`  ::: So it is with the definition of an irrational number as a convergent sequence of rational numbers.  Georg Cantor had to posit ordinal numbers, in particular w (omega), to get to the irrational numbers.  There is a huge conceptual leap from _descending intervals_ to _point_ and it is this vagueness in definitions (why can it not just ``converge`` to another ``interval``?) that causes self-contradictions. What is your objection to my assertion about the ``definability, countability, computability and well-ordering of all real numbers`` in the first sentence above? [BenCawaling@Yahoo.com (14 Dec 05)]`