Cantor's diagonal argument
Argumento de la diagonal de Cantor
- Date
- 1891 · confidence high
- Place
- Halle, Germany
- Credited to
- Georg Cantor
- Field
- Knowledge & symbols
What was discovered
Cantor devised a proof that constructs, from any supposedly complete list of real numbers, a number not on the list by changing its diagonal digit at each position, thereby proving that the real numbers cannot be counted one by one. The same technique, applied more generally, also proves that the power set of any set always has more elements than the set itself (Cantor's theorem), and it became a fundamental tool of 20th-century mathematical logic.
This same technique, applied to the subsets of a set, also proves Cantor's theorem about the size of the power set; both results come from the same 1891 paper and are recorded here as a single hito.
What it led to
- Modern set theory and the hierarchy of infinities
- Gödel's incompleteness theorems
- Turing's halting problem (undecidability)
Built on
- Cantor's 1874 proof of the uncountability of the real numbers