| Description: Define the value of an
operation. Definition of operation value in
[Enderton] p. 79. Note that the syntax
is simply three class expressions
in a row bracketed by parentheses. There are no restrictions of any kind
on what those class expressions may be, although only certain kinds of
class expressions - a binary operation 𝐹 and its arguments 𝐴 and
𝐵- will be useful for proving
meaningful theorems. For example, if
class 𝐹 is the operation + and arguments
𝐴
and 𝐵 are 3 and 2 ,
the expression ( 3 + 2 ) can be proved to equal 5 . This definition is
well-defined, although not very meaningful, when classes 𝐴 and/or
𝐵 are proper classes (i.e. are not
sets); see ovprc1 6060 and ovprc2 6061.
On the other hand, we often find uses for this definition when 𝐹 is a
proper class. 𝐹 is normally equal to a class of
nested ordered pairs
of the form defined by df-oprab 6027. (Contributed by NM,
28-Feb-1995.) |
