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## Main Question or Discussion Point

Wolfram says that an example of an inner product space is the vector space of real functions whose domain is an closed interval [a,b] with inner product ##\langle f, g\rangle = \int_a^b f(x) g(x) dx##. But ##1/x## is a real function, and ##\langle 1/x, 1/x\rangle## does not converge... So how is this an inner product space?