Making Light:  Open thread 40 ::: May 10, 2005, 06:02 PM

Dave MB:

  If each element of the set can be named by a different sequence of
  bits with a single "..." in it, then the cardinality of the set is
  at most c.  (This is a mapping from natural numbers to bits, or an
  "omega-sequence" of bits.)  So real numbers can be named by their
  binary expansion, which ends in a "..." [....]

This description is dependent on what we mean by "named".  The problem
is that each of the names you propose refers to many* different real
numbers.  That isn't too surprising, since there are only aleph-null
such names.  I doubt that the description in terms of ellipses adds
non-illusory clarity to the issue.

* Where many=c.