Posts Tagged ‘-1’
Friday, November 6th, 2009
Identity Matrix Explained
Description
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.
Tags: -1, 0, algebra, diagonal, i, identity, linear, main, matrices, matrix, multiplication, one, properties, square, uniquem, variable, zero
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
Successor Properties of Natural Numbers
Description
A detailed tutorial on the successor properties of natural numbers. Step by step tutorial including several examples of the successor properties of natural numbers for reference.
Overview
The successor properties are one of eight sets of properties of natural numbers. The successor properties deal with the actual set of natural numbers, not just parts of the set. It especially concerns the placement of the number 1 in the set of natural numbers. As the term successor implied, these properties deal with what numbers are successors of other numbers. They can be proven by the definition of a successor and the set of natural numbers.
Tags: -1, after, arithmetic, follows, natural, number, properties, set, successor, unique, x
Posted in Arithmetic | 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 »
Tuesday, October 6th, 2009
How to Test for Convergence Using the Alternating Series Test
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.
Tags: -1, alternating, AST, Calculus, converge, convergence, decreasing, diverge, divergence, fraction, function, limit, Math, negative, one, series, test, zero
Posted in Calculus | No Comments »
Friday, September 11th, 2009
An Introduction to Imaginary Numbers
Description
A detailed tutorial on imaginary numbers. Step by step tutorial including several examples of how to solve problems using imaginary numbers for reference.
Overview
An imaginary number is a number that is considered to not be real – for instance, the square root of a negative number. You could never take a square root of a negative number – until you met i. i stands for “imaginary”, and it is the square root of negative one. Many previously impossible problems can now be solved by pulling out i from the equation.
Tags: -1, algebra, i, imaginary, imaginary number, Math, negative, real, real number, sqrt(-1), square root
Posted in Math | No Comments »
