What we have allowed to happen in casually accepting any decimal expansion is to open the door to what are known as the transcendental numbers, those numbers that lie beyond those that arise through euclidean geometry and ordinary algebraic equations. Cantor’s argument shows us that transcendental numbers exist and, in addition, there must be infinitely many of them, for ifthey formed only afinite collection, they could be placed in front of our list of algebraic numbers(the non-transcendentals), so yielding a listing of all real numbers,which we now know is impossible. What is striking is that we have discovered the existence of these strange numbers without identifying a single one of them!Their existence was revealed simply through comparing certain in finite collections to one another. The transcendentals are the numbers thatll the huge void between the more familiar algebraic numbers and the collection of all decimal expansions:to borrow an astronomical metaphor, the transcendentals are the dark matter of the number world.