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Transitive Relations: Difference between revisions
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=== Examples of Transitive Relations === | === Examples of Transitive Relations === | ||
{| class="wikitable" | {| class="wikitable sortable" style="width: 65%;" | ||
|- | |- | ||
! R | ! scope="col" style="background:#efefef;" align="left"; "width: 25%"| R | ||
! | ! scope="col" style="background:#efefef;" align="left"; "width: 75%"| Explanation | ||
|- | |- | ||
| precedes | | precedes | ||
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The generic phrase ''''is subordinate to'''' can be used to represent any of the above relations. | The generic phrase ''''is subordinate to'''' can be used to represent any of the above relations. | ||
Without it, the development | |||
of knowledge would have been considerably more | |||
difficult. On the other band, its prevalence may induce a | |||
tendency to take it for granted when it is not present. The | |||
contextual relation "is preferred to" is a good case in point. | |||
Preference is subjective, and subjective relations may or | |||
may not be transitive. Thus if a person says "blue is | |||
preferred to red" and "red is preferred to yellow," it still | |||
may be that the person will say "yellow is preferred to | |||
blue," hence, transitivity is violated. For this particular | |||
contextual relation, one can speak of"transitive preference" | |||
and "intransitive preference." | |||
This mathematical definition of transitivity can be | This mathematical definition of transitivity can be | ||