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Proposition: Contraposition of Cancellative Law for Multiplying Natural Numbers

If any two natural numbers \(x,y\) are unequal, then the inequality is preserved if and only if we multiply both sides of the inequality by an arbitrary natural number \(z\neq 0\):\[x \neq y\Longleftrightarrow \begin{cases} z \cdot x\neq z \cdot y,&\text{or}\\ x \cdot z\neq y \cdot z. \end{cases}\]

Table of Contents

Proofs: 1

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References

Bibliography

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