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Posts Tagged ‘reflexive’

Relations: Reflexive Property

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 »

Equivalence Relations

Thursday, October 29th, 2009

Introduction to Equivalence Relations

Description

A detailed tutorial on equivalence relations and how to find them. Step by step tutorial on finding equivalence relations for reference.

Overview

An equivalence relation is a relation that specifies how a set can be split into subsets. Relations can only be considered equivalence relations if they are reflexive, symmetric, or transitive. It is possible for an equivalence relation to be one of these, two of these, or all three of these, If the relation is none of them, then it is not an equivalence relation. An empty set is considered to be an equivalence relation, because it is both symmetric and transitive.

Tags: discrete math, element, empty, equivalence, reflexive, relation, set, subset, symmetric, transitive
Posted in Discrete Math | No Comments »

Reflexive Angles

Tuesday, September 29th, 2009

Identifying Reflexive Angles

Description

A detailed tutorial on identifying reflexive angles. Step by step tutorial including several examples of how to identify reflexive angles for reference.

Overview

Reflexive angles are angles that are facing in the wrong direction – another common term for them is a negative angle. An angle is really from a circle, and a circle is 360 degrees around. Let’s just say you draw a 30 degree angle. There is a negative angle that is along the flip side of it – a 330 degree angle. This angle is called reflexive not because it is an opposite angle, but because it is over 180 degrees and less than 360 degrees. So to identify a reflexive angle, remember it must be less than the full circle, but cannot be stretched out to a straight line (on a visual representation).

Tags: 180, addition, angle, angles, complimentary, degrees, Geometry, Math, negative, reflexive, sums, supplementary
Posted in Geometry | No Comments »