What does it mean when one says that "The domain is the whole world."?
(e.g. p. 45, problem 11).
On a set containing all sets:
Russell's paradox.
"Russell's paradox is the most famous of the logical or set-theoretical
paradoxes. The paradox arises within naive set theory by considering the set of
all sets that are not members of themselves. Such a set appears to be a member
of itself if and only if it is not a member of itself, hence the paradox.
"Some sets, such as the set of all teacups, are not members of
themselves. Other sets, such as the set of all non-teacups, are members of
themselves. Call the set of all sets that are not members of themselves S. If S
is a member of itself, then by definition it must not be a member of
itself. Similarly, if S is not a member of itself, then by definition it must
be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has
prompted much work in logic, set theory and the philosophy and foundations of
mathematics."