Exchange of Order of Summations over Finite Sets/Cartesian Product/Proof 1
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Theorem
Let $f: S \times T \to \mathbb A$ be a mapping.
Then we have an equality of summations over finite sets:
- $\ds \sum_{s \mathop \in S} \sum_{t \mathop \in T} \map f {s, t} = \sum_{t \mathop \in T} \sum_{s \mathop \in S} \map f {s, t}$
Proof
This theorem requires a proof. In particular: using Summation over Cartesian Product as Double Summation You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |