완전순서

노트

• What does it mean by saying "take place in a single total order"?
• Definition of "total order" from Wikipedia can't help much.
• The binary relation ≤ is then called a total order or a linear order (or total ordering or linear ordering).
• A totally ordered set is also sometimes called a chain, especially when it is considered as a subset of some other poset.
• Some people prefer to define the binary relation < as a total order, rather than ≤ .
• The problem of finding a strict total order for a finite set of multiple criteria alternatives is considered.
• Each multicast sender thread walks through the stages for sending a message in the total order algorithm (see the state diagram).
• To facilitate proper testing, we needed a way to introduce nondeterminism into the execution of the total order algorithm.
• the total order intake in 2001 (in cgt).
• There is obvious pragmatic justification for choosing the standard total order; it's utility is not in question.
• A total order is a partial order that has one additional property - any two elements in the set should be related.
• each other, total order requires us to be able to order all elements in a set.
• We can define a total order between square boxes, however, as long as their sizes are unique.
• A partially ordered set \(\left( {A, \preccurlyeq} \right)\) in which any two elements are comparable is called a total order.
• To convert a partial order into a total order, we need to replace the reflexivity property by the stronger connexity property.
• Find a chain of length \(4\) in the poset \(\left( {A, \mid} \right),\) where \(\mid\) represents the divisibility relation.
• Example 3 Determine which of the following subset relations are total orders.
• The height of a poset denotes the cardinality of its largest chain in this sense.
• In other words, a total order on a set with k elements induces a bijection with the first k natural numbers.
• (the reflexive closure of the direct product of the corresponding strict total orders).