Explanation Given: − 0 = 0 . Approach: (1) ( x + y ) + z = x + ( y + z ) , ( x ⋅ y ) ⋅ z = x ⋅ ( y ⋅ z ) for all x , y , z in ℝ . (2) x + y = y + x , x ⋅ y = y ⋅ x for all x , y in ℝ . (3) There exists a unique element of ℝ called zero, denoted by 0 , such that x + 0 = x for all x ∈ ℝ . There exists a unique element of ℝ called one, different from 0 and denoted by 1 , such that x ⋅ 1 = x for all x ∈ ℝ . (4) For each x in ℝ , there exists a unique y in ℝ such that x + y = 0

2nd Edition

ISBN: 9780134689517

Author: Munkres, James R.

Publisher: Pearson,

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Chapter 1.4, Problem 1.3E

To determine

To proof:

The given law of algebra −0=0 for ℝ.

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Chapter 1.4, Problem 1.2E

Chapter 1.4, Problem 1.4E

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