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 distinct variable group (meaning cannot depend on ) and
that and do not share a distinct
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 4002. Theorem uniiun 4020 provides
a definition of ordinary union in terms of indexed union. Theorems
fniunfv 5467 and funiunfv 5468 are useful when is a function.
(Contributed by NM, 27-Jun-1998.) |
