Definition:Absolute Value of Cut

Definition

Let $\alpha$ be a cut.

The absolute value of $\alpha$ is denoted and defined as:

$\size \alpha = \begin {cases} \alpha & : \alpha \ge 0^* \\ -\alpha & : \alpha < 0^* \end {cases}$

where:

$0^*$ denotes the rational cut associated with the (rational) number $0$

$\ge$ denotes the ordering on cuts.

Sources

• 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Dedekind Cuts: $1.24$. Definition