An Example of Structural Analogy
We begin with some general remarks that follow from CRKS theory, including a tentative description of the notion of similarity. We then present a CRKS description of some of the structural properties of the set of displacements in a plane, and show how isomorphism can be used to predict properties of the set of all triples of real numbers. In each structure we start with an observed cluster. Next we present a CRKS description of the structural properties, and some simple theorems, of a group, showing, in the process, how some of this data can be isomorphically abstracted from the “common ground” of the displacements and triples structures. We then show how a CRKS can be used to display each of three simple proofs in group theory.
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