User blog comment:Vel!/Hilbert ITTMs/@comment-10429372-20140724163701

You say that the photo tape is indexed by {0,1}^Z (I assume that is a function {0,1} -> Z?) and then that this can be visualized by associating each cell with an arbitrary real number in the interval [0,1).

However, there are only Beth_0 functions {0,1} -> Z, while there are Beth_1 real numbers in the interval [0,1). So, what went wrong?