a to the b power IIa
Good thing that I defined E to operate on forms of more than one variable. The obvious thing to look at first is powers of (w + x) where we then substitute 1 for w. (Our notation is formally inadequate, because no order has been given to the variables corresponding to the order of the list of substituents, but we'll content ourselves by saying that "x" comes last.) OK...
Z[E[(w - x)^4](1, x)] = ZE[(1 - x)^4], of course, while
ZE[(w - x)^4](1, x) = 4 ZE[(1 - x)^3]. Huh?
(And there's plenty more where that came from.) As shonk's comment (see earlier "a to the b power II") illustrated, the notion that applying Z has cut the semantic correspondence to binomial powers is untrue. Even the appearance of factorials cast doubt on that. And here, again, the properties of the binomial coefficients shape the result.
Z[E[(w - x)^4](1, x)] = ZE[(1 - x)^4], of course, while
ZE[(w - x)^4](1, x) = 4 ZE[(1 - x)^3]. Huh?
(And there's plenty more where that came from.) As shonk's comment (see earlier "a to the b power II") illustrated, the notion that applying Z has cut the semantic correspondence to binomial powers is untrue. Even the appearance of factorials cast doubt on that. And here, again, the properties of the binomial coefficients shape the result.
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