Principle of Recursive Definition/Also presented as

Theorem

The Principle of Recursive Definition can also be presented as:

For any mapping $f: T \to T$ and any $a \in T$, there exists an infinite sequence $a_0, a_1, \ldots, a_n, a_{n + 1}, \ldots$ such that:
$a_0 = a$
$a_{n + 1} = \map g {a_n}$


Sources

  • 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 8$ Definition by finite recursion
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