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Informally speaking, a recursive definition defines something (e.g., a function or a procedure) in terms of itself (but not in such a way to create an unending process!). For example, we can define the function f(n) for n! the following way:


Often definitions or descriptions by recursion lend themselves to proofs by induction.

Here is another example, for the Towers of Hanoi. We define the procedure move(n,a,b,c) for moving a stack of disks numbered tex2html_wrap_inline1331 from peg a to peg b using peg c:

  1. If n>1 then move(n-1,a,c,b).
  2. Move disk n from a to b.
  3. If n>1 then move(n-1,c,b,a).

Carl Lee
Wed Apr 21 08:17:28 EDT 1999