Irrational Numbers

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Here Ivan Niven gives a wholly self-contained, masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. Notes are provided at the end of each chapter citing the main sources used by the author and suggesting further reading.

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