Posts Tagged ‘r’
Thursday, October 29th, 2009
Overview of Quasitransitive Relations
Description
A detailed tutorial on the property of quasitransitive relations. Step by step tutorial including several examples of quasitransitive relations for reference.
Overview
A quasitransitive relation can be mathematically defined as for all x, y, and z belonging to A, if x R y, y R z, ~(y R x), and ~(z R y), then x R z and ~(z R x). In this statement, A is a set, and R is a relation of that set. A quasitransitive relation is considered to be a weak version of a transitive relation. If the relation also happens to be asymmetric, then it is considered transitive.
Tags: arithmetic, asymmetric, negation, opposite, property, quasitransitive, r, relation, transitive, 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 »
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 »
Friday, October 23rd, 2009
The Notation of Basic Number Sets
Description
A detailed tutorial on basic number sets. Step by step tutorial including several examples of the notation of basic number sets for reference.
Overview
There are four basic number sets – N, Z, Q, R. N belongs to Z, and Z and Q belongs to R. This means N also belongs to R. N is the set of all natural numbers. Z is the set of all integers. Q is the set of all rational numbers. R is the set of all real numbers. All the notations of these sets were picked because they relate to certain words. N and R were chosen because they stand for natural and real – which is what the sets are. Q means quotient, because rational numbers are a quotient of any integer provided the denominator is not 0. Z was picked because it stands for zahlen – a German word meaning numbers, and Z is indeed a set of (almost) all numbers.
Tags: all, arithmetic, integer, n!, natural, notation, number, Q, quotient, r, rational, real, set, z, zahlen
Posted in Arithmetic | No Comments »
Thursday, October 8th, 2009
Joint Variation Explained
Description
A detailed tutorial on joint variation. Step by step tutorial including several examples of joint variation and what joint variation is for reference.
Overview
Joint variation is the same as direct variation, only it is occuring for more than one variable, while direct variation only deals with one variable. Because of the similarities, joint variation is performed in the same way as direct variation, although for two variables and not one. Joint variation can be expressed as d = r * t.
Tags: d, direct, joint, joint variation, Math, one, r, similar, similarties, statistics, t, two, variable, variation
Posted in Statistics | No Comments »
Tuesday, October 6th, 2009
How to Test for Convergence Using the Geometric Series Test
Description
A detailed tutorial on how to test for convergence using the geometric series test. Step by step tutorial including several examples of testing for convergence using the geometric series test for reference.
Overview
A geometric series is a series that maintains a constant ratio between a set of terms. This series is an addition series, and would be expressed as 1/a + 1/2a + 1/4a, extending as far as you wish in either direction. If a series does not have that constant ratio, then it is not a geometric series. The series should converge at one, because as all the numbers are added they get closer and closer to one. The first term of a geometric series is given by a, and the ratio of a geometric series is given by r. If the ratio is less than one, then the geometric series converges to a / (1 – r). If the ratio is greater than or equal to one, then the series diverges. Usually the series will converge, which is why this is considered a test for convergence and not for divergence.
Tags: a, addition, Calculus, converge, convergence, diverge, divergence, equal to, first term, geometric, greater than, less than, Math, notation, r, ratio, series, summation, test
Posted in Calculus | No Comments »
Tuesday, October 6th, 2009
Plotting Points in the Polar Coordinate System
Description
A detailed tutorial on plotting points in the polar coordinate system. Step by step tutorial including several examples of how to plot points on the polar coordinate system for reference.
Overview
By this point, everyone should know how to plot points on a normal graph. But what about a circular graph? This circular graph is called the polar coordinate system or the polar plane. Instead of using the points (x, y), the polar coordinate system uses the points (r, theta). Theta is a greek letter that looks like a zero with a horizontal line drawn through the center. Most of the points you will be finding for the polar coordinate system will be used with trigonometric functions – sine, cosine, and tangent. Graphing occurs in about the same way as it would on a normal graph – just match up the points, even if they are on a circle.
Tags: Calculus, circle, coordinate, cosine, function, functions, graph, Math, points, polar, r, sine, system, tangent, theta, trig, trigonometric, x, y
Posted in Calculus | No Comments »
