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List of undecidable problems
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{{Short description|Computational problems no algorithm can solve}} In [[computability theory]], an '''[[undecidable problem]]''' is a [[decision problem]] for which an [[effective method]] (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a [[recursive set]]; see the article [[Decidable language]]. There are [[uncountable set|uncountably]] many undecidable problems, so the list below is necessarily incomplete. Though undecidable languages are not recursive languages, they may be [[subset]]s of [[Alan Turing|Turing]] recognizable languages: i.e., such undecidable languages may be recursively enumerable. Many, if not most, undecidable problems in mathematics can be posed as [[word problem (mathematics)|word problems]]: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see [[List of statements undecidable in ZFC]].
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