Recursive Definition
- Tags
- math
A [see page 4, recursive] definition is one which uses the word or concept being defined in the definition itself. For example consider the recursive sequence of powers of 2 defined as \begin{align*} a_0 &= 1 & an+1 = 2a_n \qquad n ≥ 0 \end{align*}.
Any function with a domain of the natural numbers can be [see page 8, defined] recursively by specifying the value of the function at zero and then giving a rule for finding its value at any integer in terms of values at smaller integers.