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Rice's theorem
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==Examples== Given a program ''P'' which takes a natural number ''n'' and returns a natural number ''P''(''n''), the following questions are undecidable: * Does ''P'' terminate on a given ''n''? (This is the [[halting problem]].) * Does ''P'' terminate on 0? * Does ''P'' terminate on ''all'' ''n'' (i.e., is ''P'' [[general recursive function|total]])? * Does ''P'' terminate and return 0 on every input? * Does ''P'' terminate and return 0 on some input? * Does ''P'' terminate and return the same value for all inputs? * Is ''P'' equivalent to a given program ''Q''?
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