The Archimedean Property states that the set N of natural numbers is unbounded above in R. It is equivalent to the following. (a) For each z ∈ R, there exists an n ∈ N such that n > z. (b) For each x > 0 and for each y ∈ R, there exists an n ∈ N such that nx > y. (c) For each x > 0, there exists an n ∈ N such that 0 <1/n < x.

The Archimedean Property states that the set N of natural numbers is unbounded above in R. It is equivalent to the following. (a) For each z ∈ R, there exists an n ∈ N such that n > z. (b) For each x > 0 and for each y ∈ R, there exists an n ∈ N such that nx > y. (c) For each x > 0, there exists an n ∈ N such that 0 <1/n < x.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...

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