Search results
Results from the WOW.Com Content Network
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. Informally, a finite set is a set which one could in principle count and finish counting.
A set function is called finite if for every , the value () is finite (which by definition means that () and (); an infinite value is one that is equal to or ). Every finite set function must have a finite mass .
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number.
Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers. Partially ordered sets and sets with other relations have applications in several areas. In discrete mathematics, countable sets (including finite sets) are the main focus
A set of real numbers (hollow and filled circles), a subset of (filled circles), and the infimum of . Note that for totally ordered finite sets, the infimum and the minimum are equal. A set A {\displaystyle A} of real numbers (blue circles), a set of upper bounds of A {\displaystyle A} (red diamond and circles), and the smallest such upper ...
An abstract simplicial complex is a set family (consisting of finite sets) that is downward closed; that is, every subset of a set in is also in . A matroid is an abstract simplicial complex with an additional property called the augmentation property .
Alternatively, consider the real numbers with the counting measure, which assigns to each finite set of reals the number of points in the set. This measure space is not σ-finite, because every set with finite measure contains only finitely many points, and it would take uncountably many such sets to cover the entire real line. The σ-finite ...