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How can we prove $\bigtriangledown = \bigtriangleup E^{-1}$?

where,$\bigtriangleup \rightarrow \text{ Forward difference operator }$ $\bigtriangledown \rightarrow \text{ Backward difference operator }$ $E \rightarrow \text{ Shift operator }$ I tried to utilize the method of seperation of symbol but not quite there...

Give some hints for this proof.

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How about writing $\bigtriangleup(f(x))=f(x+1)-f(x)$, $E^{-1}(f(x))=\ldots$, so $\bigtriangleup E^{-1}(f(x))=$?

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    I have also seen the forward difference with a subscript $\bigtriangleup_h$ to show you what the size of the interval is.2011-02-07