Countability and Uncountability: The Precursors of “Encoding”

Abstract

The theory of countability (and uncountability) began with Georg Cantor’s deliberations on the nature of infinity [10]. Cantor concentrated on questions that can be framed intuitively as follows: Are there “more” rational numbers than integers? Are there “more” real numbers than integers? (Note that we need to put “more” in quotes, because all three sets, the integers, the rational numbers, and the real numbers, are infinite—so what does “more” mean?)