Since I am on the topic of Venn Diagrams, I decided to review the history of "set theory". Given that a Venn Diagram is just a graphical representation of sets of data, producing an accurate Venn Diagram requires understanding the underlying data. While the sets of data presented in Venn Diagrams are normally finite, the whole theory of sets and the interest to mathematicians to develop the theory derived from debates over the possibility of infinity. The German mathematician Georg Cantor created the concept of set theory. Prior to Cantor, mathematicians and philosophers recognized sets of data but only considered they were possible in limited (finite) amounts. Cantor's work proved it is possible to have infinite amounts of data within a set. He also proved that different sets of infinity are not equinumerous. Hence if two sets are presented and they both have infinite data, is is possible that both sets may not have the same amount of data. Part of his proof showed that there are an infinite amount of real numbers and an infinite amount of natural numbers but there are more real numbers than infinite numbers. His proofs were controversial to philosophers of his day, but future mathematicians embraced his work and developed it into the modern concept of set theory. Thus what is normally taught as a beginning skill in statistics, actually has its roots as a topic that changed philosophy and the world view of mathematics.
For deeper information on Georg Cantor, see the Wikipedia article, or read a biography.
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