Answer to Question #140736 in Abstract Algebra for Kenrick Lee

Question

*Question: Use the definition of negative numbers to justify that -(-5) equals 5.

Definition of negative numbers: -a is the number when added to a equals 0.

*Throw out and avoid the standard/traditional integer rules that you've learned and use only the knowledge we have gained working with negative numbers using the definition and number lines.
*This is a justification by proof type problem

Answer 1

By the definition of negative numbers

5 +(-5) = 0

Adding -(-5) to both sides we have

5 + (-5) + (-(-5)) = 0 + (-(-5))

Then by definition we have

5 + 0 = 0 + (-(-5))

Then by cancellation law

5=-(-5)