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Rational Numbers

We have observed that in the set of natural numbers

The set

The set

is called the set of rational number, and we ask the readers to note that the divisions by

The fundamental compositions defined in

For convenience, by

**N**, there was no additive identity so it was extended to a set**W**, the set of whole numbers which we defined as**W = {0, 1, 2, 3, …. }**and then we thought of the operation of subtractor, and found that the subtraction was not unrestrictedly possible in the system of whole and, therefore, W was extended to the set of integers**I**. We now draw our attention towards the operation of division and observe that**15/3 = 5**has a meaning in**I**whereas**15/4**is an undefined term in**I**. So to**I**we now attach new elements so as to obtain another family, to be denoted by**Q**, and call it the set of rational numbers.The set

**Q**of rational numbersThe set

**Q = {p/q | p, q****I and q ≠ 0}**is called the set of rational number, and we ask the readers to note that the divisions by

**0**is not permissible and**I ⊂ Q**.The fundamental compositions defined in

**Q**are also addition and multiplication. We shall now state the properties of addition and multiplication and order relation in**Q**.For convenience, by

**m**in**Q**we shall understand an element of the form**p/q; p, q I, q ≠ 0**etc.**Services: -**Rational Numbers Homework | Rational Numbers Homework Help | Rational Numbers Homework Help Services | Live Rational Numbers Homework Help | Rational Numbers Homework Tutors | Online Rational Numbers Homework Help | Rational Numbers Tutors | Online Rational Numbers Tutors | Rational Numbers Homework Services | Rational NumbersSubmit Your Query ???

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Topics

Real Number Absolute Value
Addition Of Matrices
Square Matrix Adjoint
Algebraic Structures
Alternating Series
Linear Equations Determinants
Archimedean Real Numbers
Binary Operation
Binary Relation In A Set
Bounded, Unbounded Sets
Cauchy Root Test
Caylay Hamiltion Theorem
Circular Permutation
Common Roots
Complex Numbers
Complex Number Conjugate
Conjugate Of A Matrix
Constant Sequences
Convergence Of A Sequence
Cosets
Cubic, Biquadratic Equations
De Moivre Theorem
Real Number Denseness
Order 3 Determinants
Differences Of Matrices
Direct Sum Of Vector Subspaces
Eigen Vector
Elementary Matrices
Matrix Elem. Transformations
Equal Matrices
Equal Roots
Two Permutations Equity
Equivalent Matrices
Trigonometry Function Expansion
Field
Function
Algebra Fundamental Theorem
Gaussian Integer
Geometric Series
Group
Ideals
Quantity Increasing Roots
Infinite Series Convergent
Integers
Inverse Of Square Matrix
Inverses Of Elementary Matrices
Iota, Imaginary Numbers
Left-Right Identity
Sequence Limit Points
Linear Combination Vectors Span
Linear Dependence, Independence
Linear Homogeneous Equations
Two Subspaces Linear Sum
Matric Polynomial
Matrix
Linear Equation Matrix Inverse
Matrix Multiplication
Matrix Scalar Multiplication
Method Of Difference
Minors And Co-factors
Multiplication Modulo P
Normal Sub-Group
Normalizer Or Centalizer
Orbit Of Permutation
Peano Axioms
Permutation Function
Pigeon Hole Principle
Matrices Integral Powers
Mathematical Induction Principal
Two Determinants Product
Two Permutations Product
Properties Of Modulus
Rank Of A Matrix
Rational Numbers
Rational, Integral Polynomial
Reciprocal Roots
Relation Of Sets
Rings Of A Set
Row By Column Matrix
Sequence
Series
Series Of Positive Terms
Series Partial Sum Sequence
Subrings
Sum Of A Series
Cosine Series Sum
Sum Of Sine Series
Symmetric/Skew Symm. Matrices
Roots Symmetric Functions
Symmetric Set Degree N
Synthetic Division
Transformation In General
Transformations Of Equations
Transpose Of A Matrix
Matrix Transposed Conjugate
Transposition
Complex Numbers Representation
Vector Space
Vector Sub-spaces
Whole Numbers

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