Definition 3.1.2: A function f: _* ___* is called extendible if f(_) = _, and for each x,y___*, there is z___* so that f(xy) = f(x) z.
Definition 3.1.3: Given an extendible function f: _*____* and x___* we associate a derived function fx: _*____* defined for each y___* by fx(y) = z if f(xy) = f(x) z.
Definition 3.1.4: An extendible function f: _* ___* is said to be of finite index if the set of distinct derived functions {fx| x___*} is finite. The cardinality of this set is called the index of f and f is of infinite index if this set is infinite.
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