Infinity: A Very Short Introduction by Ian Stewart

Author:Ian Stewart [Stewart, Ian]
Language: eng
Format: epub, pdf
Tags: Mathematics, Philosophy, Religion, Science
ISBN: 9780191071515
Google: HDNdDgAAQBAJ
Amazon: B06XH3GY44
Publisher: Oxford University Press
Published: 2017-03-13T03:00:00+00:00

Infinite series

With the rigorous formulation of the concept ‘limit’, calculus powered ahead to become just one part of a much broader area of mathematics, analysis. Limits resolved several other basic issues to do with infinity and infinitesimals, by recasting them in finite terms. Aristotle would have been proud, because the essence of this resolution is a move from actual to potential infinity. The definition of a limit is based on a process that assigns to any specific finite positive ε a specific finite positive δ.

Limits also make sense of infinite series. The definition is modified slightly; in place of a real number δ whose main role involves being small, infinite series involve a natural number n whose main role is to be large. Specifically, an infinite series

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