Arnauld's Paradox

Paradox

Suppose negative numbers exist.

Then:

$\dfrac {-1} 1 = \dfrac 1 {-1}$

Thus the ratio of a smaller quantity to a larger quantity equals the ratio of the same larger quantity to the same smaller quantity.

Resolution

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Source of Name

This entry was named for Antoine Arnauld.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $-1$ and $i$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $-1$ and $i$