Difference between revisions of "Ordered relation"

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An [[ordered relation]], or a [[directed relation]] can be considered as the building block of [[Partially ordered set]]s. It can be visualized as an [[arrow]] that relates two [[object]]s with an explicit direction. This directionality breaks the symmetry of symbolic representation, which is the smallest amount of information in all contexts. This data element is also the building block of [[Partially ordered set]].
An [[ordered relation]], or a [[directed relation]] is the generic building block of [[Partially ordered set]]s<ref name=Outline>{{:Paper/Outline of a Mathematical Theory of Computation}}</ref>. It can be visualized as an [[arrow]] that relates two [[object]]s with an explicit direction. The directionality of a [[directed relation]] breaks the symmetry of symbolic representation, which is the smallest amount of information, therefore, [[directed relation]]s can be used to represent any other kinds of information content<ref extends=Outline>Section 2. Data Types and Mappings, Page 6, Axiom 1:A data type is a partially ordered set.</ref>. Ordered relations are particularly useful in representing [[causal relation]]s<ref>{{:Book/The Book of Why}}</ref>.
 
=Prefix and Postfix Expressions=
Since order matters, the sequence of how certain symbols appears in an expression also matters a lot. There are two kinds of expressions:
# [[Prefix Expression]]
# [[Postfix Expression]]


<noinclude>
<noinclude>
=References=
{{PagePostfix
<references/>
|category_csd=Arrow,Order,Relation,Function,Structuralism,Universal Component,Commutator
 
}}
==Related Pages==
*[[logically related::Arrow]]
*[[logically related::Tuple]]
[[Category:Order]]
</noinclude>
</noinclude>

Latest revision as of 12:41, 17 July 2022

An ordered relation, or a directed relation is the generic building block of Partially ordered sets[1]. It can be visualized as an arrow that relates two objects with an explicit direction. The directionality of a directed relation breaks the symmetry of symbolic representation, which is the smallest amount of information, therefore, directed relations can be used to represent any other kinds of information contentCite error: Invalid <ref> tag; invalid names, e.g. too many. Ordered relations are particularly useful in representing causal relations[2].

Prefix and Postfix Expressions

Since order matters, the sequence of how certain symbols appears in an expression also matters a lot. There are two kinds of expressions:

  1. Prefix Expression
  2. Postfix Expression


References

  1. Scott, Dana (January 1, 1970). "Outline of a Mathematical Theory of Computation". local page: Oxford University Computing Laboratory Programming Research Group. 
  2. Pearl, Judea (2018). The Book of Why: The New Science of Cause and Effect. local page: Basic Books. ISBN 978-0-465-09761-6. 

Related Pages