transitivityn.
/ˌtranzᵻˈtɪvᵻti/, /ˌtrɑːnzᵻˈtɪvᵻti/, /ˌtransᵻˈtɪvᵻti/, /ˌtrɑːnsᵻˈtɪvᵻti/, U.S. /ˌtrænzəˈtɪvədi/, /ˌtræn(t)səˈtɪvədi/ 1. Mathematics.
a. With reference to a group (group n. 7): the state or fact of being transitive (transitive adj. 8a).
ΚΠ
1891 Amer. Jrnl. Math. 13 120 The irreducibility implies the transitivity of the group G.
1969 Jrnl. Algebra 13 166 Because of the transitivity of G, it is easily seen that the components..are also transitive.
2010 P. Ramond Group Theory ii. 30 The notion of transitivity plays an important role in the classification of finite groups.
b. With reference to an action (action n. 12b) on a group: the state or fact of being transitive (transitive adj. 8b).
ΚΠ
1965 Amer. Jrnl. Math. 87 809 We conclude from the transitivity of the action of G on V that every point of V is normal.
2013 H. Ringström On Topol. & Future Stability of Universe iii. 36 The condition of transitivity of the group action corresponds to the homogeneity of the metric.
2. Grammar. The fact of a verb being transitive; the fact of whether a verb is transitive or intransitive.
ΘΚΠ
the mind > language > linguistics > study of grammar > other grammatical categories or concepts > [noun] > transitivity or intransitivity
transitivity1897
intransitivity1971
1897 Från Filologiska Föreningen 1 54 Similarly, the same verb may..have differing senses, and, consequently, varying degrees of transitivity.
1928 Mod. Lang. Rev. 23 144 The following chapters [of Jespersen's Modern English Grammar] are concerned with..transitivity and predicatives.
1969 J. C. Wells E.U.P. conc. Esperanto & Eng. Dict. 17 Many English verbs are of varying transitivity, since they can be used either transitively or intransitively.
2013 Oceanic Linguistics 52 285 Transitivity in Tamambo is determined by the verb root itself.
3. Mathematics and Logic. With reference to a mathematical or logical relation: the state or fact of being such that if a first item is related to second as the second is related to a third, then the first is related to the third in the same way. See transitive adj. 7.
ΘΚΠ
the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > propositional relation > transitivity or intransitivity
transitiveness1856
intransitivity1933
transitivity1942
1905 Trans. Amer. Math. Soc. 6 378 Here too we deal with a type of transitivity whose consequences are of great importance.
1942 J. C. Cooley Primer Formal Logic viii. 339 The generalized postulate for the transitivity of the relation, older than, could not be expressed without variables.
2011 V. S. Ramachandran Tell-tale Brain (2012) vi. 185 Where do these obvious deductions, based on the rules of transitivity, come from?
This entry has been updated (OED Third Edition, March 2019; most recently modified version published online March 2022).
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n.1891