Intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics studying constructive mental activity of humans. Any mathematical object is considered to be a product of a construction of a mind, and therefore, an existence of an object is equivalent to the possibility of its construction. It contrasts with classical approach stating that the existence can be proved by refuting its non-existence and applying the law of the excluded middle.
Intuitionism also rejects the abstraction of actual infinity, i.e. it does not consider as given objects infinite entities such as the set of all naturals or an arbitrary sequence of rationals. This requires the reconstruction of the most part of set theory and calculus, leading to theories highly differing from their originals.