◀ ▲ ▶Branches / Analysis / Section: Real Intervals and Bounded Real Sets
Section: Real Intervals and Bounded Real Sets
When we introduced the number system of real numbers \(\mathbb R\), we saw that this field as an ordered field. This means that any given two real numbers \(a,b\in \mathbb R\) can be compared with each other. This comparison always has exactly one of the following results:
 either \(a\) is "equal" \(b\), or
 \(a\) is "smaller" than \(b\), or
 \(a\) is "greater" than \(b\).
Moreover, it is Archimedean, meaning that the ordering is "regular" in the sense that for any two positive real numbers $x,y > 0$, there exist a natural number $n$ such that $nx > y.$
Table of Contents
 Definition: Real Intervals
 Definition: Supremum, Least Upper Bound
 Definition: Maximum (Real Numbers)
 Definition: Extended Real Numbers
 Definition: Supremum of Extended Real Numbers
 Definition: Infimum, Greatest Lower Bound
 Definition: Minimum (Real Numbers)
 Definition: Infimum of Extended Real Numbers
 Proposition: Closed Formula for the Maximum and Minimum of Two Numbers
 Definition: Nested Real Intervals
 Proposition: Limit of Nested Real Intervals
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