## Continuum Hypothesis

Georg Cantor originally proposed that there is no infinite set with a cardinal number between that of the “small” infinite set of natural numbers (N) and the “large” infinite set of real numbers C (the “continuum”). “There is no set whose cardinality is strictly between that of the integers and that of the real numbers.” This means that N=Aleph0, C=Aleph1. Gödel showed that no contradiction arises if the continuum hypothesis is added to conventional Zermelo-Fraenkel set theory. However, Paul Cohen proved in 1963 that no contradiction arises if the negation of the continuum hypothesis is added to set theory. Together,...