A Treatise on the Theory of Functions (Classic Reprint) - Hardcover

Harkness, James

9780265369708: A Treatise on the Theory of Functions (Classic Reprint)

Hardcover

ISBN 10: 0265369703 ISBN 13: 9780265369708

Publisher: Forgotten Books, 2018

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Excerpt from A Treatise on the Theory of Functions

The complex number is constructed out of two elements, each of which is capable of assuming a singly infinite series of values; this is the reason that it needs for its representation a doubly infinite series of points. The plane is chosen as the field on which these points are to lie; and the figure formed by representing points in this way is referred to as Argand's diagram. Other representations are possible; as, for instance, on a Sphere. We shall have occasion to establish a (1, 1) correspondence between the points of a Sphere and the doubly infinite series of values Of z, and thus to use the Sphere as the field on which z is represented.

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