Naïve set theory MOC

Totally ordered set

A totally ordered set or connex is a poset in which any two elements are in relation. order Hence it a set equipped with a Relation set that is

1. reflexive — for all ,
2. transitive — if and , then
3. antisymmetric — if and , then
4. total — for all , or

Viewing Posets as categories, a this is equivalent to a connex category. A subset of a poset that is total is called a chain.

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