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Show that if a and b are positive irrational numbers such

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 14E Chapter 4.SE

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 14E

Show that if a and b are positive irrational numbers such that 1/a + 1/b = 1, then every positive integer can be uniquely expressed as either ?ka? or ?kb? for some positive integer k.

Step-by-Step Solution:

SolutionStep 1In this problem, we have to show that if two positive irrational number such that = 1 where a and b are irrational number.Step 2Proof by ContradictionLet us assume that A(p, n) be the set of positive integer then is less than or equal to n where x be an positive integer.It is given that have a unique value and a and b are irrational number.So, according to the property of floor function If a is...

Step 2 of 3

Chapter 4.SE, Problem 14E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Show that if a and b are positive irrational numbers such

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