4. Let I denote the set of irrational numbers. (a). Prove that if r e I then V n E Z*, nr € I.
4. Let I denote the set of irrational numbers. (a). Prove that if r e I then V n E Z*, nr € I.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A full step by step solution please to the attached image hwk question. Both part a and b and c.
Transcribed Image Text:4. Let I denote the set of irrational numbers.
(a). Prove that if r E I then Vn e Z*, nr E I.
(b). Explain True or False of statement: “If S is an infinite subset of I, then S is uncountable."
(c). Prove by contradiction: "I is uncountable."
Expert Solution
Step 1
PART A
Let and
Suppose i.e. i.e. i.e. is rational so,
where
Therefore,
Clearly, so and
So r is rational which contradict the fact that r is irrational.
Hence is irrational.
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