Please validate my understanding. You have used a technique similar to the argument used in Hotel Infinity Paradox - To make room available ask every occupant to shift to the next room.
Consider F: [0,1]->[0,1]
If I remove finite points from the range - I can use your argument to construct a bijection. Correct?
Say if range is (0,1), I will map 1/n -> 1/(n+2) and 0 -> 1/2
I just have one more question, when im looking at these two sets how would I know to
separate it into a function like that?
is it just practice? or is there anything from that set that is setting off some alarms in your head?
thanks a bunch!