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Infinity does not = Infinity

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  • This is all well known and old math. Of course there are more points in the plane than on a line.
    All that is missing is the dimensionality of the set of point. The dimensionality does not have to be an integer. Some infinite sets have dimension 0.7

Every nonzero finite dimensional inner product space has an orthonormal basis. It makes sense, when you don't think about it.

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