| Subsets, set theory: subsets are not to be confused with elements of sets which are not themselves sets. Individual sets can be formed from individual elements if additional assumptions are introduced. On the other hand, subsets may consist of 0 or more elements. Subsets are in each case related to a set whose subset they are. The cardinality of a set results from the counting of its elements and not from the counting of its subsets, since these can overlap. The set of all subsets of a set is called a power set. The empty set {0} is a subset of each set, but not an element of it. See also set theory, sets, power set, element relation._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
