Dense relation

In mathematics, a binary relation R is said to be dense if, for all R-related x and y, there is a z such that x and z and also z and y are R-related.

Formally:

$\forall x\ \forall y\ xRy\Rightarrow (\exists z\ xRz \land zRy).$

For example, a strict partial order < is a dense order iff < is a dense relation.

Every reflexive relation is dense.

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Dense relation

See also