Nonassociativity

Part of speech: noun

Definitions

1. The property of an operation where the grouping of operands does not affect the outcome, indicating that changing how terms are grouped yields different results
2. A characteristic of certain mathematical operations where the order in which elements are combined does not alter the final result due to a lack of associative attributes
3. The condition in which the application of an operation on a set does not adhere to the associative law, resulting in varied outcomes based on grouping of elements

Etymology: "Nonassociativity" is simply "non-" attached to "associativity," so the history lies in the second half. "Associativity" is the mathematical property, named for the verb "associate" in the sense of combining or grouping things together. Its formal meaning is the one given here: an operation is associative when grouping does not change the result, as with addition, where (2+3)+4 and 2+(3+4) are both 9. The prefix "non-" comes from Latin "non," meaning "not," and reverses that property. Nonassociativity therefore names the opposite case. Subtraction is a clear example: (8−4)−2 gives 2, while 8−(4−2) gives 6, so the grouping changes the answer. The word is a plain technical formation, built by mathematicians in the usual way of adding a negating prefix to an established term, rather than a word with a dramatic backstory.