Cantor's Publications

Taken from the excellent book [Hallett, 1986]. See there for precise references. [Cantor, 1932] is the collected works. See also the book [Cantor, 1955].

[Hallett, 1986] Second paperback reprint of `Cantorian Set Theory and Limitation of Size', by Michael Hallett, Oxford Logic Guides, 10, 1984. (16.F.96)


[1872]
Uber die Ausdehnung eines Satzes aus der Theorie der trignometrischen Reihen.
[1874]
Uber eine Eigenschaft des Inbegriffes aller reellen algebraischeen Zahlen.
[1878]
Ein Beitrag zur Mannigfaltigkeitslehre
[1879a]
Uber einen Satz aus der Theorie der stetigen Mannigfaltigkeiten.
[1879-1884]
Uber unendliche, lineare Punktmannigfaltigkeiten, parts 1-6, in Mathematische Annalen.

  1. [1879b]
  2. [1880]
  3. [1882]
  4. [1883a]
  5. [1883b] Introduces well orderings and ordinal numbers.
  6. [1884a]

[1883d]
republication of [1883b], with a new forward.
[1883c]
Surs diverse theoremes de la theorie de points situes dans un espace continu a n-dimensions.
[1884a]
[1884b]
De la puissance des ensembles parfaits de points.
[1885a,b]
[1886a,b]
[1887-88]
Mitteilungen zur Lehre vom Transfiniten, I,II.
[1891]
[1895],[1897]
Beitrage zur Begrundung der transfiniten Mengenlehre, 1 and 2.
[Cantor, 1932]
Gessamelte Abhandlungen mathematischen und philosophischen Inhalts. (ed E. Zermelo), Springer, Berlin (reprinted 1980)
[Cantor, 1955]
Contributions to the founding of the theory of transfinite numbers, Dover paperback reprint of the 1915 English translation of Cantor's [1895] and [1897], with a long introduction, by P. Jourdain, (16.D.303)

Cantor's definition of real numbers as (equivalence classes of) Cauchy sequences of rational numbers is in his [1872]. Cantor lived in Berlin, 1863-1869 where he was influenced by Weierstrass. Weierstrass had been lecturing in Berlin since 1859. He had his own `definition' of real number, probably the first person to attempt a definition. The idea is somewhat obscurely presented in the introduction to [Cantor, 1955].