Let
, define
where "count" denote the number of elements in that set.
Let M be the set of all even numbers, N be the set of all odd numbers, and P be the set of all perfect squares.
Q1: Find
Q2: If A and B are disjoint sets, show that
Q3: Is it a measure?
My solutions so far:
Q1: For
, and I have
since only half of those will be even, so the whole limit would equal to
, same goes for all odd numbers.
For the perfect squares, should it be
?
And if I can prove Q2, doesn't that automatically prove Q3?
Thank you!