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Construction of Numbers
We have used the notion of natural numbers and real numbers informally in previous chapters. In this chapter, we shall construct the number system using the axioms of set theory. The 10th axiom, which is the infinity axiom, will be formally introduced, completeing our axiom list.
It is also possible to first construct the real number system by a set of axioms for the real numbers and work from them. Then the set of natural numbers is a subset of the set of real numbers. We will also use this axiomatic approach as well as the constructive approach.
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