MA2321 - Analysis in Several Real Variables Dr. David R. Wilkins Resources - Michaelmas Term 2018

Miscellaneous Topics

Dedekind sections (or cuts)

Dedekind cut (Wikipedia)

Essays on the Theory of Numbers by Richard Dedekind (published online by Project Gutenberg)

This book, freely available online through Project Gutenberg, contains translations by Wooster Woodruff Beman (1850–1922) of the essays Stetigkeit und irrationale Zahlen (Continuity and irrational numbers, 1872) and Was sind und was sollen die Zahlen (The nature and meaning of numbers, 1888) by Richard Dedekind (1831–1916). This translation was published by the The Open Court Publishing Company in 1901, has been republished by Dover Publications

When the rational and irrational numbers are formally constructed so as to be represented as Dedekind sections (or cuts), the resulting ‘numbers’ constitute a Dedekind-complete ordered field. This is discussed in detail in the Appendix to Chapter 1 of Principles of Mathematical Analysis by Walter Rudin, and also in Chapter 28 of Calculus by Michael Spivak.

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Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.