Total Order

aka linear order

--- https://en.wikipedia.org/wiki/Total_order

see partial order, preorder

equiv set of paths of a "directed" list

definition a relation is a non-strict total order or simply total order if it is a antisymmetric ‹relation, a reflexive ‹relation, transitive ‹relation and a strongly connected ‹relation

definition a relation is a non-strict total order or simply total order if it is a non-strict partial order and a connected ‹relation

example less than or equal to is a non-strict total order and therefore a non-strict partial order and therefore a non-strict preorder on the set of reals

definition a relation is a strict total order if it is a asymmetric ‹relation, a irreflexive ‹relation, a transitive ‹relation and a connected ‹relation

definition a relation is a strict total order if it is a strict partial order and a connected ‹relation

example less than is a strict total order and therefore a strict partial order and equivalently a strict preorder on the set of reals