A relation is irreflexive if nothing bears it to itself: ¬(∃x )Rxx. Nothing is larger than itself, so ‘is larger than’ is an irreflexive relation.

Philosophy dictionary. . 2011.

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  • irreflexive — adjective Date: circa 1890 being a relation for which the reflexive property does not hold for any element of a given set …   New Collegiate Dictionary

  • irreflexive — irreflexiveness, irreflexivity, n. /ir i flek siv/, adj. not reflexive. [1885 90; IR 2 + REFLEXIVE] * * * …   Universalium

  • irreflexive — adjective Of a binary relation R on X: such that no element of X is R related to itself. See Also: reflexive …   Wiktionary

  • irreflexive — ir·reflexive …   English syllables

  • irreflexive — …   Useful english dictionary

  • aliorelative — Irreflexive (see relation ) …   Philosophy dictionary

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  • Relation binaire — En mathématiques, une relation binaire entre deux ensembles E et F (ou simplement relation entre E et F) est caractérisée par un sous ensemble du produit cartésien E × F, soit une collection de couples dont la première composante est dans E et la …   Wikipédia en Français

  • Binary relation — Relation (mathematics) redirects here. For a more general notion of relation, see Finitary relation. For a more combinatorial viewpoint, see Theory of relations. In mathematics, a binary relation on a set A is a collection of ordered pairs of… …   Wikipedia

  • Admissible rule — In logic, a rule of inference is admissible in a formal system if the set of theorems of the system is closed under the rule. The concept of an admissible rule was introduced by Paul Lorenzen (1955).DefinitionsThe concept of admissibility, as… …   Wikipedia

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