aka order, or order Relation. A set with an ordering is referred to as an ordered set/space

A type of Relation in a set. When said without adjective, it refers to a Total ordering, by default

However, it can also refer to a Partial ordering, if specified.

Order type: Suppose that A and B are two sets with order relations $<_A$ and $<_B$ respectively. We say that A and B have the same order type if there is a Bijection between them that preserves order; that is, if there exists a Bijection $f: A \rightarrow B$ such that

$a_1 <_A a_2 \Rightarrow f(a_1) <_B f(a_2)$

Every nonempty finite totally ordered set has the order type of a section $\{1,...,n\}$ of $\mathbb{Z}_+$ (so it is well-ordered)

Well-ordered set

Dictionary ordering

Open interval

Bounded above

Bounded below

Least upper bound property

Greatest lower bound property