Notation
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We use the following (ASCII) notation for hyperoperations:
b [1] x = b + x
b [2] x = b*x
b [3] x = b^x
For the left- and right-inverse we write:
b [r] x = y (r is called the rank of the operation)
y /[r] x = b
b [r]\ y = x
This is adapted from the quasigroup naming.
Forum Discussion
http://math.eretrandre.org/tetrationforum/showthread.php?tid=114&pid=1655#pid1655