Real Numbers and the Dedekind Cut
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Bounded sets of numbers
Equations are omitted for technical reasons - download the original pdf
Open and closed intervals. When the end-points of an interval are included in it, the interval is said to be closed; if the end-points are not included, the interval is open. The set [Equation goes here - download the original to see it.] , also written [Equation], is a closed interval; the set [Equation], also written [Equation], is a open interval. An interval of the form [Equation] is called a finite interval; one of the form [Equation] is an infinite interval.
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Contents of
Real Numbers and the Dedekind Cut
1 Numbers as solutions to equations
2 The irrationality of root 2
3 The set of all rational numbers is dense
4 The Dedekind cut
5 The set of real numbers as an ordered field
6 The ordered field axioms
7 The sets of rational and real numbers are ordered fields.
8 Axiom of completeness
9 Bounded sets of numbers
10 Maximum and minimum
11 Bounded set
12 Least upper bound
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