Question

12. Definition : Let Λ be a non-empty set. If for each a є Л there is a set Aa, the collection (Aa : α Ε Λ is called an indexed collection of sets. The set A is called the index set. Traditionally Λ is often the natural numbers-you are probably pretty used to seeing sets indexed by the natural numbers but it can in fact be any other set! Here's the exercise: Let Л-R+ (meaning the positive real numbers, not including 0) and for each α Ε Λ let Aa-(-a, a). Find n{A, : a e A} (meaning the intersection of the collection {A, : α Ε Λ) and UA, : α Ε Λ} (meaning the union of the collection (A : o E Л). For this exercise you don't need to prove your answers are correct. I just want you to get familiar with the definition. 13. Extra Credit: Prove your answers in Problem 12 are correcet.

Answer 1

Natw Λ S Aa :。< e A1の イ0 주 .re 81malatone. Set containiヴQ ov o U 13, p10哘=r@囚eA3Ad NOw NaA