[FOM] history of modern notation for sets defined by a property

Arnold Neumaier Arnold.Neumaier at univie.ac.at
Thu Feb 12 07:47:48 EST 2009

Does anyone know who invented the notations {x in A | P(x)} and
{x in A : P(x)} for sets defined by a property P(x)?

McShane, Integration, 2nd ed. (1947) uses {x | S},
I don't have access to the first edition from 1944
- is it perhaps already there?

Halmos, Measure Theory (1950) uses {x: pi(x)}.

These are the earliest occurrences of the modern notations known
to me (communicated to me by Viktor Losert).

Maybe someone is able to trace back the use even further.
Please send information directly to me (Arnold.Neumaier at univie.ac.at);
the newest state of the investigation will always be visible on my
web page http://www.mat.univie.ac.at/~neum/contrib/set.txt

Note that variants of the modern notations are used in the older
literature. For example, a paper by Von Neumann 1928 uses M(x; E(x)),
and in ''On rings of operators'' (1936), he uses (x; epsilon(x)).
I am interested only in the modern forms.

Arnold Neumaier

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