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===The recursion theorem===
In [[set theory]], this is a theorem guaranteeing that recursively defined functions exist. Given a set {{mvar|X}}, an element {{mvar|a}} of {{mvar|X}} and a function {{math|''f'': ''X'' → ''X''}}, the theorem states that there is a unique function
:<math>F(0) = a</math>
:<math>F(n + 1) = f(F(n))</math>
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