Historical Remarks
Cantor himself defined the set in a general, abstract way, and mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense. The original paper provides several different constructions of the abstract concept.
This set would have been considered abstract at the time when Cantor devised it. Cantor himself was led to it by practical concerns about the set of points where a trigonometric series might fail to converge. The discovery did much to set him on the course for developing an abstract, general theory of infinite sets.
Read more about this topic: Cantor Set
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