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 ..