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