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===Mathematical Definition=== | |||
A binary relation R defined on a set S is said to be transitive if, for any elements A, B, and C in the set S, given that A R B and B R C, it necessarily follows that A R C. | |||
=== Examples of Transitive Relations === | |||
{| class="wikitable" | |||
|- | |||
! precedes | |||
! if A precedes B, and B precedes C, necessarily A precedes C. This would be true whatever the nature of A, B, and C,although the ideas can be made more precise by thinkingof A, B, and C as events occurring at specific times. | |||
|- | |||
| includes | |||
| if A includes B, and B includes C, necessarily A includes | |||
|} | |||
This mathematical definition of transitivity can be | |||
readily interpreted for many contextual relations. | |||
{{#ev:youtube|https://www.youtube.com/watch?v=q0xN_N7l_Kw|||||start=287}} | {{#ev:youtube|https://www.youtube.com/watch?v=q0xN_N7l_Kw|||||start=287}} | ||