
Concept explainers
(A)
To define:
The definition of integers
(A)

Explanation of Solution
Given:
The integer number
Concept used:
The set of integers consists of zero
Calculation:
An integer (from the latin integer meaning whole) is colloquially defined as a number that can be written without a fraction component
For example :-
The set of integers consists of zero
It is denoted by
The integers from the smallest group and the smallest ring the natural numbers
(B)
To define:
The definition of a rational number
(B)

Explanation of Solution
Given:
The rational number
Concept used:
Anrational number is a number that can be expressed as the quotient or fraction
Calculation:
In mathematics
Anrational number is a number that can be expressed as the quotient or fraction
Since q may be equal to
Every integeris a rational number
The set of all rational numbers , the rationals, field of rational , or the field of rational numbers is usually denoted by
The decimal expansion of a rational number always either terminates aftera finite number of digits
Any repeating or terminating decimal represents a rational number
(C)
To define:
The definition of airrational number
(C)

Explanation of Solution
Given:
The irrational number
Concept used:
The set of all irrrationalnumbers , the irrationals, field of irrational , or the field of irrational numbers is usually denoted by
Calculation:
In mathematics
An irrational number is a number that can notbe expressed as a fraction for any integers and irrational numbers have decimal expansions that neither terminate nor become periodic
Every transcendental number is irrational number
The irrational numbers are all the real numbers
The ratio of lengths of two line segments is an irrational number
Irrational numbers are the ratio
The set of all irrrationalnumbers , the irrationals, field of irrational , or the field of irrational numbers is usually denoted by
(C)
To define:
The definition of a real number
(C)

Explanation of Solution
Given:
The real number
Concept used:
The set of all real numbers, field of real , or the field of real numbers is usually denoted by
Calculation:
In mathematics
A real number is a value of a continuous quantity that can represent a distance along a line
The real numbers include all the rational numbers
Such as the integers abd fraction and all irrational numbers
The set of real numbers is uncountable
That is both the set of all natural numbers and the set of all real numbers are infinite sets
The cardinality of the set of all real numbers is strictly greater than the cardinality of the set of all natural numbers
The set of all real numbers, field of real , or the field of real numbers is usually denoted by
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Chapter 1 Solutions
Precalculus - A Custom Text for UNLV
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