Definition:Dedekind Cut/Definition 2
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Definition
Let $\struct {S, \preceq}$ be a totally ordered set.
A Dedekind cut of $\struct {S, \preceq}$ is an ordered pair $\tuple {L, R}$ such that:
- $(1): \quad \set {L, R}$ is a partition of $S$.
- $(2): \quad L$ does not have a greatest element.
- $(3): \quad \forall x \in L: \forall y \in R: x \prec y$.
Also see
Source of Name
This entry was named for Julius Wilhelm Richard Dedekind.