The Irrationals by Havil Julian;

Author:Havil, Julian;
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2011-03-09T16:00:00+00:00

and so

Making the an Integers

We move closer to the contradiction that an expression is a positive integer less than 1.

To that end we shall need to address the fact that the an are themselves not integers but become so when multiplied by the expression 2[1, 2, 3, . . . , n]3: this is not obvious, but as a first step we can look to table 5.2 for hope. Refer back to page 141 for the definition of an; cn,k is what makes an a fraction and its first component is

If we were to write this as a single fraction, that fraction’s denominator (before possible cancellation) would be [1, 2, 3, . . . , n]3 and so multiplying by this gives us an integer.

The 2 deals with the 2 in the denominator of the second part of the expression for cn,k but we must borrow one of the

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