In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who, in 1897, published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Cantor. Bertrand Russell subsequently noticed the contradiction, and when he published it in his 1903 book Principles of Mathematics, he stated that it had been suggested to him by Burali-Forti's paper, with the result that it came to be known by Burali-Forti's name. Stated in terms of von Neumann ordinals We will prove this by reductio ad absurdum. Let be a set consisting of all ordinal numbers. is transitive because for every element of (which is an ordinal number and can be any ordinal number) and every element of (i.e. under the definition of Von Neumann ordinals, for every
En la teoría ordinaria, un campo de la matemática, el paradojo de Burali-Forti demuestra que construir "el conjunto de todos los números ordinarios" conduce a una contradicción y por lo tanto muestra una antinomia en un sistema que permite su construcción. Se llama Cesare Burali-Forti, quien, en 1897, publicó un artículo que demostra un teorema que, desconocido para él, contradice un resultado previamente probado por Cantor. Bertrand Russell posteriormente notó la contradicción, y cuando lo publicó en su libro de 1903 Principles of Mathematics, afirmó que había sido sugerido a él por el artículo de Burali-Forti, con el resultado de que llegó a ser conocido por el nombre de Burali-Forti.