Definitions for preorder
pre·order

WiktionaryRate this definition:0.0 / 0 votes

1. preordernoun

   A binary relation that is reflexive and transitive.

   The relation of logical implication over sentences is an example of a preorder.

2. preorderverb

   To order (goods) in advance, before they are available.

3. preorderadjective

   Of a tree traversal, recursively visiting the root before the left and right subtrees.

WikipediaRate this definition:0.0 / 0 votes

1. Preorder

   In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. Preorders are more general than equivalence relations and (non-strict) partial orders, both of which are special cases of a preorder: an antisymmetric (or skeletal) preorder is a partial order, and a symmetric preorder is an equivalence relation. The name preorder comes from the idea that preorders (that are not partial orders) are 'almost' (partial) orders, but not quite; they are neither necessarily antisymmetric nor asymmetric. Because a preorder is a binary relation, the symbol ≤ {\displaystyle \,\leq \,} can be used as the notational device for the relation. However, because they are not necessarily antisymmetric, some of the ordinary intuition associated to the symbol ≤ {\displaystyle \,\leq \,} may not apply. On the other hand, a preorder can be used, in a straightforward fashion, to define a partial order and an equivalence relation. Doing so, however, is not always useful or worthwhile, depending on the problem domain being studied. In words, when a ≤ b , {\displaystyle a\leq b,} one may say that b covers a or that a precedes b, or that b reduces to a. Occasionally, the notation ← or → or ≲ {\displaystyle \,\lesssim \,} is used instead of ≤ . {\displaystyle \,\leq .} To every preorder, there corresponds a directed graph, with elements of the set corresponding to vertices, and the order relation between pairs of elements corresponding to the directed edges between vertices. The converse is not true: most directed graphs are neither reflexive nor transitive. In general, the corresponding graphs may contain cycles. A preorder that is antisymmetric no longer has cycles; it is a partial order, and corresponds to a directed acyclic graph. A preorder that is symmetric is an equivalence relation; it can be thought of as having lost the direction markers on the edges of the graph. In general, a preorder's corresponding directed graph may have many disconnected components.

Webster DictionaryRate this definition:0.0 / 0 votes

1. Preorderverb

   to order to arrange beforehand; to foreordain

WikidataRate this definition:5.0 / 1 vote

1. Preorder

   In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. All partial orders and equivalence relations are preorders, but preorders are more general. The name 'preorder' comes from the idea that preorders are 'almost' orders, but not quite; they're neither anti-symmetric nor symmetric. Because a preorder is a binary relation, the symbol ≤ can be used as the notational device for the relation. However, because they are not anti-symmetric, some of the ordinary intuition associated to the symbol ≤ may not apply. On the other hand, a pre-order can be used, in a straightforward fashion, to define a partial order and an equivalence relation. Doing so, however, is not always useful or worthwhile, depending on the problem domain being studied. In words, when a ≤ b, one may say that b covers a or that b precedes a, or that b reduces to a. Occasionally, the notation ← or is used instead of ≤. To every preorder, there corresponds a directed graph, with elements of the set corresponding to vertices, and the order relation between pairs of elements corresponding to the directed edges between vertices. The converse is not true: most directed graphs are neither reflexive nor transitive. Note that, in general, the corresponding graphs may be cyclic graphs: preorders may have cycles in them. A preorder that is antisymmetric no longer has cycles; it is a partial order, and corresponds to a directed acyclic graph. A preorder that is symmetric is an equivalence relation; it can be thought of as having lost the direction markers on the edges of the graph. In general, a preorder may have many disconnected components.

Chambers 20th Century DictionaryRate this definition:0.0 / 0 votes

1. Preorder

   prē-or′dėr, v.t. to arrange beforehand.—n. Preor′dinance, a rule previously established.

How to pronounce preorder?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say preorder in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of preorder in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of preorder in Pythagorean Numerology is: 9

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References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Preorder
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Preorder
3. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/preorder
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=preorder
5. ^ Chambers 20th Century Dictionary
   https://www.gutenberg.org/files/37683/37683-h/37683-h.htm#:~:text=preorder