EVIDENCE FOR DARK NUMBERS

This book contains several arguments for the existence of dark numbers, i.e., numbers which cannot be manipulated as individuals but only collectively. Their existence depends on the premise of actual infinity. Whether actually infinite sets exist is unknown and cannot be proven; it can only be assumed as an axiom. But if actually infinite sets exist then dark elements are unavoidable. This concept helps to explain many paradoxes of set theory like Zeno’s paradox or the paradox of the binary tree or the completely scattered space of the real axis.