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I'm trying to understand Hilbert spaces and I need a little help. I know that it's a vector space of vectors with an infinite number of components, but a finite length. My biggest question is: how is a Hilbert space used to represent a function? Is each component of the vector a point on the function? Also, the text I'm reading says that the inner product of a function equals the length of that function and I don't really understand what this length is. Any help would be appreciated. Thanks!