Posts Tagged ‘k’
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 »
Thursday, November 5th, 2009
Linear Subspaces Explained
Description
A detailed tutorial on linear subspaces and how to identify linear subspaces. Step by step tutorial including several examples of linear subspaces for reference.
Overview
A linear subspace is usually referred to as simply a subspace, when it needs to be distinguished from other types of subspaces. Linear subspaces are also sometimes referred to as vector subspaces. In mathematical terms, to identify a linear subspace, we say that K is a field (or a set, like of real numbers), and V is a vector space over K. Elements of V are vectors and elements of K are scalars. W is said to be a subset of V. If W is a vector space itself, with the same vector space operations as V, then it has a subspace of V.
Tags: algebra, element, field, k, linear, number, operations, real, scalar, set, space, subset, subspace, v, vector, W
Posted in Algebra | No Comments »
Thursday, October 8th, 2009
Inverse Variation Explained
Description
A detailed tutorial on inverse variation. Step by step tutorial including several examples of inverse variation and what inverse variation is for reference.
Overview
Inverse variation states that two variables are inversely proportional if one of the variables is directly proportional with the multiplicative inverse of the other, or equivilently if their product is a constant. Inverse variation can be expressed mathematically as y = k / x, where x and y are the variables and k is a nonzero constant
Tags: constant, direct, division, inverse, k, Math, multiplicative inverse, non-zero, proportionality, reciprocal, statistics, variable, variation, x, y
Posted in Statistics | No Comments »
Thursday, October 8th, 2009
Direct Variation Explained
Description
A detailed tutorial on direct variation. Step by step tutorial including several examples of direct variation and what direct variation is for reference.
Overview
Direct variation states that given two variables x and y, y is directly proportional to x if there is a non-zero constant k such that y = k * x. The variable k is referred to as the proportionality constant or the constant of proportionality.
Tags: constant, direct, inverse, k, Math, non-zero, proportionality, statistics, variable, variation, x, y
Posted in Statistics | No Comments »
Thursday, October 8th, 2009
Combined Variation Explained
Description
A detailed tutorial on combined variation. Step by step tutorial including several examples of combined variation and what combined variation is for reference.
Overview
Combined variation refers to using both direct variation and inverse variation at the same time. Combined variation can be expressed as y = (k * x) / (z^2). Typically when both direct and inverse variation are being used, the same variable will variate directly at one point and inversely at another.
Tags: combine, combined variation, direct, inverse, k, Math, point, statistics, variable, variation, x, y, z
Posted in Statistics | No Comments »
Thursday, October 8th, 2009
Introduction to the Principle of Mathematical Induction
Description
A detailed tutorial of the principle of mathematical induction. Step by step tutorial including several examples of the principle of mathematical induction for reference.
Overview
The principle of mathematical induction is basically a method of proof-writing, which involves trying to prove that a certain statement is true for all natural numbers. The first statement will be proved, and then the next statement, and the next one. In this way, it is similar to a proof by exhaustion. However, since the statement must be proven for all numbers, eventually an integer will be used in the calculations. This should not be confused with mathematical induction – the principle of mathematical induction is actually a type of deductive reasoning.
Tags: deductive, discrete math, exhaustion, induction, interger, k, Math, mathematical, n!, natural, number, principle, proof, reasoning, statement
Posted in Discrete Math | No Comments »
