Math from Words
Chapter Four - The Ordered Pair


James Adrian
      Definition - S is an ordered pair if and only if each following statement is true:

      S is not a set.

      Elements in S are not required to be unique in S.

      S contains exactly a pair of elements.

      Each element in S is represented by a text item.

      Element y, in S, is asymmetrically associated with element x, in S, and is next in order from that x, in S. Element X shall be recognized as The First Element in S, and element y shall be recognized as The Last Element in S.

      If S is said to contain an element or elements of a given description, and that description is faulty, then S does not contain such elements or such an element.

      S does not contain itself.




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