Now, we may map each definition to the set of natural numbers, such that the definition with the smallest number of characters and alphabetical order will correspond to the number 1, the next definition in the series will correspond to 2, and so on. Since each definition is associated with a unique integer, then it is possible that occasionally the integer assigned to a definition fits that definition. If, for example, the definition "not divisible by any integer other than 1 and itself" happened to be 43rd, then this would be true. Since 43 is itself not divisible by any integer other than 1 and itself, then the number of this definition has the property of the definition itself. However, this may not always be the case. If the definition: "divisible by 3" were assigned to the number 58, then the number of the definition does not have the property of the definition itself, since 58 is itself not divisible by 3. This latter example will be termed as having the property of being Richardian. Thus, if a number is Richardian, then the definition corresponding to that number is a property that the number itself does not have. (More formally, "x is Richardian" is equivalent to "x does not have the property designated by the defining expression with which x is correlated in the serially ordered set of definitions".) Thus in this example, 58 is Richardian, but 43 is not.
Now we may map each definition to the set of natural numbers such that the definition with the smallest number of characters and alphabetical order will correspond to the number 1 the next definition in the series will correspond to 2 and so on Since each definition is associated with a unique integer then it is possible that occasionally the integer assigned to a definition fits that definition If for example the definition "not divisible by any integer other than 1 and itself" happened to be 43rd then this would be true Since 43 is itself not divisible by any integer other than 1 and itself then the number of this definition has the property of the definition itself However this may not always be the case If the definition "divisible by 3" were assigned to the number 58 then the number of the definition does not have the property of the definition itself since 58 is itself not divisible by 3 This latter example will be termed as having the property of being Richardian Thus if a number is Richardian then the definition corresponding to that number is a property that the number itself does not have (More formally "x is Richardian" is equivalent to "x does not have the property designated by the defining expression with which x is correlated in the serially ordered set of definitions") Thus in this example 58 is Richardian but 43 is not