The one stated under von Neumann definition of the ordinals is expressed as an order type associated with each well-ordering, and is named for Burali- Forti. A reparametrization of conditional probability density functions to show the lack of invariance under transformations lies behind the one named for Borel and Kolmogorov. The congruence of measures for subsets and unions of subsets is one of these stated by Hausdorff, while the another one of these assumes that a set of infinities exists, and hence must be infinite, as stated by Cantor. A ball dissected into six pieces and reassembled to form two balls identical to the original is a statement of this type named for Banach and Tarski. FTP a set containing sets which are not members of themselves leads to one of these named for Russell, a statement of mathematical contradiction.
The one stated under von Neumann definition of the ordinals is expressed as an order type associated with each well-ordering, and is named for Burali- Forti. A reparametrization of conditional probability density functions to show the lack of invariance under transformations lies behind the one named for Borel and Kolmogorov. The congruence of measures for subsets and unions of subsets is one of these stated by Hausdorff, while the another one of these assumes that a set of infinities exists, and hence must be infinite, as stated by Cantor. A ball dissected into six pieces and reassembled to form two balls identical to the original is a statement of this type named for Banach and Tarski. FTP a set containing sets which are not members of themselves leads to one of these named for Russell, a statement of mathematical contradiction.
The one stated under von Neumann definition of the ordinals is expressed as an order type associated with each well-ordering, and is named for Burali- Forti.