Which of the following collections of sets is a partition of [0,∞)?
A. $S_i$ = (i-1,i) for i =1, 2, 3, …
B. $S_i$ = (i-1,i] for i =1, 2, 3, …
C. $S_1$ = (0,1], $S_i$ = [i-1,i] for i = 2, 3, 4, …
D. $S_1$ = (0,π], $S_2$ = (π,350π), $S_2$ = [350π,∞)
E. All of these
I'm having trouble answering this, I know what a partition is, however I'm having trouble with the notation of this problem... Is the the set [0,∞)= {0,1,2,3,4,5....}
For example, choice (A. $S_i$ = (i-1,i) for i =1, 2, 3, …) the sets would be
$S_1$ = (0,1), $S_2$ = (1,2), $S_3$ = (2,3)....
So are these sets disjoint, and additionally is the union of them equal to [0,∞)?
Thanks