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Siegel's Paradox

If a fixed Fraction $x$ of a given amount of money $P$ is lost, and then the same Fraction $x$ of the remaining amount is gained, the result is less than the original and equal to the final amount if a Fraction $x$ is first gained, then lost. This can easily be seen from the fact that

$\displaystyle {[}P(1-x)](1+x)$ $\textstyle =$ $\displaystyle P(1-x^2)<P$  
$\displaystyle {[}P(1+x)](1-x)$ $\textstyle =$ $\displaystyle P(1-x^2)<P.$  

© 1996-9 Eric W. Weisstein