"A Study of the Diagonalization Technique and
       Infinitely Morphing Objects"
This paper contains proofs that the real numbers
are countable, that the Diagonalization Theorem
is false, that the Power Set Theorem is false,
etc.  Many new mappings, concepts, theorems,
algorithms, definitions, etc. on Transfinite
Set Theory.  It contains mappings from 2
countable sets to all of R(0,1).  Also, a mapping
from 2 countable sets to the Power Set of the
Counting/Natural Numbers.  Mathematically based.