Rational and Irrational Numbers Introduction
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} The set of rational n..
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} The set of rational n..Sequences and Series
A set of numbers arranged in a definite order according to some definite rule is called a sequence. A sequence is a function whose domain is the set N of natural numbers. Indicated sum of the terms in a sequence is called a series. The result of performing the additi..
Proof:
The null set f is a subset of every set, in particular f A. By hypothesis, A f . The two conditions imply A = f..
Elementary Transformation
Elementary transformations are of the following three types: Interchange of any two rows (or columns) The multiplication of the elements of a row (or column) by a non-zero number. The addition to the elements of any row (or column) the corresponding elements o..
Properties of Symmetric and Skew Symmetric Matrices
1. A square matrix A is said to be skew-symmetric if A ' = -A. 2. The diagonal elements of a skew-symmetric matrix are all ze..
Associative laws
If A, B, C are three sets, then..
If A, B, C are three sets, then..Commutative laws
If A, B are two sets, then..
If A, B are two sets, then..Introduction
A set of numbers arranged in a definite order according to some definite rule is called a sequence . Sequences have wide applications. For example, the amount of money in a fixed deposit in a bank, over a number of years increases in a sequenc..
Minors
Let |aij| be a determinant of order n. The determinant obtained by deleting the i t h row and j t h column in which the element a i j lies is called the minor of element a i j and is denoted by M i ..
Real Numbers
The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real number..
The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real number..See what our Users say :
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