Description: Define indexed union.
Definition indexed union in [Stoll] p. 45. In
most applications, is independent of (although this is not
required by the definition), and depends on i.e. can be read
informally as . We call the index, the index
set, and the
indexed set. In most books, is written as
a subscript or underneath a union symbol . We use a special
union symbol to make it easier to distinguish from plain class
union. In many theorems, you will see that and are in the
same disjoint variable group (meaning cannot depend on ) and
that and do not share a disjoint
variable group (meaning
that can be thought of as i.e. can be substituted with a
class expression containing ). An alternate definition tying
indexed union to ordinary union is dfiun2 3883. Theorem uniiun 3902 provides
a definition of ordinary union in terms of indexed union. (Contributed
by NM, 27-Jun-1998.) |