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