Prove that the set of Real numbers R can be partitioned into a denumerable collection of uncountable sets Prove that the set of Real numbers R can be partitioned into a denumerable collection of uncountable sets
My thoughts on the problem were to show the break down of the set of real numbers into subsets such as rational, irrational, and integers.
Im not sure if im over complicating this. The wording is confusing to me because i have never done something like this in class. 

How about the union of the intervals $[n, n+1); n $
in $\mathbb Z^+ $ ? and $(n-1,n]$ for $n$ in the negative integers less than or equal
to $-1$, and $(-1,0)$. 
Basically, the partition is : { $ \cup (n-1,n ]; n \leq -1 \cup (-1,0) \cup [0,1) \cup [1,2) \cup....\cup [n, n+1) \cup.....$} 
