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Proposition: Contraposition of Cancellative Law for Multiplying Rational Numbers

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

Table of Contents

Proofs: 1

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References

Bibliography

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