Posts Tagged ‘infinity’
Thursday, December 17th, 2009
The Story of the Infinite Hotel
Description
A detailed tale of the Infinite Hotel. Step by step story including several pictures and an explanation of the Infinite Hotel for reference.
Overview
The Infinite Hotel is a famous math story and puzzle that was thought of by David Hilbert, a German mathematician. Sometimes the Infinite Hotel is called Hilbert’s Paradox of the Grand Hotel. It states that if one person comes into the hotel and all the rooms are full, they can all move down one room and the person can then take the first room. If k number of people come into the hotel and all the rooms are full, everyone can move down k number of rooms to make room for the people that just arrived. And, if double the amount of people that are already there are looking for rooms, everyone in room n can move to room 2n, making room for all the new arrivals in the odd-numbered rooms. This example of the Infinite Hotel can be used in certain forms of mathematical induction, and also in set theory and studies dealing with infinite numbers.
Tags: algebra, arrivals, David Hilbert, double, down, German, grand, Hilbert, hotel, induction, infinite, infinity, k, move, n!, new, numbers, paradox, room, set, space, theory
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
Identifying Zero Polynomials
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.
Tags: addition, additive, algebra, coefficient, degree, group, identity, infinity, negative, one, polynomial, properties, property, undefined, zero
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Saddle-Point Approximation Explained
Description
A detailed tutorial on saddle-point approximation. Step by step tutorial including several examples of saddle-point approximation for reference.
Overview
Saddle-point approximation is also referred to as the method of steepest descent and Laplace’s method. It is a way of approximating integrals in the form 
. f(x) is some twice-differentiable function, M is a large number, and the integral endpoints a and b have a possibilty of being infinite.
Tags: a, approximation, b, Calculus, descent, differentiable, function, infinite, infinity, integral, Laplace, large, m, method, number, point, saddle, saddle-point, steepest, twice, twice-differentiable
Posted in Calculus | No Comments »
Thursday, November 5th, 2009
Introduction to Projections
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Description
A detailed tutorial on projections. Step by step tutorial including several examples of what a projection is for reference.
Overview
A projection is another term for a transformation. But a projection is a different kind of transformation than a real transformation is. A projection is a transformation of points and lines from one plane to another plane. This is done by connecting corresponding points on the planes with parallel lines. Typically projections are used with vectors, which are entirely composed of points and lines.
Tags: corresponding, dot, infinity, lines, parallel, plane, point, product, projection, transformation, vector
Posted in Algebra | 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 »
Thursday, October 22nd, 2009
How to Find Nonlinear Asymptotes
Description
A detailed tutorial on finding nonlinear asymptotes. Step by step tutorial including several examples of how to find nonlinear asymptotes for reference.
Overview
An asymptote is used to describe the behavior of a curve as it heads away from the origin and towards infinity. Typically it is meant to describe two curves that are doing this, and these curves are said to be asymptotic. In most cases, the asymptote is linear – which means the curves have the same behavior. Whenever someone is talking about an asymptote, they are talking about a linear asymptote unless they specify a different type of asymptote. In rare cases, asymptotes are nonlinear. Both curves are still heading towards infinity, but they do not have the same behavior. This can be determined by the limit of either the subtraction or the division of these curves.
Tags: algebra, asymptote, asymptotic, behavior, curve, division, function, horizontal, infinity, limit, linear, nonlinear, oblique, origin, subtraction, vertical
Posted in Algebra | No Comments »
Tuesday, October 20th, 2009
How to Graph the Tangent Function
Description
A detailed tutorial on solving the graph of the tangent function. Step by step tutorial including several examples of how to solve the graph of the tangent function for reference.
Overview
The graph of the tangent function looks a great deal like the graph of x cubed – just repeated several times. The graph of tangent is drawn in a period of pi – meaning a “line” is put down every pi spaces for a guideline on where to draw the graph – and hits all of the major points of the graph, also in intervals of pi. There is no amplitude of the tangent function because it extends up to both negative infinity and positive infinity in vertical directions.
Tags: amplitude, asymptote, function, graph, infinity, intervals, negative, period, pi, positive, tangent, trigonometric, trigonometry, vertical, x, y
Posted in Trigonometry | No Comments »
Thursday, October 15th, 2009
Introduction to Infinite Sets
Description
A detailed tutorial on infinite sets. Step by step tutorial including several examples of infinite sets and how to identify them for reference.
Overview
There are two types of sets, finite sets and infinite sets. The tutorial will focus on infinite sets. An infinite set is a set that has at least one endpoint of infinity, which can be implied either by having infinity in the set or by having a trailing end of the set, with no number at the end. Infinite sets can either be countable or uncountable – meaning they either have a pattern you can use to follow to infinity, or there is no pattern present.
Tags: algebra, countable, element, endpoint, finite, infinite, infinity, Math, number, set, trailing, uncountable
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
How to Find Oblique Asymptotes
Description
A detailed tutorial on how to find oblique asymptotes. Step by step tutorial including several examples of how to find oblique asymptotes for reference.
Overview
There are several different types of asymptotes. In this tutorial, we will be discussing oblique asymptotes. In order to find the oblique asymptotes of a function, you must first determine if the asymptote slants. If the numerator of a rational function has exactly one degree greater than the denominator, then the function slants and therefore has an oblique asymptote. When you divide the numerator and the denominator, the term or polynomial you get is the oblique asymptote.
Tags: algebra, asymptote, asymptotes, closer, curves, degree, denominator, distance, farther, function, horizontal, infinity, limit, linear, lines, Math, negative, nonlinear, numerator, oblique, origin, polynomial, positive, slant, straight, vertical, zero
Posted in Algebra | No Comments »
Friday, October 2nd, 2009
Definition of a Lemniscate
Description
A detailed tutorial on the definition of a lemniscate. Step by step tutorial including a visual example of a lemniscate for reference.
Overview
A lemniscate is any figure 8 type shape that shows up in mathematics. These figure 8 type shapes are sideways, instead of the normal vertical format of a figure 8. One of the best known lemniscates is the infinity symbol, which resembles a figure 8 tipped on its side.
Tags: 8, figure 8, Geometry, infinity, leminscate, Lemniscate of Bernoulli, loop, Math, shape, sideways, symbol, toric section, torus
Posted in Geometry | No Comments »
