totally ordered การใช้

• The maximal totally ordered sets are horizontal lines in  ! 2.
• After defining multiplication, the decimal numbers form a positive, totally ordered, commutative semiring.
• A totally ordered set without infinite descending chains is called well-ordered.
• A notable exception to the braces notation is used to express totally ordered.
• The set of isolated subgroups is totally ordered by inclusion.
• Unlike the latter, the product order of two totally ordered sets is not total.
• Directed sets are a generalization of nonempty totally ordered sets.
• He's totally ordered, regular structure today is because people up.
• From any totally ordered set of representations, we can construct a representation as follows.
• A sequence is usually indexed by the natural numbers, which are a totally ordered set.
• All authors agree that a cycle is totally ordered.
• Zorn's lemma describes partially ordered sets where every totally ordered subset has an upper bound.
• If and are each totally ordered, then the result is a total order as well.
• These concepts generalize respectively those of preordered set, partially ordered set and totally ordered set.
• Join and meet are symmetric totally ordered set is simply its maximal / minimal element.
• The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.
• This generalized lexicographical order is a total order, if each factor set is totally ordered.
• This covers series, which is PM's term for what is now called a totally ordered set.
• Let ? be a totally ordered abelian group.
• The lexicographic order of totally ordered sets is however a linear extension of their product order.