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.
- [1879b]
- [1880]
- [1882]
- [1883a]
- [1883b] Introduces well orderings and ordinal numbers.
- [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].