Changes

MyWikiBiz, Author Your Legacy — Thursday October 31, 2024
Jump to navigationJump to search
Line 1,096: Line 1,096:  
I recall the objective genre of ''properties and instances'' and re-introduce the symbols <math>\lessdot</math> and <math>\gtrdot</math> for the converse pair of dyadic relations that generate it.  Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms "property of <math>x\!</math>" and "instance of <math>x\!</math>" by means of a case inflection on <math>x\!,</math> that is, as "<math>x\!</math>&rsquo;s property" and "<math>x\!</math>&rsquo;s instance", respectively.  Described in this way, <math>\operatorname{OG} (\operatorname{Prop}, \operatorname{Inst}) = \langle \lessdot, \gtrdot \rangle,</math> where:
 
I recall the objective genre of ''properties and instances'' and re-introduce the symbols <math>\lessdot</math> and <math>\gtrdot</math> for the converse pair of dyadic relations that generate it.  Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms "property of <math>x\!</math>" and "instance of <math>x\!</math>" by means of a case inflection on <math>x\!,</math> that is, as "<math>x\!</math>&rsquo;s property" and "<math>x\!</math>&rsquo;s instance", respectively.  Described in this way, <math>\operatorname{OG} (\operatorname{Prop}, \operatorname{Inst}) = \langle \lessdot, \gtrdot \rangle,</math> where:
   −
:{|
+
{| align="center" cellpadding="8"
| ''x'' <math>\lessdot</math>
+
| <math>x \lessdot</math>
| =
+
| <math>=\!</math>
| ''x''&rsquo;s Property
+
| <math>x \operatorname{'s~Property}</math>
| =
+
| <math>=\!</math>
| Property of ''x''
+
| <math>\operatorname{Property~of}\ x </math>
| =
+
| <math>=\!</math>
| Object above ''x''&nbsp;,
+
| <math>\operatorname{Object~above}\ x,</math>
 
|-
 
|-
| ''x'' <math>\gtrdot</math>
+
| <math>x \gtrdot</math>
| =
+
| <math>=\!</math>
| ''x''&rsquo;s Instance
+
| <math>x \operatorname{'s~Instance}</math>
| =
+
| <math>=\!</math>
| Instance of ''x''
+
| <math>\operatorname{Instance~of}\ x </math>
| =
+
| <math>=\!</math>
| Object below ''x''&nbsp;.
+
| <math>\operatorname{Object~below}\ x.</math>
 
|}
 
|}
  
12,080

edits

Navigation menu