|Description: Define the mapping
operation or set exponentiation. The set of all
functions that map from B to A is written (A ↑m B) (see
mapval 6011). Many authors write A followed by B as a superscript
for this operation and rely on context to avoid confusion other
exponentiation operations (e.g. Definition 10.42 of [TakeutiZaring]
p. 95). Other authors show B as a prefixed superscript, which is
read "A pre B " (e.g. definition of [Enderton] p. 52).
Definition 8.21 of [Eisenberg] p. 125
uses the notation Map(B,
A) for our (A ↑m B). The up-arrow is used by Donald Knuth
for iterated exponentiation (Science 194, 1235-1242, 1976). We
the first case of his notation (simple exponentiation) and subscript it
with m to distinguish it from other kinds of exponentiation.
(Contributed by NM, 15-Nov-2007.)|