FINITE AND INFINITE
I was once shown a statement made by an eminent mathematician of
Cambridge from which one would conclude that this mathematician thought
that finite distances became infinite when they were great enough. In
one of those splendidly printed books, bound in blue, published by the
University Press, and sold at about a guinea as a guide to some advanced
branch of pure mathematics, one may read, even in the second edition
published in 1900, the words: "Representation [of a complex variable] on
a plane is obviously more effective for points at a finite distance from
the origin than for points at a very great distance."
Plainly some of the points at a very great distance are at a _finite_
distance, for the same author mentions that Neumann's sphere for
representing the positions of points on a plane "has the advantage ...
of exhibiting the uniqueness of _z_ = [infinity symbol] as a value of
the variable."