Concept explainers
In 35-39 find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.
39. “Proof: Suppose r and s are rational numbers. If
which is a quotient of two integers with a nonzero denominator. Hence it is a rational number. This is what was to be shown.”
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Discrete Mathematics With Applications
- Prove that if is a nonzero rational number and is irrational, then is irrational.arrow_forward13. Prove that if and are rational numbers such that then there exists a rational number such that . (This means that between any two distinct rational numbers there is another rational number.)arrow_forwardProve that if is a nonzero rational number and is irrational, then is irrational.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell