Total relation: Difference between revisions
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:<math>\forall a, b \in X,\ a R b \or b R a.</math> |
:<math>\forall a, b \in X,\ a R b \or b R a.</math> |
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Basically this means that if you are relating members of ''X'' (imagine ''X'' is a set {''a'', ''b'', ''c'', ...} ), then for the relation to be total, every |
Basically this means that if you are relating members of ''X'' (imagine ''X'' is a set {''a'', ''b'', ''c'', ...} ), then for the relation to be total, every member must be truthfully related to every other member — i.e. ''xRy'' is true or ''yRx'' is true or they are both true. |
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For example, "is less than or equal to" is a total relation over the set of real numbers, while "is less than" is not. The relation "is a subset of" is also not total. |
For example, "is less than or equal to" is a total relation over the set of real numbers, while "is less than" is not. The relation "is a subset of" is also not total. |
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Revision as of 22:31, 19 November 2005
In mathematics, a binary relation R over a set X is total if it holds for all a and b in X that a is related to b or b is related to a (or both).
In mathematical notation, this is
Basically this means that if you are relating members of X (imagine X is a set {a, b, c, ...} ), then for the relation to be total, every member must be truthfully related to every other member — i.e. xRy is true or yRx is true or they are both true.
For example, "is less than or equal to" is a total relation over the set of real numbers, while "is less than" is not. The relation "is a subset of" is also not total.
A common total relation is the total order.