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.

Also see

 * Product of Positive Cuts is Positive Cut which proves existence and uniqueness of $\alpha \beta$