In the preceding three chapters, we have looked at some very different areas of mathematics. We began with numbers and number systems; we discussed vectors, matrices and modular arithmetic. Next, we constructed a theory of permutations. Finally, we investigated geometrical symmetry. In each case, we found it convenient to identify an ‘arithmetic system,’ with at least one fundamental ‘arithmetic operation’. The operations all had properties of ‘good behaviour’. Not only that, but the properties that arose always seemed to be the same ones.
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