Discrete Math Notes:
Chapter 7: Recursion
7.4 Recursive definitions
Factorial, function f(n) = n! for n 0
recursive definition, the value of the function is defined in terms of the output value of the function on smaller input values
Recursion, is the process of computing the value of a function using the result of the function on smaller input values.
Basis, states that one or more specific elements are in the set.
recursive rule, shows how to construct larger elements in the set from elements already known to be in the set.
exclusion statement, states that an element is in the set only if it is given in the basis or can be
constructed by applying the recursive rules repeatedly to elements given in the basis.
Overview:
The value of a function is defined in terms of the output value of the function on smaller input values in
until the desired n! is reached, one can use the recursive definition for n! to find the value of the factorial function on a certain number for n. The procedure is known as recursion. The process of computing the value of a function using the function's result on smaller input values is known as recursion. Functions, sequences, and sets can all be defined via recursion. A recurrence relation,for example, is a recursive formulation of a sequence (along with initial values) since it explains how to compute the value of a term as a function of terms with smaller indices (i.e., terms that occur earlier in the sequence). A sequence is
a type of function in which the domain is a set of successive integers