Transitiveness


Also found in: Dictionary, Thesaurus.

Transitiveness

 

a property of some logical relations between objects or quantities.

The relation a*b is said to be transitive if a*c follows from a*b and b*c. For example, the relation “a is equal to b” (a = b) is transitive because a = c follows from a = b and b = c. Similarly, the relation “a is greater than b” (a > b) is transitive. The relation “a is not equal to b” (ab) is not transitive because ac does not necessarily follow from ab and bc.

In geometry, the relation of parallelism between two lines is transitive: if α is parallel to β and β is parallel to γ, then α is parallel to γ. By contrast, the relation of perpendicularity between lines is not transitive.

Mentioned in ?
References in periodicals archive ?
Finland which generally dominated Denmark and as Denmark generally dominated next country namely Austria it will by transitiveness ipso facto have dominated all the other states.
The dictionary can indeed be useful if the student knows that a violation of the verb's transitiveness or intransitiveness has occurred.
Here, one might ask whether the category of conjugation is more significant than that of transitiveness, that is.
significance of what he calls their 'transitiveness', implying