Functions as vector spaces

Oneiromancy

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Sep 28, 2007
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On 15, I don't understand how to work with that notation exactly. I guess I'm just confused as to what [x p(x)] is telling me. When I check closure properties, how is that going to look?

Also, my book gives me no examples of a function as a vector space, much less check that. I guess it's the same thing as with polynomials right?

And on 19, to prove it in the forward direction, I just let S be a vector space, then show p(x)=ax for some scalar a. Then in the backwards direction I let p(x)=ax, then show S is a vector space. I don't know what p(x)=ax is telling me though.

Thx.
 
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