# Proof about Integers and Rationals

Show that the definition of negation on the integers is well-defined in the sense that if (a----b)=(a'----b'), then -(a----b)= -(a'----b') (so equal integers have equal negations)

where a----b is the space of all pairs equivalent to (a,b)

© BrainMass Inc. brainmass.com October 10, 2019, 4:25 am ad1c9bdddfhttps://brainmass.com/math/discrete-math/proof-about-integers-rationals-459483

#### Solution Preview

Suppose [(a,b)]=[(a',b')]. Show that -[(a,b)]=-[(a',b')].

Proof: Let ~ be an equivalence relation on the set of ordered pairs of natural numbers N×N ...

#### Solution Summary

The expert provides proof about integers and rationals.

$2.19