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