you choose to do so, please link to that post.

Standard Notations
Arrow Notation

Chained Arrow Notation

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)