User blog comment:Vel!/Hilbert ITTMs/@comment-10429372-20140724163701/@comment-1605058-20140724173050

Incorrect. There is Beth_1 functions from {0,1} to Z, and the same number of reals between 0 or 1 (inclusively or exclusively). Beth_1 is also known as continuum and is denoted c, or R when it's clear from context we mean cardinality.