Question: What Is Total Order 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 a partial order plus an additional condition known as the comparability condition.

Every finite totally ordered set is well ordered.

What is set order?

In mathematics, a total order, simple order, linear order, connex order, or full order is a binary relation on some set , which is antisymmetric, transitive, and a connex relation. A set paired with a total order is called a chain, a totally ordered set, a simply ordered set, or a linearly ordered set.

What are the components of a total order?

The relation R⊂S×S, where (x,y)∈R⇔x≤y is given by R={(a,a),(a,b),(a,c),(a,d),(b,b),(b,d),(c,c),(c,d),(d,d)}.

What is a simply ordered set?

A simply ordered set M is a set such that if any two of. its elements are given it is known which one precedes.

Is a partial order?

Formally, “A relation on set is called a partial ordering or partial order if it is reflexive, anti-symmetric and transitive. A set together with a partial ordering is called a partially ordered set or poset. The poset is denoted as .”