ThmDex – An index of mathematical definitions, results, and conjectures.
Partition of random basic number into positive and negative parts
Formulation 0
Let $X \in \mathsf{Random} [-\infty, \infty]$ be a D4381: Random basic number such that
(i) $X^+$ is the D1289: Basic function positive part of $X$
(ii) $X^-$ is the D1290: Basic function negative part of $X$
Then \begin{equation} X = X^+ - X^- \end{equation}
Proofs
Proof 0
Let $X \in \mathsf{Random} [-\infty, \infty]$ be a D4381: Random basic number such that
(i) $X^+$ is the D1289: Basic function positive part of $X$
(ii) $X^-$ is the D1290: Basic function negative part of $X$
This result is a particular case of R1022: Partition of basic function into positive and negative parts. $\square$