Definition:Very Strong Zero
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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
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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 $k = 0$.
Sources
- 1992: Donald E. Knuth: Two Notes on Notation (Amer. Math. Monthly Vol. 99: pp. 403 – 422) www.jstor.org/stable/2325085