La somme de nos connaissances est toujours inférieure à la somme de celles qui nous manquent. - yduf

see also

• Georg Cantor and His Heritage / HN - $Z$ and $Q$ are countable and $R$ is uncountable
  • Turing extended to the computable numbers K, which can be conceptualized as a number where you can write a f(n) that returns the nth digit in a number.
  • The reals numbers are un-computable almost everywhere, this property holds for all real numbers in a set except a subset of measure zero, the computable reals K which is Aleph Zero, a countable infinity.
  • The set of computable reals is only as big as N, and can be mapped to N.