Definition:Very Strong Zero

Definition
A very strong zero or very strongly zero is a variation of zero such that multiplication with another expression results in $0$ even if the other expression is undefined, such as for example if it contains division by zero.

Examples
The very strong zero is used in Iverson's convention, where $\sqbrk P$ evaluates to zero whenever $P$ is false.

Thus, for example:
 * $\ds \sum_{k \mathop \in \Z} \frac 1 k \sqbrk {k = 1} = 1$

even though $\dfrac 1 k$ is not defined for $k = 0$.