**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 4001. Theorem uniiun 4019 provides
a definition of ordinary union in terms of indexed union. Theorems
fniunfv 5466 and funiunfv 5467 are useful when is a function.
(Contributed by NM, 27-Jun-1998.) |