# Ordered Sets

### Some articles on ordered sets, ordered, sets, set, ordered set:

Lexicographical Order - Definition
... Given two partially ordered sets A and B, the lexicographical order on the Cartesian product A × B is defined as (a,b) ≤ (a′,b′) if and only if a < a ... If A and B are totally ordered, then the result is a total order as well ... one can define the lexicographic order on the Cartesian product of n ordered sets, on the Cartesian product of a countably infinite family of ordered sets, and on the union of such sets ...
List Of Programs Broadcast By UPN - Drama/Sci-fi
... Because of this, The WB ordered a full season of 22 episodes for the series' second season ... to the problems the series had with ratings during its first season, The WB ordered the relationship-driven standalone episodes of the early first season to be replaced with more science fiction themes and multi-ep ... Starting with the second season, which was ordered by the network after a fierce fan-driven campaign involving bottles of Tabasco sauce—a favorite condiment of the show's alien ...
Back-and-forth Method - Application To Densely Ordered Sets
... Suppose that (A, ≤A) and (B, ≤B) are linearly ordered sets They are both unbounded, in other words neither A nor B has either a maximum or a minimum They are densely ordered, i.e ... Fix enumerations (without repetition) of the underlying sets A = { a1, a2, a3, … }, B = { b1, b2, b3, … } ... In the easy case of unbounded dense totally ordered sets it is possible to avoid step 2 by choosing the element bj more carefully (by choosing j as small as possible), but this does not work for more complicated ...
Paradoxes Of Set Theory - Basics - Ordinal Numbers
... cardinality, which describes the size of a set, ordered sets also form a subject of set theory ... The axiom of choice guarantees that every set can be well-ordered, which means that a total order can be imposed on its elements such that every nonempty subset has a first element ... The order of a well-ordered set is described by an ordinal number ...
Colexicographical Order
... or colex order, is a natural order structure of the Cartesian product of two or more ordered sets ... Given two partially ordered sets A and B, the colexicographical order on the Cartesian product A × B is defined as (a,b) ≤ (a′,b′) if and only if b < b′ or (b = b′ and a ... If A and B are totally ordered, then the result is a total order also ...

### Famous quotes containing the words sets and/or ordered:

The poem has a social effect of some kind whether or not the poet wills it to have. It has kinetic force, it sets in motion ... [ellipsis in source] elements in the reader that would otherwise be stagnant.
Denise Levertov (b. 1923)

Today everything is different. I can’t even get decent food. Right after I got here I ordered some spaghetti with marinara sauce and I got egg noodles and catsup. I’m an average nobody, I get to live the rest of my life like a schnook.
Nicholas Pileggi, U.S. screenwriter, and Martin Scorsese. Henry Hill (Ray Liotta)