I’d thought the Hilbert space was uncountably dimensional because the number of functions of a real line is uncountable.
A mere typo. I meant, of course, that I’d thought the quantum Hilbert space was uncountably dimensional, because a point in that Hilbert space corresponded to an amplitude distribution over points in a real space, and a function of a real space has uncountable degrees of freedom.
I’d thought the Hilbert space was uncountably dimensional because the number of functions of a real line is uncountable.
A mere typo. I meant, of course, that I’d thought the quantum Hilbert space was uncountably dimensional, because a point in that Hilbert space corresponded to an amplitude distribution over points in a real space, and a function of a real space has uncountable degrees of freedom.