nLab strict and non-strict orders

Idea

In order theory, there are usually two different versions of an order relation, a reflexive version which is usually referred to as a reflexive order or non-strict order and an irreflexive version which is usually referred to as an irreflexive order, strong order, or strict order. Examples include:

• preorder, strict preorder

• partial order, strict partial order

• total order, strict total order

• weak order, strict weak order

• linear order, strict linear order

References

• Wikipedia, Preorder

• Wikipedia, Partial order

• Wikipedia, Total order

• Wikipedia, Weak order

category: disambiguation