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* The binary relation ≤ is then called a total order or a linear order (or total ordering or linear ordering).<ref name="ref_f166">[https://planetmath.org/totalorder total order]</ref> | * The binary relation ≤ is then called a total order or a linear order (or total ordering or linear ordering).<ref name="ref_f166">[https://planetmath.org/totalorder total order]</ref> | ||
* A totally ordered set is also sometimes called a chain, especially when it is considered as a subset of some other poset.<ref name="ref_f166" /> | * A totally ordered set is also sometimes called a chain, especially when it is considered as a subset of some other poset.<ref name="ref_f166" /> | ||
2020년 12월 16일 (수) 11:07 판
노트
- The binary relation ≤ is then called a total order or a linear order (or total ordering or linear ordering).[1]
- A totally ordered set is also sometimes called a chain, especially when it is considered as a subset of some other poset.[1]
- Some people prefer to define the binary relation < as a total order, rather than ≤ .[1]
- The problem of finding a strict total order for a finite set of multiple criteria alternatives is considered.[2]
- Each multicast sender thread walks through the stages for sending a message in the total order algorithm (see the state diagram).[3]
- To facilitate proper testing, we needed a way to introduce nondeterminism into the execution of the total order algorithm.[3]
- the total order intake in 2001 (in cgt).[4]
- There is obvious pragmatic justification for choosing the standard total order; it's utility is not in question.[5]
- A total order is a partial order that has one additional property - any two elements in the set should be related.[6]
- each other, total order requires us to be able to order all elements in a set.[6]
- We can define a total order between square boxes, however, as long as their sizes are unique.[6]
- A partially ordered set \(\left( {A, \preccurlyeq} \right)\) in which any two elements are comparable is called a total order.[7]
- To convert a partial order into a total order, we need to replace the reflexivity property by the stronger connexity property.[7]
- Find a chain of length \(4\) in the poset \(\left( {A, \mid} \right),\) where \(\mid\) represents the divisibility relation.[7]
- Example 3 Determine which of the following subset relations are total orders.[7]
- The height of a poset denotes the cardinality of its largest chain in this sense.[8]
- In other words, a total order on a set with k elements induces a bijection with the first k natural numbers.[8]
- (the reflexive closure of the direct product of the corresponding strict total orders).[8]
소스
- ↑ 1.0 1.1 1.2 total order
- ↑ Constructing a strict total order for alternatives characterized by multiple criteria: An extension
- ↑ 3.0 3.1 nvanbenschoten/total-order-multicast: An implementation of the ISIS total order multicast algorithm
- ↑ French translation – Linguee
- ↑ Why do we choose the standard total order on the integers?
- ↑ 6.0 6.1 6.2 Partial and Total Orders
- ↑ 7.0 7.1 7.2 7.3 Total Orders
- ↑ 8.0 8.1 8.2 Total order