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Cutler's bar notation ：ウィキペディア英語版

Cutler's bar notation

In mathematics, Cutler's bar notation is a notation system for large numbers, introduced by Mark Cutler in 2004. The idea is based on iterated exponentiation in much the same way that exponentiation is iterated multiplication.
==Introduction==
A regular exponential can be expressed as such:
:

\begin   a^b & = & \underbrace \\   & & b\mboxa  \end

However, these expressions become arbitrarily large when dealing with systems such as Knuth's up-arrow notation. Take the following:
:

\begin & \underbrace}}} & \\  & b\mboxa  \end

Cutler's bar notation shifts these exponentials counterclockwise, forming

\bar a

. A bar is placed above the variable to denote this change. As such:
:

\begin  \bar a = & \underbrace}}} & \\   & b\mboxa  \end

This system becomes effective with multiple exponent, when regular denotation becomes too cumbersome.
:

\begin ^^}}} & \\   & }}  \bar a =  \bar a\\   c \mbox b  \end

The same pattern could be iterated a fourth time, becoming

\bar a_

. For this reason, it is sometimes referred to as Cutler's circular notation.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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