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(Or in other words) Defining , a formula or functions, for all
with by defining and then defining
for , in terms of ,
, , .
The obvious example is factorials, which can be defined by
for and .
The number of ways to order a set of
Another example is the Ackermann function, which appears on example sheet 2.
This is true for
. So, to order an
-set, choose the
ways and then order the remaining