Abstract: In this paper we introduce the concept of exploded and compressed real number such that the set of exploded real numbers contains the set of real numbers. Moreover, the concept of equality, ordering, neighbourhood and convergence will be extended for the set of exploded real numbers. We will find operations for exploded real numbers such that the set of exploded real numbers will be isomorphic to the set of real numbers. The set of compressed real numbers is a subset of 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 the repeated explosions and compressions.
Keywords: Exploded numbers, compressed numbers, super-addition, super-multiplication, exploded-function, super-function.
Classification (MSC2000): 03C30
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