Posts Tagged ‘rational’
Tuesday, January 5th, 2010
How to Determine Dedekind Cuts
Description
A detailed tutorial on how to determine Dedekind cuts. Step by step tutorial including several examples of Dedekind cuts for reference.
Overview
A Dedekind cut is a partition of rational numbers into two non-empty sets A and B, such that all elements of A are less than elements of B, and A has no greatest element. The cut itself is a gap that is located between A and B, which is normally found by creating a new, irrational number, and setting it in the gap. What irrational number you use depends on what numbers you have partitioned into the two sets. It is like the number line of advanced algebra, that has both rational and irrational numbers on it instead of just integers. The Dedekind cut was named after Richard Dedekind.
Tags: algebra, between, cut, Dedekind, elements, empty, gap, greater, integer, irrational, less, line, non, non-empty, numbers, partition, rational, Richard, sets, than
Posted in Algebra | 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
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Friday, October 23rd, 2009
The Notation of Basic Number Sets
Description
A detailed tutorial on basic number sets. Step by step tutorial including several examples of the notation of basic number sets for reference.
Overview
There are four basic number sets – N, Z, Q, R. N belongs to Z, and Z and Q belongs to R. This means N also belongs to R. N is the set of all natural numbers. Z is the set of all integers. Q is the set of all rational numbers. R is the set of all real numbers. All the notations of these sets were picked because they relate to certain words. N and R were chosen because they stand for natural and real – which is what the sets are. Q means quotient, because rational numbers are a quotient of any integer provided the denominator is not 0. Z was picked because it stands for zahlen – a German word meaning numbers, and Z is indeed a set of (almost) all numbers.
Tags: all, arithmetic, integer, n!, natural, notation, number, Q, quotient, r, rational, real, set, z, zahlen
Posted in Arithmetic | No Comments »
Friday, September 18th, 2009
Introduction to Irrational Numbers
Description
A detailed tutorial on the definition of an irrational number. Step by step tutorial including several examples of irrational numbers for reference.
Overview
An irrational number is a number that cannot be written as the ratio of 2 integers. However, this does not mean they have no place on a number line. One of the most famous irrational numbers is pi, which is approximately equal to 3.14 – however, this is just a simplified version of the actual number. Another famous irrational number is the square root of 2. This is equal to around 1.41. Both irrational numbers and rational numbers are real numbers, which include all integers.
Tags: arithmetic, imaginary, integers, irrational, Math, natural, number, numbers, pi, ratio, rational, real, sqrt(2), square root
Posted in Arithmetic | No Comments »
