# Arnauld's Paradox

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## 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 $i$