[FOM] A little trouble with definition of "binary relation" in Wikipedia
Victor Makarov
viktormakarov at hotmail.com
Sun Jan 28 11:43:14 EST 2007
The following definition of "binary relation" one can find in Wikipedia:
( http://en.wikipedia.org/wiki/Binary_relation#Formal_definition )
"A binary relation R is usually defined as an ordered triple (X, Y, G) where
X and Y are arbitrary sets (or classes), and G is a subset of the Cartesian
product X × Y."
But usually in set theories with classes (for example, NBG) an ordered
triple (X, Y, G) is definend as
the ordered pair (X, (Y, G)); and an ordered pair(a,b) is defined as the
set { {a}, {a, b} }.
Because elements of sets must be sets, X, Y, G must be also sets (not proper
classes).
My question is:
Are there set theories with classes, where proper classes can be elements of
other classes?
Thanks in advance,
Victor Makarov
More information about the FOM
mailing list