The set theory is a branch of the Mathématiques initially creates by the German Mathématicien Georg Cantor at the end of the 19th century.

The basic concepts of the set theory are the concepts of “element”, “Ensemble” and “membership”. One gives oneself at the beginning basic objects. These basic objects can be joined together to form units, to which they belong : a unit can thus be seen like a collection of objects, the elements (or members ) that it contains . The units can also be seen like additional elements allowing the creation of new units which, in their turn, could be joined together in units, and so on…

The set theory was bitterly discussed, initially because of the new vision of the mathematical Infini that she proposed, through the cardinal .

Then, one discovered that this theory, known as naive because not formalized, carried out to paradoxes such as Paradox of Russell, because it supposed that one could carry out any operation on the units, without any restriction. To answer these problems, several mathematicians rebuilt the set theory, by using this time an axiomatic approach .

Thus, initially disputed, the set theory changed to become a fundamental theory modern mathematics: the latter is used to justify the assumptions made in mathematics concerning the existence of mathematical objects, such as the numbers or the functions, and their properties.

However, the initial theory of Cantor, with some installations, is remained interesting because of its intuitive aspects, and this is why, currently, the set theory in two parts is separated: the field of the naive Set theory and that of the axiomatic Set theory.

See too

• Paradox of Russell and consequences
• general Algèbre
• Together-product
• Fondation of mathematics
• naive Théorie of the units
• axiomatic Théorie of the units
• Opérations ensemblists
• Produces Cartesian

Be-X-old: Тэорыямностваў Fiu-vro: Hulgateooria Simple: Set theory Zh-classical: 集論 Zh-min-nan: Chi̍p-ha̍p-lūn