[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
http://www.ams.org/notices/199904/rev-varadarajan.pdf
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
http://en.wikipedia.org/wiki/Andr%C3%A9_Weil
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
http://www.icmihistory.unito.it/portrait/nevanlinna.php
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.
Cheers
Vaughan
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