Posts Tagged ‘equal’
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, 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
Definition of an Outlier
Description
A detailed tutorial on the definition of an outlier. Step by step tutorial including several examples of definitions of outliers for reference.
Overview
An outlier is a type of observation of statistical data. It is usually very far away from the other values in the data set, hence the name. Usually it is a number that is much smaller than the other numbers, although it could be much larger than the other numbers as well. Outliers have an equal chance of occuring in any random observation, but they are still rare. Typically when an outlier is found it means there is some sort of mistake, usually a measurement error.
Tags: chance, data, elements, equal, error, larger, measurement, mistake, numbers, observation, outlier, random, set, smaller, statistical, statistics, values
Posted in Statistics | 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 »
Friday, November 6th, 2009
Introduction to Injective and Surjective Functions
Description
A detailed tutorial on injective and surjective functions. Step by step tutorial including several examples of injective and surjective functions for reference.
Overview
When given a function, there are two properties it can possess: it can be either injective or surjective. An injective function is a function that associates distinct arguments in one domain with distinct values in one codomain, and every unique argument produces a unique result. A surjective function is a function where the range is equal to the codomain. A surjective function is also called a surjection or said to be onto. For both cases, the function could be bijective if all elements in the codomain are mapped, which means that it would be both injective and surjective at the same time.
Tags: algebra, arguments, bijective, codomain, equal, function, injective, mapped, onto, range, subjection, surjective, unique, values
Posted in Algebra | No Comments »
Friday, November 6th, 2009
Overview of Symmetry
Description
A detailed tutorial on symmetry and symmetric images. Step by step tutorial including several examples of symmetry for reference.
Overview
Symmetry is a very basic concept in geometry. It is similar to invariance. It is when something is equal to itself through both of its sides. If you compare the two sides of something and they match, then the object is said to be symmetric. When testing an image for symmetry, the easiest test is to draw an imaginary line down the middle. Then pretend to fold the image over. If the two sides are perfect matches of each other, then the image is symmetric.
Tags: arithmetic, center, equal, fold, Geometry, imaginary, invariance, line, match, middle, same, symmetric, symmetrical, symmetry
Posted in Arithmetic | No Comments »
Thursday, November 5th, 2009
Cancellation Properties of Natural Numbers
Description
A detailed tutorial on cancellation properties of natural numbers. Step by step tutorial including several examples of cancellation properties for reference.
Overview
Cancellation properties of natural numbers state that when two terms are equal to each other, if the same number is being multiplied or added on both terms, you may cancel them out and the terms will still be equal to each other. Knowledge of the cancellation properties is extremely important for simplification of equations and when trying to find the value of a variable. Mathematically stated, the cancellation properties are that if x + z = y + z or xz = yz, then x = y.
Tags: add, arithmetic, cancel, cancellation, equal, multiply, natural, number, out, properties, property, simplification, simplify, term, value, variable
Posted in Arithmetic | No Comments »
Tuesday, November 3rd, 2009
Introduction to Square Matrices
Description
A detailed tutorial on square matrices and how to identify them. Step by step tutorial including several examples of square matrices for reference.
Overview
A square matrix is a simple matrix in the shape of a square. It has the same number of rows and columns. Square matrices are called nxn matrces. The most common values for n are 2 and 3. Two columns and rows is the smallest amount of rows and columns a square matrix can have – matrices with only one value are not considered to be square.
Tags: 2, 2x2, 3, 3x3, algebra, columns, equal, equivalent, linear, matrices, matrix, n!, number, nxn, rows, same, shape, square, three, two, values
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
Order Properties of Natural Numbers
Description
A detailed tutorial on the order properties of natural numbers. Step by step tutorial including several examples of the order properties of natural numbers for reference.
Overview
The order properties are one of the eight sets of properties of natural numbers. The order properties are all based off of inequalities and how to order inequalities. Less than and less than or equal to are the two that are used in the order properties. There are five order properties in all. Since the order properties are of natural numbers, in order to prove the order properties your examples must be natural numbers, or positive integers greater than or equal to one.
Tags: arithmetic, equal, greater than, greater than or equal to, inequalities, less than, less than or equal to, n!, natural, number, order, property, x, y, z
Posted in Arithmetic | No Comments »
Thursday, October 29th, 2009
Overview of Symmetric Relations
Description
A detailed tutorial on the property of symmetric relations. Step by step tutorial including several examples of symmetric relations for reference.
Overview
A symmetric relation can be mathematically defined as for all x, y, and z belonging to A, if x R y and y R z, then x R z. In this statement, A is a set, and R is a relation of that set. An empty set is considered to be symmetric. Since a symmetric relation is defined by a conditional sentence, a proof for the symmetric property of relations would be written as a direct proof.
Tags: conditional, direct, discrete math, empty, equal, equivalence, married, odd, proof, property, r, relation, set, symmetric, x, y
Posted in Discrete Math | No Comments »
