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 selfcontradictions What is your objection to my assertion about the definability countability computability and wellordering of all real numbers in the first sentence above BenCawalingYahoocom  Dec