Cantor and Dedekind's Early Correspondence (1873-74)

The origins of set theory

Colorized photographs of Georg Cantor in 1870 (left) and Richard Dedekind around 1886 (right).

On November 29th, 1873 mathematician Georg Cantor (1845-1918) sent a letter to Richard Dedekind (1831-1916) asking whether or not the collection of natural numbers and the collection of positive real numbers “can be corresponded so that each individual of one collection corresponds to one and only one individual of the other?”. Dedekind replied by writing that he did not know the answer, and that the question was not of much practical interest.

At this point in time, it seems Cantor agreed with Dedekind’s contention, stating that his interest in the matter was related to Joseph Liouville (1809-82)’s 1844 theorem proving the existence of transcendental numbers:

Halle, December 2nd 1873
”I was exceptionally pleased to receive your answer to my last letter. I put my question to you because I had wondered about it already several years ago, and was never certain whether the difficulty I found was s…