Transitive Relations: Difference between revisions

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| if A includes B, and B includes C, necessarily A includes
| if A includes B, and B includes C, necessarily A includes
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| included in
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|is less than
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|is greater than
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|supports
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|implies
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|causes
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The generic phrase ''''is subordinate to'''' can be used to represent any of the above relations.




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{{#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}}




[[Category:Linear Algebra]]
[[Category:Linear Algebra]]

Revision as of 14:07, 9 January 2022


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

R
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
included in
is less than
is greater than
supports
implies
causes

The generic phrase 'is subordinate to' can be used to represent any of the above relations.


This mathematical definition of transitivity can be readily interpreted for many contextual relations.