Posts Tagged ‘real’
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 »
Tuesday, November 24th, 2009
How to Find the Absolute Value of a Complex Number
Description
A detailed tutorial on the absolute value of a complex number. Step by step tutorial including several examples on the absolute value of a complex number for reference.
Overview
The absolute value of a complex number is a little different than the absolute value of a real number, because complex numbers deal with imaginary numbers. However, the answer is still a non-negative real number, just like the numbers you deal with in other math classes every day. Say that a complex number z is equal to a + bi, where i is an imaginary number. The |z| is equal to the square root of a^2 plus b^2. In other words, square both a and b, add them together, and find the square root in order to have to absolute value of a complex number z.
Tags: a, absolute, add, addition, b, complex, imaginary, number, real, root, square, squareroot, sum, trigonometry, z
Posted in Trigonometry | No Comments »
Friday, November 13th, 2009
An Overview of Composite Numbers
Description
A detailed tutorial on what composite numbers are. Step by step tutorial including several examples of composite numbers and their definition for reference.
Overview
A composite number is the opposite of a prime number. Some people say they are any number that is not prime, but that is not exactly accurate – negative numbers are not prime (even negative prime numbers), and a composite number is not a negative number, it is a positive number. A composite number is any positive integer that has more divisors than itself and one – which are the only two numbers a prime number can be divided by.
Tags: accurate, arithmetic, composite, examples, integer, negative, number, opposite, positive, prime, real
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Find the Reciprocal of a Number
Description
A detailed tutorial on how to find the reciprocal of a number. Step by step tutorial including several examples of reciprocals for reference.
Overview
A reciprocal is a way of saying the opposite of a number, although it is not a true opposite. A true opposite of a negative number would be a positive number, and a true opposite of a positive number would be a negative number – that is why there are such things as opposite reciprocals. A more accurate name for a recirpocal would be the reverse of a number. In a fraction, the reciprocal of a number is when the numerator and the denominator are flipped. This also works for whole numbers, because you can think of the number as a numerator with denominator one.
Tags: accurate, arithmetic, denominator, flipped, fraction, integer, negative, number, numerator, opposite, positive, real, reciprocal, reverse, whole
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
An Overview of Magic Squares
Description
A detailed tutorial of magic squares. Step by step tutorial including several examples of magic squares for reference.
Overview
Magic squares are a fun mathematical trick and puzzle. It is an arrangement such as 3×3, 4×4, or any other nxn pattern of numbers. Typically a magic square will contain any of the integers between 1 and n^2. Magic squares are set up so that all rows and columns, and both diagonals, add up to the same constant. It does not matter what constant it is, as long as all rows, columns, and diagonals add up to the same one.
Tags: arithmetic, column, constant, diagonal, integer, magic, n!, normal, number, perfect, real, row, square, sum, word
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Identify Perfect Numbers
Description
A detailed tutorial on how to identify perfect numbers. Step by step tutorial including several examples of perfect numbers for reference.
Overview
A perfect number is a number that is the sum of all it’s divisors (excluding the number itself, which is also a proper divisor). The way that you identify a perfect number is to find all of its divisors. Once you have them all, add them together. If they equal the number, then it is a perfect number. If they don’t, then it is not a perfect number.
Tags: add, addition, arithmetic, division, divisor, excluding, identify, integer, natural, number, perfect, proper, real, sum
Posted in Arithmetic | No Comments »
Friday, November 6th, 2009
Introduction to Scalars
Description
A detailed tutorial on what a scalar is. Step by step tutorial including several examples of scalars and how they relate to vectors for reference.
Overview
A scalar is a number that relates vectors on a vector space through the process of scalar multiplication. A scalar can be taken from any set of numbers, including rational, algebraic, real, and complex sets of numbers. The scalar is always a real number. A scalar is a single component, and things such as vectors, matrices, and tensors can be reduced to a scalar.
Tags: algebra, algebraic, complex, component, compound, matrices, matrix, number, quaternions, rational, real, scalar, single, space, tensor, vector
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Overview of the Monotone Convergence Theorem
Description
A detailed tutorial on the monotone convergence theorem. Step by step tutorial including several examples of the monotone convergence theorem for reference.
Overview
There are several different theorems that the term “monotone convergence” can apply to. However, the most important one, and the one most common called the monotone convergence theorem, is the Lebesgue Monotone Convergence Theorem. This particular monotone convergence theorem deals with calculus, and with integrals and limits specifically. It is a more general form of the other two monotone convergence theorems, which is why it is considered to be the most important.
Tags: Calculus, converge, convergence, form, general, integral, Lebesgue, limit, monotone, number, real, sequence, series, theorem
Posted in Calculus | 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 »
Friday, October 23rd, 2009
Introduction to the Four-Vector
Description
A detailed tutorial on the four-vector. Step by step tutorial including several examples of the four-vector and how to solve it for reference.
Overview
In linear algebra, a four-vector is defined as a vector in four-dimensional real vector space. The difference between a vector and a four-vector is that a four-vector can be transformed by Lorentz transformations. The concept of four-vectors branches out throughout vector mathematics, and to special relativity and general relativity. The concepts are a little different in each, but not enough to make it confusing if you are learning about them from a different standpoint. Four-vectors are often used in combination with matrices.
Tags: algebra, concept, four-dimensional, four-vector, general, Lorentz, matrices, real, relativity, space, special, transformations, vector
Posted in Algebra | No Comments »
