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{\displaystyle { ext{for all integers }}n> ,~{ ext{ fib}}(n):={ ext{fib}}(n- )+{ ext{fib}}(n- ).} many mathematical axioms are based upon recursive rules. for example, the formal definition of the natural numbers by the peano axioms can be described as: "zero is a natural number, and each natural number
has a successor, which is also a natural number." [ ] by this base case and recursive rule, one can generate the set of all natural numbers. other recursively defined mathematical objects include factorials , functions (e.g., recurrence relations ), sets (e.g., cantor ternary set ), and fractals . [...
https://en.wikipedia.org/wiki/Recursion