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Finite set. 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. For example, is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the ...
Finite number. Finite number may refer to: Natural number, a countable number less than infinity, being the cardinality of a finite set. Real number, such as may result from a measurement (of time, length, area, etc.) In mathematical parlance, a value other than infinite or infinitesimal values and distinct from the value 0, see List of ...
A finite field is a finite set that is a field; this means that multiplication, addition, subtraction and division (excluding division by zero) are defined and satisfy the rules of arithmetic known as the field axioms . The number of elements of a finite field is called its order or, sometimes, its size.
The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in "discrete" steps and ...
[1] [3] For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. [4] In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object.
The union of any number of open sets, or infinitely many open sets, is open. [4] The intersection of a finite number of open sets is open. [4] A complement of an open set (relative to the space that the topology is defined on) is called a closed set. A set may be both open and closed (a clopen set).
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. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the ...
Transfinite number. In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to ...