Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics by Friedrich Waismann

Author:Friedrich Waismann [Waismann, Friedrich]
Language: eng
Format: epub
Publisher: Dover Publications
Published: 2012-10-12T16:00:00+00:00

proves to be so much more convenient and appropriate than the complicated system of inequalities that it is advantageous to retain infinity as a facon de parler. This concept therefore is a symbol which we use in order to describe certain intricate relations in a concise and clear manner.

We will now give a general formulation of the concept of limiting value. The nonending sequence of numbers

a1, a2, a3, . . . an,. . .

is said to converge to the limiting value a, in symbols

if the sequence of numbers, continued sufficiently far, draws arbitrarily near to a, that is, if

a—an < ε,

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