The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1 (Classic Reprint) - Hardcover

Hobson, Ernest William

9781527951815: The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1 (Classic Reprint)

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ISBN 10: 1527951812 ISBN 13: 9781527951815

Verlag: Forgotten Books, 2018

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Excerpt from The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1

On controversial matters connected with the fundamentals of the Theory of Aggregates, the considerable diversity of Opinion which has arisen amongst Mathematicians has been taken into account, but in general no attempt has been made to give dogmatic decisions between opposed opinions. In view of the delicate questions which arise as to the legitimacy and meaning of the axiom known as the Multiplicative Axiom, or as the Principle of Zermelo, the policy has been adopted of so framing the proofs of theorems as to avoid an appeal to the axiom, whenever that course appeared to be possible; in other cases, the necessity for the employment of the axiom has been pointed out.

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