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Numbers, Sets and Axioms: The Apparatus of Mathematics [Hardcover]

A. G. Hamilton


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Book Description

13 Jan 1983 0521245095 978-0521245098 1
Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.


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First we consider what are the basic notions of mathematics, and emphasise the need for mathematicians to agree on a common starting point for their deductions. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Amazon.com: 4.0 out of 5 stars  1 review
1 of 1 people found the following review helpful
4.0 out of 5 stars A good starter kit 22 July 2009
By Matt Westwood - Published on Amazon.com
Format:Paperback
For getting a feel for the axiomatic definition of the classic number systems, it's pretty good. Rigorous it ain't but then that's not what it sets out to be. It also leaves out proving quite a few important steps. But a lot of the works out there are difficult to follow and it's not easy to see where they're going. Hamilton's strength is the lucidity of his exposition and his ability to understand exactly where the difficult bits are that need explaining.
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