or inductive definition, n. the definition of a sequence by specifying its first term (by the base clause) and an algorithm (the recursion clause) by which to derive any term from its predecessor; for example, aⁿ is defined by
a⁰ = 1, a^k+1 = a × a^k;
and n! is defined by
0! = 1, n! = n(n - 1)!