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Impossible? by Julian Havil

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Chapter 15

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THE POWER OF POWERS

Sometimes it is useful to know how large your zero is.

Anon

Given its importance to the chapter, ‘Some consequences of the irrationality of log10 2’ could have been a reasonable alternative title. Yet the title stands, as the subject matter that follows concentrates on some rather surprising consequences relating to the decimal expansion of 2n; we prove the elementary result that log10 2 is indeed irrational in the appendix (page 226), expending our efforts over the next few pages appealing to that result.

A Great Deal of Nothing

In a note to the journal Mathematics of Computation (E. and U. Karst, The first power ...

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