Transitiveness


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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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