Arnauld's Paradox
Contents
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
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Source of Name
This entry was named for Antoine Arnauld.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $-1$ and $i$
