Sets, Cardinality, and Ordering by Jon Ford, California State Sacramento Student and Sierra College Graduate
Set theory is the backbone of modern mathematics, and George Cantor is the
father of set theory. One of Cantor’s many conjectures was the continuum
hypothesis: There is no set “between” the real numbers and the integers. Gödel
showed there is no contradiction if we suppose the continuum hypothesis but Paul
Cohen showed there is no contradiction if we deny the continuum hypothesis,
leaving the question undecidable. The Continuum Hypothesis was an attempt to
order the cardinality of sets. If we accept the continuum hypothesis, we will
look at a possible partial ordering of cardinality that is constructed by
repeatedly taking the power set of the natural numbers.