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NeonMerlin (talk | contribs) →Strict partial orders: Looks better with thick space Tags: Mobile edit Mobile web edit |
kind of confusing to have a quantifier without a symbol, use neg |
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An '''irreflexive''', '''strong''',<ref name=Wallis/> or '''{{visible anchor|strict partial order|Strict partial order|Irreflexive partial order}}''' is a homogeneous relation < on a set <math>P</math> that is [[Irreflexive relation|irreflexive]], [[Asymmetric relation|asymmetric]], and [[Transitive relation|transitive]]; that is, it satisfies the following conditions for all <math>a, b, c \in P:</math>
# [[Irreflexive relation|Irreflexivity]]: <math>\
# [[Asymmetric relation|Asymmetry]]: if <math>a < b</math> then not <math>b < a</math>.
# [[Transitive relation|Transitivity]]: if <math>a < b</math> and <math>b < c</math> then <math>a < c</math>.
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