Posts Tagged ‘cardinality’
Tuesday, January 5th, 2010
An Overview of the Cantor-Bernstein-Schroeder Theorem
Description
A detailed tutorial on the Cantor-Bernstein-Schroeder Theorem. Step by step tutorial including several examples of the Cantor-Bernstein-Schroeder Theorem for reference.
Overview
The Cantor-Bernstein-Schroeder Theorem states that if there exist injective functions f: A –> B and g: B –> A between the sets A and B, then there exists a bijective function h: A –> B. This means that if |A| < |B| and |B| < |A|, then they are equipollent. Equipollent is a term that is similar to equal, and is denoted in the same way. However, the word equipollent means equal in cardinality, but not in any other way.
Tags: Bernstein, bijective, Cantor, cardinality, denoted, discrete math, equal, equipollent, Ernst, Felix, function, Georg, injective, Schroeder, theorem
Posted in Discrete Math | No Comments »
Friday, December 18th, 2009
How to Define Cardinal Numbers
Description
A detailed tutorial on the definition of cardinal numbers. Step by step tutorial including several examples of how to define cardinal numbers for reference.
Overview
Cardinal numbers are natural numbers that are used to measure cardinality of sets. Cardinality is a fancy way of saying the size of a set. This means the cardinality is the number of elements in a set, provided that the set is finite. If the set is infinite, something called a transfinite cardinal number is used to describe the cardinality of the set. Cardinal numbers are a very important part of set theory, even though they are not studied often or used constantly.
Tags: abstract, algebra, analysis, cardinal, cardinality, combinatorics, elements, finite, infinite, mathematical, measure, natural, number, set, set theory, size, transfinite
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
Definition of a Finite Set
Description
A detailed tutorial on the definition of a finite set. Step by step tutorial including several examples of finite sets for reference.
Overview
There are many different types of sets, but one of the most common ones to run into a finite sets. A finite set is a set that has a finite number of elements – meaning a set with a definite number of elements, such as five, or ten. The number of elements in the set must be a natural number, and it is called the cardinality of a set. An empty set is considered to be finite, with a cardiality of zero, even though zero is not considered to be a natural number.
Tags: algebra, cardinality, element, elements, empty set, finite, infinite, Math, natural number, set, sets, zero
Posted in Algebra | No Comments »
