Posts Tagged ‘inequality’
Tuesday, December 29th, 2009
Overview of the Trichotomy Property
Description
A detailed tutorial on the trichotomy property. Step by step tutorial including several examples of the trichotomy property for reference.
Overview
The trichotomy property is one of the ordering properties of natural numbers. It tells us what order you need to put the natural numbers in – in other words, it tells you the placement of each element of the set of natural numbers. The trichotomy property states that is there are two natural numbers m and n, that m must be either less than n, equal to n, or greater than n. The smaller number is to be placed first, with the larger number after it. If the numbers are equal, then only one number needs to be included as part of the set.
Tags: arithmetic, element, equal, greater, inequality, larger, less, natural, number, order, placement, property, set, smaller, than, trichotomy
Posted in Arithmetic | No Comments »
Friday, November 20th, 2009
Overview of Isoperimetric Inequalities
Description
A detailed tutorial on isoperimetric inequalities. Step by step tutorial including several examples of isoperimetric inequalities for reference.
Overview
An isoperimetric inequality is actually a geometric inquality. It deals with the square of a circumference of a closed curve in a plane and the area of the region it encloses. Isoperimetric means to have the same perimeter. The isoperimetric problem is used in conjunction the isoperimetric inequality to determine the measure of the plane figure.
Tags: area, circumeference, closed, curve, differential equations, figure, geometric, inequalities, inequality, isoperimetric, meausre, perimeter, plane, problem, region, square
Posted in Differential Equations | No Comments »
Tuesday, November 17th, 2009
How to Draw a Boundary Line
Description
A detailed tutorial on how to draw a boundary line. Step by step tutorial including several examples on how to draw a boundary line for reference.
Overview
A boundary line is used when graphing inequalities on a number line or a regular Cartesian graphing system. What the boundary line does is connect the two points in the inequality – in other words, it sets a boundary of what an unknown variable would be on that inequality. The boundary line can either be solid or dashed. The boundary line is only dashed when it is drawn on a regular graph, to express that the line was somewhere else at one point and was then moved. In all other cases, the boundary line is solid.
Tags: algebra, boundary, closed, coordinates, dashed, equal, graph, greater, inequality, interval, less, line, number, open, points, solid, then, to
Posted in Algebra | No Comments »
Tuesday, September 22nd, 2009
Cauchy-Schwarz Inequality Explained
Description
A detailed tutorial on the solving of the Cauchy-Schwarz Inequality. Step by step tutorial including several examples of how to solve the Cauchy-Schwarz Inequality for reference.
Overview
The Cauchy-Schwarz Inequality is also known as the Schwarz Inequality, the Bunyakovsky Inequality, and the Cauchy-Bunyakovsky-Schwarz Inequality. It was published by Augustin Cauchy and was first stated by Viktor Yakovlevich Bunyakovsky. It was later rediscovered by Hermann Amandus Schwarz. This is used mostly in linear algebra, when solving vectors. It is also used in probability theory.
The Cauchy-Schwarz Inequality states that for all vectors x and y of an inner product space, 
By taking the square root of both sides, it can be written as 
If the two sides are equal, and if x and y are both independent, then the formula may be restated as 
Tags: Augustin Cauchy, Bunyakovsky Inequality, Cauchy-Bunyakovsky-Schwarz Inequality, Cauchy-Schwarz Inequality, Hermann Amandus Schwarz, inequality, linear algebra, Math, probability theory, product space, Schwarz Inequality, square root, vectors, Viktor Yakovlevich Bunyakovsky
Posted in Algebra | No Comments »
