Summation of Zero/Finite Set
< Summation of Zero(Redirected from Summation over Finite Set of Zero)
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Theorem
Let $\mathbb A$ be one of the standard number systems $\N, \Z, \Q, \R, \C$.
Let $S$ be a finite set.
Let $0 : S \to \mathbb A$ be the zero mapping.
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Then the summation of $0$ over $S$ equals zero:
- $\ds \sum_{s \mathop \in S} 0 \left({s}\right) = 0$
Proof
At least three proofs are possible:
- using the definition of summation and Indexed Summation of Zero
- using Indexed Summation of Sum of Mappings
- using Summation of Multiple of Mapping on Finite Set.
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