Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

LECTURE XIII
Variables and Limits
A GLANCE AT THE SHADOWY BACKGROUND OF SCIENTIFIC
IDEAS-THE MEANINGS OF VARIABLE AND CONSTANT —
RANGES OF VARIATION AND THE IDEA OF NEIGHBORHOOD-VARIOUS DEFINITIONS OF LIMIT CLARIFIED
BY SIMPLE EXAMPLES-THE SCANDAL OF A STARVING
NURSE IN THE RICHEST LAND KNOWN TO HISTORY.
IN the introductory lecture, I spoke at length on the
mathematical obligations of philosophy. In preparing to
discharge them it is imperatively necessary for students
of philosophy to gain genuine understanding of those
great concepts that are as vital organs in the body of
mathematics, giving the science not only its life but its
character and its power. It is one of the aims of these
lectures to assist students primarily interested in philosophy to gain such an understanding. In pursuance of that
aim it is, I believe, essential to devote one or two lectures
to the nature and the significance of the mathematical
concept denoted by the term " limit." There are in current use several concepts of the term, but for the present
we may speak as if there were only one. The importance
and the power of the concept have been so long recognized
by mathematicians that the notion of limit and what is
often called the method of limits have found their way
down into text-books of algebra, geometry and trigonom233