Ordinary mathematics

Ordinary mathematics

In the philosophy of mathematics, ordinary mathematics is an inexact term, used to distinguish the body of most mathematical work from that of, for example, constructivist, intuitionist, or finitist mathematics.

Ordinary mathematics is usually studied within the universe SN, or sometimes Vω+ω (see Von Neumann universe). Contrast with finitist mathematics, which limits to the study of Vω (see hereditarily finite sets), or with metamathematics and the study of large cardinals, which study objects contained in a larger universe.

Ordinary mathematicians generally assume the axiom of choice (at least, because it makes their work easier), whereas constructivists reject it on the grounds that it is "non-constructive", and also reject the law of excluded middle, which can be derived from it.



Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Mathematics of radio engineering — A complex valued function. The mathematics of radio engineering is a pleasant and very useful subject. This article is an attempt to provide a reasonably comprehensive summary of this almost limitless topic. While the ideas have historically… …   Wikipedia

  • Mathematics and art — have a long historical relationship. The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid,[1] the Parthenon …   Wikipedia

  • Mathematics, Form and Function — is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane. Contents 1 Mac Lane s relevance to the philosophy of mathematics 2 Mathematics and human activities …   Wikipedia

  • Mathematics (Junior Cert) — Mathematics is one of the mandatory subjects on the Junior Cert examination in secondary schools in Ireland. There are three levels: Higher, Ordinary and Foundation. v …   Wikipedia

  • mathematics, philosophy of — Branch of philosophy concerned with the epistemology and ontology of mathematics. Early in the 20th century, three main schools of thought called logicism, formalism, and intuitionism arose to account for and resolve the crisis in the foundations …   Universalium

  • Mathematics and Physical Sciences — ▪ 2003 Introduction Mathematics       Mathematics in 2002 was marked by two discoveries in number theory. The first may have practical implications; the second satisfied a 150 year old curiosity.       Computer scientist Manindra Agrawal of the… …   Universalium

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • Ordinary differential equation — In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable. A simple example is Newton s second law of… …   Wikipedia

  • Ordinary language philosophy — For the philosophy of language, see Philosophy of language. Ordinary language philosophy is a philosophical school that approaches traditional philosophical problems as rooted in misunderstandings philosophers develop by distorting or forgetting… …   Wikipedia

  • mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …   Universalium

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”