Bernoulli's Paradox

Suppose the Harmonic Series converges to $h$:

$$\sum_{k=1}^\infty {1\over k}=h.$$

Then rearranging the terms in the sum gives

$$h-1=h,$$

which is a contradiction.

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.