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Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = and s = a I,r%3D for some --Select-- v a, b, c, and d with ---Select--- Write r-s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s = Both the numerator and the denominator are integers because---Select--- In addition, bd # 0 by the -Select---

Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = and s = a I,r%3D for some --Select-- v a, b, c, and d with ---Select--- Write r-s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s = Both the numerator and the denominator are integers because---Select--- In addition, bd # 0 by the -Select---

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r= and s = for some ---Select-- v a, b, c, and d with ---Select--- Write r -s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s = Both the numerator and the denominator are integers because---Select--- In addition, bd # 0 by the -Select--- Hence r - s is a --Select--- v of two integers with a nonzero denominator, and so by definition of rational, r- s is rational.
Transcribed Image Text:Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r= and s = for some ---Select-- v a, b, c, and d with ---Select--- Write r -s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s = Both the numerator and the denominator are integers because---Select--- In addition, bd # 0 by the -Select--- Hence r - s is a --Select--- v of two integers with a nonzero denominator, and so by definition of rational, r- s is rational.
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