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第251行： − + − − − − Mathematically, in its most general form, a hierarchy is a partially ordered set or poset.[9] The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class. − − "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parentheses is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: (2 + 5) × (7 - 4). In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations. − − 数学上，层次结构最一般的形式是偏序集 Partially Ordered Set或Poset。元素所组成的系统即整个偏序集。系统内每个元素都共享一些具体无歧义的属性。相同属性的元素可集结成群，最终形成类别层次。 − − “层次”专用作指称随复杂度增加而组织的偏序集。例如加法、减法、乘法和除法通常按特定序列实施。一般乘除先于加减，括号也是层次的一种表示，表达了哪些运算优先。例如在(2 + 5) × (7 - 4)中，按数学的层次规则本应先作5乘以7，但加入了括号，则表示了应当先作括号内的运算。 − − [参考译文]本例中的系统是由元素组成的整个波集。在这个系统中，每个元素都具有一个明确的特性。具有相同属性值的对象组合在一起，每个产生的级别都称为类。 − − [参考译文]本例中的系统是由元素组成的整个波集。在这个系统中，每个元素都具有一个明确的特性。具有相同属性值的对象组合在一起，每个产生的级别都称为类。 − − − − “层次结构”特别用来指按照不断增加的复杂性来组织类的偏序集。< ! ——从数学上讲，等级可以被描述为一个组合对象。 -- > − − “层次结构”特别用来指按照不断增加的复杂性来组织类的偏序集。< ! ——从数学上讲，等级可以被描述为一个组合对象。 -- > 第289行：
第269行： − 诸如加、减、乘、除等运算通常是按照一定的顺序进行的。通常，加法和减法是在乘法和除法已经应用到一个问题之后进行的。圆括号的使用也是层次结构的一种表示，因为它们显示了在下列操作之前要完成的操作。例如: − − 诸如加、减、乘、除等运算通常是按照一定的顺序进行的。通常，加法和减法是在乘法和除法已经应用到一个问题之后进行的。圆括号的使用也是层次结构的一种表示，因为它们显示了在下列操作之前要完成的操作。例如: 第303行：
第280行： − 在这个问题中，根据数学层次规则，一个人通常会先乘以5乘以7。但是当放置括号时，人们会知道在继续处理问题之前先在括号内做操作。这些规则在代数问题中占主导地位，这些问题包括需要解决的几个步骤。在数学中使用层次结构有利于快速有效地解决问题，而不必经历慢慢剖析问题的过程。这些规则中的大多数现在被认为是解决某些方程的正确方法。 − 在这个问题中，根据数学层次规则，一个人通常会先乘以5乘以7。但是当放置括号时，人们会知道在继续处理问题之前先在括号内做操作。这些规则在代数问题中占主导地位，这些问题包括需要解决的几个步骤。在数学中使用层次结构有利于快速有效地解决问题，而不必经历慢慢剖析问题的过程。这些规则中的大多数现在被认为是解决某些方程的正确方法。+ + +
→数学表达 Mathematical representation
==数学表达 Mathematical representation==
==数学表达 Mathematical representation==
{{Main|Hierarchy (mathematics)}}
{{Main|层次（数学） Hierarchy (mathematics)}}
Mathematically, in its most general form, a hierarchy is a [[partially ordered set]] or ''poset''.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings
Mathematically, in its most general form, a hierarchy is a [[partially ordered set]] or ''poset''.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings
Mathematically, in its most general form, a hierarchy is a partially ordered set or poset.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings
Mathematically, in its most general form, a hierarchy is a partially ordered set or poset.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings
|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The [[#Terminology|system]] in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting [[#Terminology|levels]] is referred to as a [[class (set theory)|class]].
|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The [[#Terminology|system]] in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting [[#Terminology|levels]] is referred to as a [[class (set theory)|class]].
|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class.
|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class.
"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a [[combinatorial]] [[object]].-->
"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a [[combinatorial]] [[object]].-->
"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a combinatorial object.-->
"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a combinatorial object.-->
Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:
Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:
Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:
Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:
(2 + 5) × (7 - 4).
(2 + 5) × (7 - 4).
In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.
In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.
数学上，层次结构最一般的形式是偏序集 Partially Ordered Set或Poset。元素所组成的系统即整个偏序集。系统内每个元素都共享一些具体无歧义的属性。相同属性的元素可集结成群，最终形成类别层次。
“层次”专用作指称随复杂度增加而组织的偏序集。例如加法、减法、乘法和除法通常按特定序列实施。一般乘除先于加减，括号也是层次的一种表示，表达了哪些运算优先。例如在(2 + 5) × (7 - 4)中，按数学的层次规则本应先作5乘以7，但加入了括号，则表示了应当先对括号内作运算。在需要多步求解的代数问题上这些规则占主导地位。在数学中使用层次结构有利于快速高效地解决问题，而不必经理漫长的剖析过程。现在认为大多数这类规则是求解特定方程的适当方法。
==亚型 Subtypes==
==亚型 Subtypes==