What does nontransitive mean?
The term nontransitive refers to a relation or a verb that does not follow the transitive property. In grammar, a nontransitive verb is one that does not take a direct object to complete its meaning. For example, 'sleep' is a nontransitive verb because it does not require an object. In logic and mathematics, a relation R is nontransitive if a R b and b R c do not imply a R c. The 'is taller than' relation is a classic example of a nontransitive relation. Understanding nontransitive relations and verbs is crucial in various fields, including linguistics, mathematics, and logic, as they help describe complex relationships and phenomena accurately.
Not transitive; specifically, in grammar, a verb that does not take a direct object.
"The verb 'sleep' is nontransitive because it does not require a direct object."
In linguistics, nontransitive often refers to verbs that do not take a direct object.
In logic and mathematics, a relation that does not satisfy the transitive property.
"The 'is taller than' relation is nontransitive because if John is taller than Jane, and Jane is taller than Bob, it does not follow that John is taller than Bob in all cases."
In logic and mathematics, the term is used to describe relations that do not satisfy the transitive property.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of nontransitive
The word nontransitive originates from the prefix 'non-', meaning 'not', and 'transitive', which comes from the Latin 'transitivus', meaning 'passing over'. The term 'transitive' itself is derived from 'transire', which means 'to go across'. The concept of transitivity has been studied in various fields, including logic, mathematics, and linguistics, leading to the development of the term nontransitive to describe relations and verbs that do not exhibit transitive properties.
Usage notes
In linguistics, nontransitive often refers to verbs that do not take a direct object, which may also be called intransitive. However, in logic and mathematics, the term is used to describe relations that do not satisfy the transitive property.