Set theory and transfinite cardinals
Teoría de conjuntos, cardinales transfinitos y no numerabilidad de los reales
- Date
- 1874 · confidence high
- Place
- Halle, Germany
- Credited to
- Georg Cantor
- People
- 👤 Georg Cantor1845–1918
- Field
- Knowledge & symbols
What was discovered
A proof that the reals cannot be put in bijection with the naturals (1874; diagonal argument in 1891) and the construction of an arithmetic of infinities of different sizes with cardinal and ordinal numbers. It turns actual infinity into a mathematical object.
Kronecker fiercely opposed it; Hilbert declared that no one shall expel us from the paradise that Cantor created.
What it led to
- the foundations of mathematics
- the continuum hypothesis
- the paradoxes and Zermelo-Fraenkel axiomatics
- Gödel's theorem and Turing's diagonal argument
- topology and measure theory
Built on
- Dedekind cuts and ideals1872
- Fourier series (sets of uniqueness)
- Bolzano (Paradoxes of the Infinite)
- Dedekind