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every two rational numbers there is an irrational number.

every two rational numbers there is an irrational number.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that between every two rational numbers there is an irrational number. Solution: By finding a common denominator, we can assume that the given rational numbers are a/b and c/b, where b is a positive integer and a and c are integers with a < c. In particular, a +1 Thus, a+1/v2 is between the two given rational numbers. Furthermore, z is irrational, because if z were rational, then 1. br would be as well, a contradiction.
Transcribed Image Text:Prove that between every two rational numbers there is an irrational number. Solution: By finding a common denominator, we can assume that the given rational numbers are a/b and c/b, where b is a positive integer and a and c are integers with a < c. In particular, a +1 Thus, a+1/v2 is between the two given rational numbers. Furthermore, z is irrational, because if z were rational, then 1. br would be as well, a contradiction.
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