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 »
Tuesday, November 10th, 2009
An Overview of Pi
Description
A detailed tutorial on what pi is. Step by step tutorial including several examples of what pi is for reference.
Overview
Pi is a special number in mathematics. It is the ratio of a circle’s circumference to its diameter. No matter what size circle you use, your answer will always be pi, showing that all circles are proportional to one another. Pi is denoted by the Greek letter pi, which looks a little bit like an “n”. The numerical value of pi is 3.1415926535… but is typically shortened to the simple 3.14. Pi is very important in math and is used in all equations dealing with circles.
Tags: 3.14, arithmetic, circle, circumference, denoted, diameter, equations, Greek, letter, pi, propertional, radius, ration, size, value
Posted in Arithmetic | No Comments »
