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Currently, a discussion started on the German Wikipedia article for Empty Set (the German discussion), whether $\emptyset$ or $\varnothing$ should be used or is more common as a symbol for an empty set.

Do you know any sources for this question? Do you know a source for the statement, that Nicolas Bourbaki was the first who used this symbol?

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    @user1729 Perhaps even more people would initially think "$\bigl|\bigl\{\{\}\bigr\}\bigr| = 0$" than "$\bigl|\{\emptyset\}\bigr| = 0$", but that's not a bad thing: after all, the main point of this question is to get the sometimes counterintuitive properties of the empty set clear. Once they've grasped it, I believe $\bigl|\bigl\{\{\}\bigr\}\bigr| = 1$ is in fact _more_ memorable and clarifies the matter very well. $\bigl|\{\emptyset\}\bigr| = 1$ doesn't look that surprising, not more than $\bigl|\{0\}\bigr| = 1$, though there is quite a big conceptual difference between these two.2012-08-22

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I would say the following should be not too controversial:

  • $\emptyset$ and $\varnothing$ are typographical variants of the same mathematical symbol designating the empty set

  • The symbol was introduced by Bourbaki, was inspired by the Norwegian character Ø, but is a distinct character from it

  • The intention was most probably to create a symbol related to $0$ (zero), not to O (Oh), distinguished from it by striking it through. After all the empty set has all kinds of relations with the number $0$, but none with the letter O. (By contrast big-Oh and little-o symbols derive from the word "order".)

  • The symbol has absolutely no relation (apart from appearance) with the lower-case Greek letter phi, with typographical variants $\phi$ and $\varphi$.

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There is a webpage where you can find mention of this: http://jeff560.tripod.com/set.html

Here's an extract

The null set symbol (Ø) first appeared in N. Bourbaki Éléments de mathématique Fasc.1: Les structures fondamentales de l'analyse; Liv.1: Theorie de ensembles. (Fascicule de resultants) (1939): "certaines propriétés... ne sont vraies pour aucun élément de E... la partie qu’elles définissent est appelée la partie vide de E, et designée par la notation Ø." (p. 4.)

André Weil (1906-1998) says in his autobiography that he was responsible for the symbol:

Wisely, we had decided to publish an installment establishing the system of notation for set theory, rather than wait for the detailed treatment that was to follow: it was high time to fix these notations once and for all, and indeed the ones we proposed, which introduced a number of modifications to the notations previously in use, met with general approval. Much later, my own part in these discussions earned me the respect of my daughter Nicolette, when she learned the symbol Ø for the empty set at school and I told her that I had been personally responsible for its adoption. The symbol came from the Norwegian alphabet, with which I alone among the Bourbaki group was familiar.

The citation above is from page 114 of André Weil's The Apprenticeship of a Mathematician, Birkhaeuser Verlag, Basel-Boston-Berlin, 1992. Translated from the French by Jennifer Gage. The citation was provided by Julio González Cabillón.

You should also note that Nicolas Bourbaki is a collective pseudonym for a group of French-speaking mathematicians.

Concerning your question, I remember one of my math professor telling us that in fact, it was a claim by both André Weil and Claude Chevalley, but I can't find the citation for Chevalley.


I've found also this lecture about history of math from a Canadian University (in French), where this issue is mentioned: http://www.mat.ulaval.ca/fileadmin/Cours/MAT-2500/Bourbaki.pdf

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    @t.b.: Thank you very much for this document! For all others: With huge, he means 108.6 MB! Huge, indeed.2012-08-22