A recursive definition is a way of defining an object in terms of itself, using a base case to provide initial values and a rule that describes how to generate subsequent values. This method allows for the construction of complex objects or sequences by repeatedly applying a rule, making it especially useful in mathematics and computer science for defining functions, sequences, and data structures. Recursive definitions can often be seen in processes like transfinite induction, where one can define functions or sets based on previously defined elements.
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