One of the mysteries of the English language finally explained.
Denoting a relation which never holds between a term and itself.
- ‘G is an irreflexive, asymmetric and transitive relation.’
- ‘A relation on a set is irreflexive provided that no element is related to itself.’
- ‘But it is not irreflexive either, since 1 is related to itself.’
- ‘Since this cannot be true, the statement x not-R x must be true; therefore R is irreflexive.’
- ‘A strict order is one that is irreflexive and transitive; such an order is also trivially antisymmetric.’
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