2. Show between any two irrational numbers there is an irrational number. (Hint: Assume r and s are irrationals. Assume there is only rational numbers between r and s. What would that say about the “size" of the interval (r, s]? Get a contradiction).
2. Show between any two irrational numbers there is an irrational number. (Hint: Assume r and s are irrationals. Assume there is only rational numbers between r and s. What would that say about the “size" of the interval (r, s]? Get a contradiction).
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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![2. Show between any two irrational numbers there is an irrational number. (Hint: Assume r
and s are irrationals. Assume there is only rational numbers between r and s. What would
that say about the "size" of the interval [r, s]? Get a contradiction).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2Fef040352-122f-432c-b983-c39a54faa03a%2Fieublrl_processed.png&w=3840&q=75)
Transcribed Image Text:2. Show between any two irrational numbers there is an irrational number. (Hint: Assume r
and s are irrationals. Assume there is only rational numbers between r and s. What would
that say about the "size" of the interval [r, s]? Get a contradiction).
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