Analysis

The Axiom of Completeness Definition: Upper bound A real number \(\alpha\) is called an upper bound for \(S\) if \(x\le \alpha\) for all \(x \in S\). The set \(S\) is said to be bounded above if it has an upper bound. Definition: Lower bound A real number \(\alpha\) is called an lower bound for \(S\) if \(\alpha \le x\) for all \(x \in S\). The set \(S\) is said to be bounded below if it has an ..