So... does this mean that this statement in the abstract: "Moreover, a better terminology for the so-called real numbers is "random numbers", as their series o

So... does this mean that this statement in the abstract: "Moreover, a better terminology for the so-called real numbers is "random numbers", as their series of bits are truly random" is demonstrably false? That there exist real, non-rational numbers with a series of bits that are not truly random? Well, thinking about this after reading other posts in this thread, perhaps the statement really means that "almost every" real, non-rational number has a series of bits that are truly random, so this isn't a counterexample.