1.8 Indexed Sets

Sets

Indexed Sets

• when taking the union, difference or intersection of many sets, it can get quite long and difficult to keep track of everything

• Given sets $A_1$, $A_2$, $A_3$, …, $A_n$, we define

Suppose $A_1$ = { 0, 2, 5 } , $A_2$ = { 1, 2, 5 } and $A_3$ = { 2, 5, 7 }

Union

• $\bigcup _{i=1}^n{A}_i$ = $A_1\cup A_2\cup A_3\cup ...\cup A_n$
  • E.g. $\bigcup _{i=1}^3{A}_i$ = {0, 1, 2, 5, 7}

Intersection

• $\bigcap _{i=1}^n{A}_i$ = $A_1\cap A_2\cap A_3\cap ...\cap A_n$
  • E.g. $\bigcap _{i=1}^3{A}_i$ = {2, 5}