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Proposition: Contraposition of Cancellative Law for Adding Rational Numbers

If any two rational numbers are unequal \(x\neq y\), then the inequality is preserved, if and only if we add an arbitrary rational number \(z\) to both sides of the inequality, formally: \[x \neq y\Longleftrightarrow \begin{cases} z + x\neq z + y,&\text{or}\\ x + z\neq y + z. \end{cases}\]

Table of Contents

Proofs: 1

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References

Bibliography

1. Landau, Edmund: "Grundlagen der Analysis", Heldermann Verlag, 2008