Recursion: Difference between revisions

Revision as of 14:21, 24 May 2002

Revision as of 14:22, 24 May 2002

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'''The recursion theorem.''' Given a set ''X'', an element ''a'' of ''X'' and a function ''f'':''X''->''X'', then there is a unique function ''F'':'''N'''->''X'' such that

:''F''(0)=''a'', and

:''F''(''n''+1)=''f''(''F''(''n''))   for any [[natural number]] ''n''>0.

''[A proof of the recursion theorem from set theory is needed]''