Posts Tagged ‘less than’
Thursday, December 10th, 2009
Overview of the Bounded Monotone Sequence Theorem
Description
A detailed tutorial on the bounded monotone sequence theorem. Step by step tutorial including several examples of the bounded monotone sequence theorem for reference.
Overview
The bounded monotone sequence theorem actually has several parts to it. First, you need to find out if something is bounded above or bounded below. The sequence is bounded above if there exists a real number B such that x sub n is less than or equal to B. The sequence is bounded below if there exists a real number B such that x sub n is greater than or equal to B. If something is a bounded sequence, that means it is bounded both above and below. Absolute values are also very important in determining the bounded sequence. The bounded monotone sequence theorem states that for every bounded monotone sequence x, there is a real number L such that x sub n implies L.
Tags: above, absolute, algebra, below, bounded, boundedness, equal to, greater than, implies, less than, monotone, number, real, sequence, theorem, value
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
Order Properties of Natural Numbers
Description
A detailed tutorial on the order properties of natural numbers. Step by step tutorial including several examples of the order properties of natural numbers for reference.
Overview
The order properties are one of the eight sets of properties of natural numbers. The order properties are all based off of inequalities and how to order inequalities. Less than and less than or equal to are the two that are used in the order properties. There are five order properties in all. Since the order properties are of natural numbers, in order to prove the order properties your examples must be natural numbers, or positive integers greater than or equal to one.
Tags: arithmetic, equal, greater than, greater than or equal to, inequalities, less than, less than or equal to, n!, natural, number, order, property, x, y, z
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 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 »
Thursday, September 17th, 2009
Explanation of the Monotonicity Theorem
Description
A detailed tutorial on the solving of the Monotonicity Theorem. Step by step tutorial including several examples of how to solve the Monotonicity Theorem for reference.
Overview
The Monotonicity Theorem is used to determine if a function is increasing or decreasing. The Monotonicity Theoream states that:
If f ‘(x) > 0 the function is increasing
If f ‘(x) < 0 the function is decreasing
This is basically a repeat of information you already know. The derivative is the same as the slope of a line, and it is obvious to anyone who has spent time studying grpahs that a positive slope increases and a negative slope descreases. Simply find your function, take a derivative, and set it to either less than or greater than 0 to figure out if your graph will be increasing or decreasing.
Tags: 0, Calculus, decreasing, derivative, function, greater than, increasing, less than, Math, monotonicity, monotonicity theorem, slope, zero
Posted in Calculus | No Comments »
