Answered: Verify that the embedding of ℚ ≥0 in ℝ…

Verify that the embedding of ℚ ≥0 in ℝ ≥0 respects ≤. That is, verify for a, b ∈ ℚ ≥0 that if a ≤ b as rational numbers, then also a ≤ b as real numbers.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 13E: 13. Prove that if and are rational numbers such that then there exists a rational number such...

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Verify that the embedding of ℚ^≥0 in ℝ^≥0 respects ≤. That is, verify for a, b ∈ ℚ^≥0 that if a ≤ b as rational numbers, then also a ≤ b as real numbers.

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