In the field axioms for R, the existence of 0 is an axiom. However, the fact that 0 is unique is not part of the axiom. Prove: there is a unique real number, denoted by 0, with the property a + 0 = 0 + a = a for all a ∈ R

In the field axioms for R, the existence of 0 is an axiom. However, the fact that 0 is unique is not part of the axiom. Prove: there is a unique real number, denoted by 0, with the property a + 0 = 0 + a = a for all a ∈ R

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.1: The Field Of Real Numbers

Problem 25E: If and are positive real numbers, prove that there exist a positive integer such that . This...

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Question

In the field axioms for R, the existence of 0 is an axiom. However, the fact that 0 is unique is not part of the axiom.

Prove: there is a unique real number, denoted by 0, with the property

a + 0 = 0 + a = a

for all a ∈ R

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