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Proposition: Contraposition of Cancellative Law for Adding Real Numbers

If any two real numbers are unequal \(x\neq y\), then the inequality is preserved, if and only if we add an arbitrary real 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