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
Famous quotes containing the words historical and/or remarks:
“Among the virtues and vices that make up the British character, we have one vice, at least, that Americans ought to view with sympathy. For they appear to be the only people who share it with us. I mean our worship of the antique. I do not refer to beauty or even historical association. I refer to age, to a quantity of years.”
—William Golding (b. 1911)
“Where do whites fit in the New Africa? Nowhere, I’m inclined to say ... and I do believe that it is true that even the gentlest and most westernised Africans would like the emotional idea of the continent entirely without the complication of the presence of the white man for a generation or two. But nowhere, as an answer for us whites, is in the same category as remarks like What’s the use of living? in the face of the threat of atomic radiation. We are living; we are in Africa.”
—Nadine Gordimer (b. 1923)