On this day in 1873

On this day, 29 November, in 1873 Georg Cantor wrote a letter to Richard Dedekind. It contained a question that inaugurated a new mathematical discipline: Set Theory.

Cantor writes:

Allow me to put a question before you that is of some theoretical interest to me, but which I have not been able to answer; maybe you can, and would you be so kind as to write me about this, it concerns the following.

One takes the aggregate of a positive whole numbers n and denotes this by (n); furthermore one considers the aggregate of all positive real numbers x and denotes this by (x); then the question is simply that whether (n) and (x) can be put into some correspondence in such a way that every individual from one aggregate belongs to just one of the other and conversely?

In modern terms: is there a bijection between the set of natural numbers and the set of positive real numbers?

Cantor goes on to say that a simple `no’ “because (n) is discrete and (x) forms a continuum” does not suffice because the same could be said of (n) versus the aggregate of positive rational numbers yet one can create a correspondence as desired between these two entities.

The full letter can be read here in German. It is a scan from Briefwechsel Cantor-Dedekind.

The answer to the question? Watch this space.

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