Bernoulli's Paradox

Suppose the harmonic series converges to :

Then rearranging the terms in the sum gives

which is a contradiction.

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area of an equilateral triangle with side length a
distinct permutations of {1, 2, 2, 3, 3, 3}
Hilbert curve, n=5

References

Boas, R. P. "Some Remarkable Sequences of Integers." Ch. 3 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 39-40, 1979.

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Bernoulli's Paradox

Cite this as:

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

Bernoulli's Paradox

See also

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References

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