Georg Cantor Quotes About Epiphany

• The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

  Georg Cantor

  Fall, Numbers, Finite Number

  "Understanding the Infinite". Book by Shaughan Lavine, 1994.

• What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.

  Georg Cantor

  Believe, Numbers, Finite Number

  "Understanding the Infinite". Book by Shaughan Lavine, 1994.

• I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

  Georg Cantor

  Discovery, Years, Diversity

  "Modern Mathematicians". Book by Harry Henderson, 1995.

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