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Proposition: Contraposition of Cancellative Law of for Multiplying Real Numbers

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

Table of Contents

Proofs: 1

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References

Bibliography

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