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

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

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