Antinomies of set theory
One of the most important basic concepts of mathematics is the concept of a set. - html homework help A set is understood to be a grouping of certain real or imaginary objects from a given or selected basic area into a whole. The individual objects are called elements of the set.
The admission of all conceivable summaries as sets can lead to contradictions, to which Bertrand Russell (1872 to 1970) drew attention and which are therefore also called Russellian antinomies.
The theoretical edifice of mathematics is based on basic concepts that are not defined, but merely characterised by their mutual relationships, as well as on normative determinations that cannot be proven in the respective mathematical system, the so-called axioms - homework help geometry . Above this basis rises a network of (derived, definitionally determined) concepts and statements secured by proofs, the mathematical theorems.
One of the most important basic concepts of mathematics is the concept of a set:
A set is understood to be a summary of certain real or imagined objects from a given or selected basic area to form a whole. The individual objects are called elements of the set.
The grouping of objects from such a basic area G into a set takes place on the basis of certain set-forming properties - https://domyhomework.club/ : A set then consists of those objects of the basic area which possess these properties.