undecidable.
Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
Meaning & usage
Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
(of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)
Where this word comes from
Etymology tree English un- English decide Proto-Indo-European *-dʰlom Proto-Italic *-ðlom Proto-Italic *-ðlis Latin -bilis Latin -ābilis Old French -ablebor. Middle English -able English -able English decidable English undecidable From un- + decidable.
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Definitions, grammatical labels, IPA, etymology and examples: Wiktionary contributors, extracted by Kaikki / Wiktextract. Adapted under CC BY-SA 4.0. Selected fields and authored examples are shown; third-party quotations and audio are omitted. See contributor history.
Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.