◀ ▲ ▶Branches / Number-systems-arithmetics / Proposition: Contraposition of Cancellative Law for Multiplying Integers
Proposition: Contraposition of Cancellative Law for Multiplying Integers
If any two integers \(x,y\) are unequal, then the inequality is preserved, if and only if we multiply both sides of the inequality by an arbitrary integer \(z\neq 0\):\[x \neq y\Longleftrightarrow \begin{cases} z \cdot x\neq z \cdot y,&\text{or}\\
x \cdot z\neq y \cdot z.
\end{cases}\]
Table of Contents
Proofs: 1
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References
Bibliography
- Landau, Edmund: "Grundlagen der Analysis", Heldermann Verlag, 2008
