Appendix II

Formal Definitions

The secret of being boring is to say everything.

—Voltaire

For notational conventions please refer to page 168.

Definition I. A finite structure is a pair image such that:

  • image is a set of primitive elements or entities of dimension 0 called the universe of image
  • image is a finite set of relations (Definition II)

Definition II. A unary (binary) relation is a set of 1-tuples [2-tuples, or pairs] of entities of dimension 0. A class (method, signature) of dimension 0 is an entity in the relation Class (Method, Signature). A class (method, signature) of dimension d is a set of classes (methods, signatures) of dimension d – 1.

Definition III. Given a binary relation BinaryRelation, the transitive closure of BinaryRelation, written BinaryRelation+, is that set of pairs imagex, yimage such that at least one of the following conditions hold:

  • x, yBinaryRelation
  • There exists an element z in ...

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