In mathematics and computer science, the quality of a problem or statement being capable of being determined as either true or false through a definite process.
From 'decidable' plus the suffix '-ity.' The term emerged in early 20th-century mathematical logic and computer science as researchers formalized what problems could be 'solved' by algorithms.
Some math problems have 'decidability' issues—like certain questions in logic that are mathematically proven to be unanswerable by any computer or method, no matter how hard you try!
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