Transitiveness

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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” (a ≠ b) is not transitive because a ≠ c does not necessarily follow from a ≠ b and b ≠ c.

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.

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Transitiveness