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Exploded and compressed numbers. (English) Zbl 1063.03048

Summary: In this paper we introduce the concepts of exploded and compressed real number such that the set of exploded real numbers contains the set of real numbers. Moreover, the concepts of equality, ordering, neighbourhood and convergence are extended for the set of exploded real numbers. We find operations for exploded real numbers such that the set of exploded real numbers is isomorphic to the set of real numbers. The set of compressed real numbers is a subset of the real numbers and a model for the relationship of the sets of real numbers and exploded real numbers, respectively. Introducing the concept of super-function we extend the concept of continuity to functions with one variable. Finally, we say a few words on repeated explosions and compressions.

MSC:

03H05 Nonstandard models in mathematics
26E35 Nonstandard analysis
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