Georg Cantor’s Big oneBy Stephen Brown | June 11, 2018George Ferdinand Ludwig Phillipp Cantor sure did have a long name, but not nearly as long as the set of infinite numbers in his theory. He was born March 3,1845 in Russia and at the age of 11 moved to Germany where he spent the rest of his life. Germany is also where he founded his Set Theory, his greatest accomplishment. Richard Dedekind was a Mathematician at the Brunswick Technical Institute and was a friend and a colleague of Georg Cantor. Their was a series of letters between Richard and Georg that sparked cantor’s ideas on the theory of sets.
These two great minds agreed that a set, infinite or not , is a collection numbers that share a particular property while retaining its own individuality. But Cantor was seeing something that Richard didn’t and began to investigate further. In 1873 Cantor showed that rational numbers, though infinite, are denumerable because they can be placed into correspondence with natural numbers. He also showed that the set of real numbers, both rational and irrational, was infinite and uncountable. Cantor’s theory became a whole new idea concerning the math behind the infinite. Without real numbers, Cantor’s set theory and all the research and work he put in to proving his theory,probably wouldn’t have the same outcome.
This speaks greatly of the necessity of real numbers.