Posts Tagged ‘greater’
Tuesday, January 5th, 2010
How to Determine Dedekind Cuts
Description
A detailed tutorial on how to determine Dedekind cuts. Step by step tutorial including several examples of Dedekind cuts for reference.
Overview
A Dedekind cut is a partition of rational numbers into two non-empty sets A and B, such that all elements of A are less than elements of B, and A has no greatest element. The cut itself is a gap that is located between A and B, which is normally found by creating a new, irrational number, and setting it in the gap. What irrational number you use depends on what numbers you have partitioned into the two sets. It is like the number line of advanced algebra, that has both rational and irrational numbers on it instead of just integers. The Dedekind cut was named after Richard Dedekind.
Tags: algebra, between, cut, Dedekind, elements, empty, gap, greater, integer, irrational, less, line, non, non-empty, numbers, partition, rational, Richard, sets, than
Posted in Algebra | 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 »
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 »
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 »
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 29th, 2009
Introduction to Magnitude
Description
A detailed tutorial of how to solve for magnitude. Step by step tutorial including several examples of how to solve for magnitude for reference.
Overview
The magnitude refers to size – in mathematical concepts, what is larger? What has a greater value or quantity? This is what you look for when arranging things in order of magnitude. Several different measurements are considered to be types of magnitude – examples are volume, area, and length. Things that can be ordered by magnitude are fractions, line segments, planes, solids, and angles. Magnitude is considered to be measured only in positive, not in negative – not to say that the absolute value is taken, just that negative numbers are not included.
Tags: angles, area, arithmetic, fractions, greater, length, line segments, magnitude, Math, measurement, planes, positive, solids, value, volume
Posted in Arithmetic | No Comments »
