In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset...

In mathematics, the well-ordering principle states that every non-empty subset of nonnegative integers contains a least element. In other words, the set...

the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if...

In mathematics, specifically order theory, a well-quasi-ordering or wqo on a set X {\displaystyle X} is a quasi-ordering of X {\displaystyle X} for which...

In order theory, a partial order is called well-founded if the corresponding strict order is a well-founded relation. If the order is a total order then...

lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences...

mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤...

∗ {\displaystyle \sigma ^{*}} . The order type of a well-ordered set X is sometimes expressed as ord(X). The order type of the integers and rationals is...

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...

linear order such that every non-empty subset has a least element is called a well-order. The axiom of choice implies that every set can be well-ordered...