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v. t. e. Foundations of mathematics is the study of the philosophical and logical [1] and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. [2] In this latter sense, the distinction between foundations of mathematics and ...
Derived set (mathematics) In mathematics, more specifically in point-set topology, the derived set of a subset of a topological space is the set of all limit points of It is usually denoted by. The concept was first introduced by Georg Cantor in 1872 and he developed set theory in large part to study derived sets on the real line .
In mathematics, for a function , the image of an input value is the single output value produced by when passed . The preimage of an output value is the set of input values that produce . More generally, evaluating at each element of a given subset of its domain produces a set, called the " image of under (or through) ".
In von Neumann's set-theoretic construction of the natural numbers, the number 1 is defined as the singleton. In axiomatic set theory, the existence of singletons is a consequence of the axiom of pairing: for any set A, the axiom applied to A and A asserts the existence of which is the same as the singleton (since it contains A, and no other ...
Dense set. In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a ...
In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2] The term map may be used to distinguish some special types of functions, such as homomorphisms.
Set theory. A Venn diagram illustrating the intersection of two sets. Set theory is the study of sets in mathematics. Sets are collections of objects. We refer to these objects as "elements" or "members" of the set. To write a set, one wraps the numbers in {curly brackets}, and separates them with commas. For example. the set holds 1, 2, and 3.
