There Are Almost No Rational Numbers(austinrochford.com)
austinrochford.com
There Are Almost No Rational Numbers
http://www.austinrochford.com/posts/2013-12-31-almost-no-rationals.html
http://www.austinrochford.com/posts/2013-12-31-almost-no-rationals.html
The odd thing about the numbers that Cantor discovered is that they exist only in bulk, not as individuals.
Any method that can specify a specfic number requires that you be able to write a finite length description of how to compute that number, so the number of numbers that can actually be specified is countable.