-
relation is
irreflexive if and only if its
complement in X × X {\displaystyle X\times X} is reflexive. An
asymmetric relation is
necessarily irreflexive. A transitive...
- investigated. A
relation R is
reflexive if xRx
holds for all x, and
irreflexive if xRx
holds for no x. It is
symmetric if xRy
always implies yRx, and...
- {\displaystyle a\in X} ),
irreflexive (that is, a R a {\displaystyle aRa} for no a ∈ X {\displaystyle a\in X} ), or
neither reflexive nor
irreflexive. A
relation is...
- a
reflexive relation but > is not.
Irreflexive (or strict) for all x ∈ X, not xRx. For example, > is an
irreflexive relation, but ≥ is not. Coreflexive...
- use the term for the
other common type of
partial order relations, the
irreflexive partial order relations, also
called strict partial orders.
Strict and...
- asymmetric: R {\displaystyle R} is
irreflexive and anti-symmetric (this is also necessary) R {\displaystyle R} is
irreflexive and transitive. A
transitive relation...
- b<a} (connected).
Asymmetry follows from
transitivity and
irreflexivity; moreover,
irreflexivity follows from asymmetry. For
delimitation purposes, a total...
- ⊆ A {\displaystyle B\subseteq A} , then A = B {\displaystyle A=B} .
Irreflexivity:
Given any set A {\displaystyle A} , A ⊊ A {\displaystyle A\subsetneq...
- is not.
Irreflexive: for all x ∈ X , {\displaystyle x\in X,} not x R x {\displaystyle xRx} . For example, > {\displaystyle >} is an
irreflexive relation...
- all
strict partial orders, the happened-before
relation is transitive,
irreflexive (and vacuously, asymmetric), i.e.: ∀ a , b , c {\displaystyle \forall...
