The Concept of Number (Ellis Horwood Series in Mathematics & Its Applications)

 
9780131711419: The Concept of Number (Ellis Horwood Series in Mathematics & Its Applications)

The motivation underlying this book is that many undergraduate courses should make room for discussion of the number-systems concept. The author treats Frobenius' theorem in some detail and offers a proof of the related theorem of Pontrajagin on the topological characterization of connected, locally compact metric skew fields. He surveys such geometrical matters as the related work concerning vector fields on spheres, and Moufang on projective planes, using arguments which are in themselves attractive and show how to use concepts which are taught in basic algebra but rarely pushed far enough to be of interest. He uses continued fractions in his treatment to illustrate Eudoxus' approach to the classical Greek notions concerning the continuum as a number-line, and employs infinite decimals to raise the question, how do you explain what real numbers are?

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