TEST BANK FOR Principles of Mathematical Analysis By Walter Rudin
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Exam (elaborations) TEST BANK FOR Principles of Mathematical Analysis By Walter Rudin (A Complete Solution Guide)
- Tentamen (uitwerkingen) • 387 pagina's • 2021
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GradeMaster1
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The Real and Complex Number Systems 
Unless the contrary is explicitly stated, all numbers that are mentioned in these exercises are understood 
to be real. 
1.1 Problems on rational numbers and fields 
Rudin Chapter 1 Exercise 1. 
Problem 1.1 
Proof. Assume that r + x was rational. Then it follows from Definition 1.12(A1), (A4) and (A5) that 
x = (r + x) − x 
is also rational, a contradiction. Similarly, if rx was rational, then it follows from Definition 1.12(M1), 
M(4) and M(5) that 
x = 
r...

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