- #1
pellman
- 684
- 5
Given an indexed collection of sets [itex]A_x[/itex] the disjoint union of these sets can be thought of as the ordinary union of the sets [itex] \{ x \} \times A_x [/itex] for all x. That is, it is the set of all pairs [itex](x, a)[/itex] where [itex]a \in A_x[/itex].
(Correct me at this point if my understanding of disjoint union is wrong.)
Does this have any practical difference from set of all [itex]A_x[/itex] ?
Denote the set of index values by X. That is, is there any practical difference between [itex] \{ (x, a) | x \in X \wedge a \in A_x \}[/itex] versus [itex]\{ A_x | x \in X \}[/itex] ?
(Correct me at this point if my understanding of disjoint union is wrong.)
Does this have any practical difference from set of all [itex]A_x[/itex] ?
Denote the set of index values by X. That is, is there any practical difference between [itex] \{ (x, a) | x \in X \wedge a \in A_x \}[/itex] versus [itex]\{ A_x | x \in X \}[/itex] ?