Transitive Relations: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
|||
Line 20: | Line 20: | ||
| if A includes B, and B includes C, necessarily A 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. | |||
Line 31: | Line 46: | ||
{{#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.