0 votes 0 votes can anyone explain what is total ordered set by giving suitable example..and also well ordered sets. Akriti sood asked Jun 21, 2016 Akriti sood 1.0k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Totally Ordered Set A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for apartial order plus an additional condition known as the comparability condition. A relation is a total order on a set (" totally orders ") if the following properties hold. 1. Reflexivity: for all . 2. Antisymmetry: and implies . 3. Transitivity: and implies . 4. Comparability (trichotomy law): For any , either or . The first three are the axioms of a partial order, while addition of the trichotomy law defines a total order. Every finite totally ordered set is well ordered. Any two totally ordered sets with elements (for a nonnegative integer) are order isomorphic, and therefore have the same order type (which is also an ordinal number). For more information plz refer the link mentioned below.... http://www.cs.elte.hu/~karolyik/SER.pdf Devshree Dubey answered Jun 21, 2016 Devshree Dubey comment Share Follow See 1 comment See all 1 1 comment reply Akriti sood commented Jun 22, 2016 reply Follow Share thanks a lot 0 votes 0 votes Please log in or register to add a comment.