Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical...

the Foundations of Mathematics (German: Bemerkungen über die Grundlagen der Mathematik) is a book of Ludwig Wittgenstein's notes on the philosophy of mathematics...

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand...

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains...

include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has...

Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types. Types...

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function...

ISBN 9780821847619. Mayberry, John P. (2000), The Foundations of Mathematics in the Theory of Sets, Encyclopedia of Mathematics and its Applications, vol. 82, Cambridge...

In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types...

modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all...

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. Writing A = { 1 , 2 , 3 , 4 } {\displaystyle...

Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics...

previously been considered as mathematics, such as mathematical logic and foundations. Number theory began with the manipulation of numbers, that is, natural...

mathematics and logic are identical. The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference. It reported...

theory at the nLab Homotopy Type Theory: Univalent Foundations of Mathematics. The Univalent Foundations Program. Institute for Advanced Study. Frank Ruda...

In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map:...

Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean...

In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the...

ISBN 978-0-619-21558-3. Pudlák, Pavel (2013). "Mathematical structures". Logical foundations of mathematics and computational complexity a gentle introduction. Cham: Springer...

Intuitionism maintains that the foundations of mathematics lie in the individual mathematician's intuition, thereby making mathematics into an intrinsically subjective...

Univalent Foundations of Mathematics Official announcement of The HoTT Book, by Steve Awodey, 20 June 2013 Monroe, D (2014). "A New Type of Mathematics?". Comm...

development of modern logic in the Begriffsschrift and work in the foundations of mathematics. His book the Foundations of Arithmetic is the seminal text of the...

All pages with titles beginning with The Foundation Foundations of mathematics, theory of mathematics This disambiguation page lists articles associated...

theory", in Buss, Samuel R. (ed.), Handbook of Proof Theory, Studies in Logic and the Foundations of Mathematics, vol. 137, Elsevier, pp. 1–78, ISBN 978-0-08-053318-6...

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern...

In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic...

A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an object is anything that has been (or could...

the sets of the formal languages that can be parsed by machines with limited computational power. In logic and the foundations of mathematics, formal languages...

of a function is a special case of a relation. In the modern foundations of mathematics, and, typically, in set theory, a function is actually equal to...

symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. Freeman...