Permutation of Indices
Jump to navigation
Jump to search
Theorem
Let $R: \Z \to \set {\T, \F}$ be a propositional function on the set of integers.
Let the fiber of truth of $R$ be finite.
Let $\pi$ is a permutation on the fiber of truth of $R$.
Then:
Permutation of Indices of Summation
- $\ds \sum_{\map R j} a_j = \sum_{\map R {\map \pi j} } a_{\map \pi j}$
Permutation of Indices of Product
- $\ds \prod_{\map R j} a_j = \prod_{\map R {\map \pi j} } a_{\map \pi j}$