[FOM] Slashed circle symbol for the empty set

Vaughan Pratt pratt at cs.stanford.edu
Sat Apr 4 02:08:09 EDT 2009

Howard, William A. wrote:
> Someone just told me that the empty set symbol resembling a slashed small
> circle was chosen from the Norwegian alphabet by Andre Weil. Does anyone
> know whether this is true, and, if so, why Weil chose this symbol?

Hi Bill,

According to the article "Earliest Uses of Symbols of Set Theory and 
Logic" at http://jeff560.tripod.com/set.html, Andre Weil claimed credit 
for the symbol in his autobiography "Souvenirs d'apprentissage" as follows:

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.

As one of Øystein Ore's 293 descendants I had to check whether any of 
them had participated in Bourbaki, which they hadn't.  The explanation 
for why Weil alone was familiar with the symbol can be found between the 
lines of the review of Weil's 1991 autobiography at


from which one infers that Weil had an outgoing personality that went 
well with his wide-ranging travels and broad linguistic interests.

Incidentally, for those given to questioning the accuracy of Wikipedia, 
one has to ask whether Wikipedia or the autobiography is more accurate 
concerning Rolf Nevanlinna's intervention when Weil was supposedly about 
to be shot as a spy.  According to


what Pekonen found in 1992 was at odds with Nevanlinna's account. 
Anyone know what Weil's response to Pekonen was?  Pekonen's own 
biography of Nevanlinna at


says "Weil, who carried visiting cards signed N. Bourbaki, was suspected 
of being a Soviet spy and was arrested by the military police. After 
Nevanlinna and other mathematicians had testified in his favour, Weil 
was released and expelled to Sweden."  So perhaps Nevanlinna merely 
exaggerated a little about the threatened firing squad.


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