Question

Problem 1. Prove, only using the axioms of an ordered field, that if $x \in \mathbb{R}$, then $-(-x) = x$. Hint: Start by taking $w = -x$. Write down the property an element must satisfy in order to be the additive inverse of $w$. Check that $x$ satisfies that property.

          Problem 1. Prove, only using the axioms of an ordered field, that if $x \in \mathbb{R}$, then
$-(-x) = x$.
Hint: Start by taking $w = -x$. Write down the property an element must satisfy in order
to be the additive inverse of $w$. Check that $x$ satisfies that property.

Problem 1. Prove, only using the axioms of an ordered field, that if x ∈ℝ, then
-(-x) = x.
Hint: Start by taking w = -x. Write down the property an element must satisfy in order
to be the additive inverse of w. Check that x satisfies that property.

Added by Summer N.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Hanlin Sun

06/03/2022

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Problem 1. Prove, only using the axioms of an ordered field, that if xinR, then -(-x)=x Hint: Start by taking w=-x. Write down the property an element must satisfy in order to be the additive inverse of w. Check that x satisfies that property. Problem 1. Prove, only using the axioms of an ordered field, that if x e R, then Hint: Start by taking w = -x. Write down the property an element must satisfy in order to be the additive inverse of w. Check that x satisfies that property. 2