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

Lexicographical Order - Definition

... Given two partially

... 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

... 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

... Suppose that (A, ≤A) and (B, ≤B) are linearly

**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

... 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

... 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)

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