|Set Theory: set theory is the system of rules and axioms, which regulates the formation of sets. The elements are exclusively numbers. Sets contain individual objects, that is, numbers as elements. Furthermore, sets contain sub-sets, that is, again sets of elements. The set of all sub-sets of a set is called the power set. Each set contains the empty set as a subset, but not as an element. The size of sets is called the cardinality. Sets containing the same elements are identical. See also comprehension, comprehension axiom, selection axiom, infinity axiom, couple set axiom, extensionality principle._____________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. |
Nicholas Bourbaki on Set Theory - Dictionary of Arguments
Thiel I 308
Quantum theory: in Bourbaki it is never spoken of logicism, always only of the set theory. Sets are genuine mathematical objects, and they are not reducible to others (logic: classes). The concept of sets is an essential tool for the unification of mathematics.
>Sets, >Set theory, >Classes, >Logic, >Unification.
Set theory: as a fundamental discipline of mathematics: basic concepts such as relation and function are traced back to the concept of the set, by explicit definition.
>Element relation, >Subset, >Relations, >Functions.
Relation functions as a symmetrical or asymmetrical pairing for a two-digit relation. Sometimes we need means to express the order: ordered pairs.
Def Functions: unambiguous relations._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Philosophie und Mathematik Darmstadt 1995