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Development of Complex Numbers

  1. Jul 12, 2009 #1
    I was wondering if someone could recommend a good text that explains the construction of complex from real, real from rational, rational from integers, and integers from natural numbers.

  2. jcsd
  3. Jul 12, 2009 #2
    Here are two books that cover what you asked for:

    https://www.amazon.com/Foundations-...=sr_1_1?ie=UTF8&s=books&qid=1247418426&sr=1-1 by Edmund Landau

    https://www.amazon.com/Number-Syste...=sr_1_1?ie=UTF8&s=books&qid=1247418469&sr=1-1 by H. A. Thurston

    Landau's book is well-known. However, as some of the Amazon reviews point out, it is extremely dry. It contains little, if any, motivational material and no exercises.

    Thurston, on the other hand, consists of approximately one-half motivational material and one-half formal definitions, theorems and proofs. It also contains exercises, but no solutions.

    Landau uses Dedekind cuts to define the real numbers, while Thurston uses Cauchy sequences. Both approaches are valid, but the Dedekind cuts approach is probably more commonly seen elsewhere.

    So, you might want to see if your library has both books and decide which one you like the most.

    Last edited by a moderator: May 4, 2017
  4. Jul 12, 2009 #3

    Thanks, I think I'll pick up Thurston's book eventually.

    Any online texts?
    Last edited by a moderator: May 4, 2017
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