Body of real numbers : Appendix: Principle of the construction of the body of real numbers

Appendix: Principle of the construction of the body of real numbers
Body of real numbers

Author : Gérard DEBEAUMARCHÉ

Publication date: April 10, 2001 | Lire en français

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3. Appendix: Principle of the construction of the body of real numbers

This principle dates back to 1872 and was defined by Dedekind in 1872.

We assume here that the field $ℚ$ of rational numbers is known, and we are interested in certain parts of $ℚ$ called cuts, which we now define.

Definition. Any non-empty major part X of the field $ℚ$ of rational numbers that satisfies the following two properties is called a cutoff:

(a) any rational less than...

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