Posts Tagged ‘equal’
Thursday, October 29th, 2009
Overview of Transitive Relations
Description
A detailed tutorial on the property of transitive relations. Step by step tutorial including several examples of transitive relations for reference.
Overview
A transitive relation can be mathematically defined as for all x and y belonging to A, if x R y, then y R x. In this statement, A is a set, and R is a relation of that set. An empty set is considered to be transitive. Since a transitive relation is defined by a conditional sentence, a proof for the transitive property of relations would be written as a direct proof.
Tags: conditional, direct, discrete math, divides, empty, equal, equivalence, great, greater, implies, proof, property, r, relation, set, subset, transitive, x, y, z
Posted in Discrete Math | No Comments »
Thursday, October 29th, 2009
Overview of Reflexive Relations
Description
A detailed tutorial on the property of reflexive relations. Step by step tutorial including several examples of reflexive relations for reference.
Overview
A reflexive relation can be mathematically defined as for all x belonging to A, x R x. In this statement, A is a set, and R is a relation of that set. If the relation is an empty set, then it is not reflexive, unless the set itself happens to be an empty set. When writing a proof for a reflexive relation, you must attempt to prove that (x, x) does not belong to R. If you cannot prove this, then you know that the relation must be reflexive.
Tags: discrete math, divide, empty, equal, equvalence, greater, less, proof, property, r, reflexive, relation, set, subset, x
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
Introduction to Vector Equality
Description
A detailed tutorial on how to determine if two vectors are equal. Step by step tutorial including several examples of vector equality for reference.
Overview
Vectors are said to be equal if they have the same magnitude and direction. They must also have the same coordinates. Using this logic, it is possible to determine if you have two vectors 
and 
, they are equal if 
.
Tags: a, algebra, b, coordinates, direction, E, equal, equality, length, magnitude, vector
Posted in Algebra | No Comments »
Friday, October 23rd, 2009
How to Solve Vectors Using Vector Subtraction
Description
A detailed tutorial on how to solve vectors using vector subtraction. Step by step tutorial including several examples of vector subtraction for reference.
Overview
Vector subtraction involves two vectors that do not have to be equal, and could have different magnitudes and directions. The vectors are referred to as a and b. The formula for vector subtraction is:
In general, vector subtraction is defined geomtrically instead of algebraically, so it is not used quite as often as vector addition is.
Tags: addition, algebra, algebraically, direction, equal, formula, geometrically, Geometry, magnitude, subtraction, vector
Posted in Algebra | No Comments »
Friday, October 23rd, 2009
How to Solve Vectors Using Vector Addition
Description
A detailed tutorial on how to solve vectors using vector addition. Step by step tutorial including several examples of vector addition for reference.
Overview
Vector addition involves two vectors that do not have to be equal, and could have different magnitudes and directions. The vectors are referred to as a and b. The formula for vector addition is:
Vector addition is also occassionally referred to as the parallelogram rule, because on a picture diagram of vector addition the shape of a parallelogram is formed.
Tags: addition, algebra, direction, equal, formula, graph, magnitude, parallelogram, picture, rule, vector
Posted in Algebra | No Comments »
Thursday, October 22nd, 2009
Inductive Sets in Set Theory
Description
A detailed tutorial on inductive sets in set theory. Step by step tutorial including several examples of inductive sets in set theory for reference.
Overview
An inductive set is a continuous set of natural numbers that follows a basic pattern of n + 1. This means that for all numbers in the set, that number plus the number one must also be included in the set.The set does not need to include all natural numbers – that is, the set may start at any natural number provided it is greater than or equal to one. However, the set must continue to infinity or it cannot be considered an inductive set.
Tags: -1, addition, complete, continuous, discrete math, element, equal, greater, induction, inductive, infinity, mathematical, natural, numbers, one, pattern, principle, set, subset, theory
Posted in Discrete Math | No Comments »
Tuesday, September 15th, 2009
An Overview of the Different Types of Triangles
Description
A detailed tutorial on the different types of triangles. Step by step tutorial including several examples of the different types of triangles for reference. Knowledge of the different types of triangles is required for all geometry classes.
Overview
Everyone knows what a triangle is, but a triangle is more than just “a triangle” – it could be one of several different types of triangles. Different types of triangles are identified by the different traits of their sides and their angles. The types are as follows:
Scalene Triangles: All sides and all angles are of different measures and lengths.
Right Triangles: One angle of the triangle is 90 degrees.
Isosceles Triangles: 2 sides and 2 angles have the same measures and lengths.
Equilateral Triangles: All side lengths are the same and all angles are 60 degrees.
Equiangular Triangles: All angles measure 60 degrees but all sides could have different lengths.
Tags: 60, 90, angle, degrees, equal, equiangular, equilateral, Geometry, isosceles, length, Math, measure, right, scalene, side, triangle
Posted in Geometry | No Comments »
Tuesday, September 15th, 2009
All About 30-60-90 Triangles
Description
A detailed tutorial on the solving of 30-60-90 triangles. Step by step tutorial including several examples of how to solve 30-60-90 triangles for reference.
Overview
A 30-60-90 triangle is a special type of right triangle. The 30-60-90 refers to the measure of the angles of the triangle. This triangle is special because if you take two of them, flip one of them over, and place the triangles back to back, then you have an equilateral and equiangular triangle – triangles that have sides and angles all of the same length.
Tags: 30, 30-60-90, 60, 90, angles, equal, equiangular, equilateral, Geometry, Math, right, sides, triangles
Posted in Geometry | No Comments »
Tuesday, September 15th, 2009
All About 45-45-90 Triangles
Description
A detailed tutorial on the solving of 45-45-90 triangles. Step by step tutorial including several examples of how to solve 45-45-90 triangles for reference.
Overview
A 45-45-90 triangle is one of the few special triangles that the angles are always the same on – the 45-45-90 part refers to the measurement of the angles. A 45-45-90 triangle is special because it is the only right triangle where the other two angles are equal. Because the angles are equal, this also means that those sides are of equal lengths.
Tags: 45, 45-45-90, 90, angles, equal, Geometry, Math, right, sides, triangles
Posted in Geometry | No Comments »
