In an ordered field R, the positive elements may be defined as that subset P ⊆ R satisfying both of the following conditions: (a) If a, b ∈ P, then a + b ∈ P and ab ∈ P. (b) If a ∈ R with a ∕= 0, then either a ∈ P or −a ∈ P but not both. For this question, find an example of Pa ⊂ R that satisfies (a) but not (b), and an example of Pb ⊂ R that satisfies (b) but not (a).

In an ordered field R, the positive elements may be defined as that subset P ⊆ R satisfying both of the following conditions: (a) If a, b ∈ P, then a + b ∈ P and ab ∈ P. (b) If a ∈ R with a ∕= 0, then either a ∈ P or −a ∈ P but not both. For this question, find an example of Pa ⊂ R that satisfies (a) but not (b), and an example of Pb ⊂ R that satisfies (b) but not (a).

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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