Definition:Partial Subtraction

Definition

Partial subtraction is the operation $\dot - : \N \times \N \to \N$ defined on the set of natural numbers $\N$ as follows:

$\forall a, b \in \N: a \mathop {\dot -} b = \begin{cases}

0 & : a < b \\ a - b & : a \ge b \end{cases}$ where $a - b$ denotes natural number subtraction.

Also known as

• Cut-off subtraction

Sources

• 1982: Martin Davis: Computability and Unsolvability (2nd ed.): Part $1$: The General Theory of Computability: Chapter $1$. Computable Functions: $3$: Some Examples: Example $3.4$