This video presents Cantor's argument that there exist different infinities by demonstrating a set that is uncountable. It will only make sense if you have watched the previous video, Part 5, which defines countable sets. In essence, the size, or cardinality, of the rational numbers (fractions) is the smallest infinity: aleph null (or aleph zero). The cardinality of the real numbers, aleph one, is probably the next largest infinity, but that fact (the continuum hypothesis) has been shown to be impossible to prove under the current axioms of set theory.