10/14/02
5
5
White Hole: The Infinitesimal
In binary notation
the number 2/3 can be written as an infinite
sequence 0.1010101***(up to aleph_0).
But, Cantor tells us that, in principle, we can extend
this to
0.1010101***(up to aleph_0)xxxxxxx***(up to aleph_1),
where the x represents a 0 or 1.
So, here is our visualization of an infinitesimal: Corresponding to every real number, there is an infinitesimal (white
hole, dedekind edge) sitting on the real line, and that infinitesimal has a nonzero, but infinitely small, length. Thus, the infinitesimal corresponding to 2/3 is the set of subsets of aleph_1 which contain all the odd integers.