transitivity
- noun
- /ˌtræn.zɪˈtɪv.ɪ.ti/
- Specialized
:
transitividad
- Mathematically, transitivity is key to establishing rankings; if John is taller than Mike and Mike is taller than Sam, then John is taller than Sam.
- topological transitivity
Examples
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Still, a chain of judgments may provide, via transitivity, grounds for judging that one world is better than another even when that judgment cannot be made directly.
Academic text (1998) -
OK, so the basic theorem that we have to begin with is what is transitivity capturing as a property of a relation?
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Completing the picture, the "better-than" relation also has the following properties: irreflexivity, by which no world is better than itself, and transitivity, by which, for any worlds w, u, and v, if w is better than u and u is better than v, then w is better than v (260-1).
Academic text (1998) -
In logic, the principle of transitivity asserts that if A is related to B and B is related to C, then A must also be related to C.
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The transitivity property is essential in set theory, as it allows us to conclude that if A is a subset of B and B is a subset of C, then A is a subset of C.
Surface Forms
Morphology
transitivity = transitive (semi-transparent) = transitive + ity
Morphologically it's 'transitive' + '-ity', but the mathematical sense is a technical usage of 'transitive' that may be unfamiliar to general learners.
Etymology
Transitivity comes from the prefix trans- meaning 'across' and the ending -ity that makes a noun, like in transport or transfer. In logic it means a relation 'goes across' steps: if it links the first to the second and the second to the third, it also links the first to the third, which is why we call this transitivity.
