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kentonyee@xxxxxxxxxxx wrote:
> But what kind of dis-continuous solution is there, now that you've
> piqued my interest by bringing up the issue.
They will be discontinuous everywhere, and probably not uniquely
specifiable in a finite expression. For example, given a basis for R
as a vector space over Q (which will have infinitely many elements),
f(x) could be the coefficient in x of one chosen basis element. More
generally f could be any linear projection in the vector space.
However, the same reasoning as in the case f(x) = x leads to the
conclusion that V(x,y) will not depend on y.
- Tim
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