Posts Tagged ‘one’

Factor Trees

Tuesday, November 10th, 2009

How to Make Factor Trees

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A detailed tutorial on how to make factor trees. Step by step tutorial including several examples on how to make factor trees for reference.

Overview

A factor tree is a type of tree diagram that splits numbers into their factors. It is a very useful method of simplification. First, start with a number and draw two lines from it. Two numbers that when multiplied equal your first number need to go there. A great number to start with is 2, if your number is an even number. you can start with any two numbers you like, provided they fit the guidelines, excluding anything paired with the number one – because then you won’t get anywhere. Then for each of your two numbers, if they are not simplified, you do the same process with them. Keep it up until you are down to simplified, or prime, numbers. You will know you have reached one when the only multiples are one and itself.

Zero Polynomial

Tuesday, November 10th, 2009

Identifying Zero Polynomials

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Description

A detailed tutorial on identifying zero polynomials. Step by step tutorial including several examples of identifying zero polynomials for reference.

Overview

A zero polynomial is the additive identity of an additive group of polynomials. So this means it is not a unique polynomial, even though it may seem like it. In order to identify a zero polynomial, you need to be aware of the two properties that zero polynomials possess. The first one is that all coefficients of a zero polynomial are zero, and add up to zero. The second is that a zero polynomial doesn’t have a degree – it is an undefined degree. Typically people will write this as a degree of -1, or more common, of negative infinity.

Identity Matrix

Friday, November 6th, 2009

Identity Matrix Explained

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A detailed tutorial on the identity matrix. Step by step tutorial including several examples of the identity matrix and how to solve it for reference.

Overview

An indentity matrix is a matrix that is said to be of size n. It is considered to be the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. The identity matrix is denoted as the variable I. The identity matrix has some extremely important properties of its own, especially multiplication properties. It is a unique type of matrix that is found rarely, but is used very often in several different branches of math.

Coprime Numbers

Thursday, October 29th, 2009

How to Identify Coprime Numbers

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

Overview

Two numbers are considered to be coprime, or relatively prime, if they have no common positive factor other than 1, or if their greatest common divisor is 1. Sometimes the notation for perpendicular is used to say that a number A is coprime to another number B. The term coprime was invented because the numbers are prime together, but are not prime themselves. A prime number can be coprime with any number.

Unit Vector

Friday, October 23rd, 2009

Definition of a Unit Vector

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A detailed tutorial on the unit vector. Step by step tutorial including several examples of the unit vector and how to solve it for reference.

Overview

In linear algebra, a unit vector is a vector that only has a length or magnitude of one. They are often used to indicate direction. There is a process used to create a unit vector, called normalizing a vector. When doing this, you must divide a vector of arbitrary length by its length. To normalize a vector with three points, you would use this formula:

<span style="font-size: x-small;">\mathbf{\hat{a}} = \frac{\mathbf{a}}{\left\|\mathbf{a}\right\|} = \frac{a_1}{\left\|\mathbf{a}\right\|}\mathbf{e_1} + \frac{a_2}{\left\|\mathbf{a}\right\|}\mathbf{e_2} + \frac{a_3}{\left\|\mathbf{a}\right\|}\mathbf{e_3}</span>

Set Theory: Inductive Sets

Thursday, October 22nd, 2009

Inductive Sets in Set Theory

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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.

Joint Variation

Thursday, October 8th, 2009

Joint Variation Explained

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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.

Alternating Series Test

Tuesday, October 6th, 2009

How to Test for Convergence Using the Alternating Series Test

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Description

A detailed tutorial on testing for convergence using the alternating series test. Step by step tutorial including several examples of testing for convergence using the alternating series test for reference.

Overview

The alternating series test, like all convergence and divergence tests, is fairly easy. The hardest part is figuring out if you should use the AST, or a different test. An easy way to tell is, is the equation negative? What would happen if you pulled a negative one out? Or maybe, there is already a negative one outside of the equation. If you see any fraction, function, or any equation at all with a -1 to an odd power at the front (or at the front of the numerator, in a fraction) then you should use the alternating series test for it. If the series is decreasing over time, and the limit is approaching zero, then the series is convergent. The alternating series test is normally used in conjunction with another test for convergence.

The Identity Properties

Thursday, October 1st, 2009

Identity Properties of Multiplication and Addition

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Description

 

A detailed tutorial of the identity properties of multiplication and addition. Step by step tutorial including several examples of the identity properties of multiplication and addition for reference.

 

Overview

 

There are two definitions of the identity property. The first deals with multiplication. It states that anything multiplied by one is itself. The second property deals with addition. It states that any number with zero added to it equals itself. As you can see, they are very similar to each other. Sometimes the zero property of multiplication is confused with the identity property for multiplication, although it is something different.

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