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Corollary: Contraposition of Cancellative Law for Adding Natural Numbers

(related to Proposition: Addition of Natural Numbers Is Cancellative)

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