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===Functional recursion===
A [[function (mathematics)|function]] may be recursively defined in terms of itself. A familiar example is the [[Fibonacci number]] sequence: ''F''(''n'') = ''F''(''n'' − 1) + ''F''(''n'' − 2). For such a definition to be useful, it must be reducible to non-recursively defined values: in this case ''F''(0) = 0 and ''F''(1) = 1.
===Proofs involving recursive definitions===
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