Category:Definitions/Densely Ordered

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This category contains definitions related to Densely Ordered.
Related results can be found in Category:Densely Ordered.


Let $\struct {S, \preceq}$ be an ordered set.


Then $\struct {S, \preceq}$ is defined as densely ordered if and only if strictly between every two elements of $S$ there exists another element of $S$:

$\forall a, b \in S: a \prec b \implies \exists c \in S: a \prec c \prec b$

where $a \prec b$ denotes that $a \preceq b$ but $a \ne b$.