A rational number is a number that can be expressed as the ratio between two integers, usually written as a / b, where the denominator? (here b) is not equal to zero. Rational numbers are commonly called "fractions". |
A rational number is a number that can be expressed as the ratio between two integers, usually written as a / b, where the denominator? (here b) is not equal to zero. Rational numbers are commonly called "fractions". |
So defined, i.e., by the quotient set defined by ~, the set of rational numbers, ℚ, forms a field. It may be shown that ℚ is the smallest field which contains the integers. |
So defined, i.e., by the quotient set defined by ~, the set of rational numbers, denoted by Q, forms a field. It may be shown that Q is the smallest field which contains the integers. |
Mathematically we may define them as an ordered pair of integers (a, b), with b not equal to zero. We can define addition and multiplication upon these pairs with the following rules:
To conform to our expectation that 2/4 = 1/2, we define an equivalence relation ~ upon these pairs with the following rule:
So defined, i.e., by the quotient set defined by ~, the set of rational numbers, denoted by Q, forms a field. It may be shown that Q is the smallest field which contains the integers.
-- integer -- irrational number -- real number --