◀ ▲ ▶Branches / Numbersystemsarithmetics / Proposition: Contraposition of Cancellative Law for Adding Rational Numbers
Proposition: Contraposition of Cancellative Law for Adding Rational Numbers
If any two rational numbers are unequal \(x\neq y\), then the inequality is preserved, if and only if we add an arbitrary rational 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
Thank you to the contributors under CC BYSA 4.0!
 Github:

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