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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

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

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Cite this as:

Weisstein, Eric W. "Siegel's Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SiegelsParadox.html

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