You should say instead of .
Regards.
Fernando Revilla
Hi
Let be a finite set. Show that the set of all subsets of , , is also finite and that it is a -algebra.
Solution (?)
Since is finite, such that . From set theory we know that the number of subsets of a finite set of cardinality is . Therefore,
, since . Hence, is finite.
and is in . Since contains all subsets of it must also contain all necessary unions, intersections and complements to make a -algebra.
Comments/improvements?
Thanks!
You should say instead of .
Regards.
Fernando Revilla
Yes.
Regards.
Fernando Revilla