Posts Tagged ‘addition’
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 »
Thursday, October 8th, 2009
Introduction to Inverse Operations
Description
A detailed tutorial on the different inverse operations. Step by step tutorial including several examples of the different inverse operations for reference.
Overview
Inverse operations are operations that undo each other – for example, if you do something a problem, and then use the inverse operation, it should be like it never happened. Common inverse functions are addition and subtraction, multiplication and division, square roots and squaring, and logarithms and exponents.
Tags: addition, arithmetic, division, exponent, inverse, logarithm, Math, multiplication, operation, square roots, squaring, subtraction
Posted in Arithmetic | 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 »
Thursday, October 1st, 2009
Introduction to Summation
Description
A detailed tutorial of summation. Step by step tutorial including several examples of summation for reference.
Overview
Summation is a simple concept – notice its similarity to the word sum. In simple terms, summation simply means the addition of a set of numbers, the result being their sum or total. The summation notation is especially useful when you are given a large set of numbers to work with. The summation notation is expressed as a large capital Sigma (a Greek letter), and when given number values the notation would look like this:
Tags: addition, algebra, associative, commutative, divergent, extrapolation, interim, Math, series, sigma, sum, summation, total
Posted in Algebra | No Comments »
Thursday, October 1st, 2009
Identity Properties of Multiplication and Addition
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.
Tags: add, addition, arithmetic, equals, identity properties, identity property, itself, Math, multiplication, multiply, one, zero
Posted in Arithmetic | No Comments »
Thursday, October 1st, 2009
Introduction to the Number Line
Description
A detailed tutorial on the number line. Step by step tutorial including several examples of when and how use the number line for reference.
Overview
The number line is a basic concept in math that helps to visualize where all the numbers are. On a traditional number line, the number zero is placed in the middle, with numbers going up by one lining either side (the left side is negative, the right side is positive). The number line stretches to infinity in both directions. The number line is used when first learning math to assist with addition and subtraction. The number line is brought up again in algebra, to help with inequalities. Often inequalities are graphed on the number line, to show possible values of the variable given.
Tags: addition, arithmetic, graph, greater than, inequalities, infinity, less than, Math, negative, number line, positive, subtraction
Posted in Arithmetic | No Comments »
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 »
Tuesday, September 29th, 2009
Identifying Supplementary Angles
Description
A detailed tutorial on identifying supplementary angles. Step by step tutorial including several examples of how to identify supplementary angles for reference.
Overview
Supplementary angles are angles which have the sum of their measurements add up to 180. If the two angles are adjacent, they should form a straight line, since 180 degrees has no true angle. Examples would be two 90 degree angles (right angles), or a 120 degree angle and a 60 degree angle. You can identify supplementary angles by adding up their measurements. If the answer is 180, the angles are supplementary.
Tags: 180, addition, angle, angles, complimentary, degrees, Geometry, Math, sums, supplementary
Posted in Geometry | No Comments »
Tuesday, September 29th, 2009
Identifying Complimentary Angles
Description
A detailed tutorial on identifying complimentary angles. Step by step tutorial including several examples of how to identify complimentary angles for reference.
Overview
Two angles are considered complimetary if their sum adds up to 90. For example, angles measuring 60 degrees and 30 degrees would be complimentary, as would two angles both measuring 45 degrees. You can identify a complimentary angle by adding up the degrees. If the result is 90, then the angles are complimentary.
Tags: 90, addition, angle, angles, complimentary, degrees, Geometry, Math, sums, supplementary
Posted in Geometry | No Comments »
Tuesday, September 29th, 2009
An Overview of Pascal’s Triangle
Description
A detailed tutorial of how to use Pascal’s Triangle. Step by step tutorial including several examples of how to use Pascal’s Triangle for reference. Knowledge of Pascal’s Triangle will prove useful in several branches of mathematics.
Overview
Pascal’s Triangle is a useful device in mathematics that can reveal the sums of almost any number. There are an infinite number of rows but it can be shortened to any number. The triangle traditionally starts at Row 0 with one number – 1. Then Row 1 has two numbers – 1 and 1. And Row 2 has three numbers – 1, 2, and 1. The number 1 lines the side of the triangle. Every other number is the sum of the two numbers found directly above it. Pascal’s triangle is constructed by using geometric shapes.
Tags: addition, arithmetic, binomial coefficients, Blaise Pascal, elements, geometric arrangement, geometric shapes, infinite, Math, Pascal's Rule, Pascal's Triangle, rows, sums, triangle
Posted in Arithmetic | No Comments »
