Very hard to get your head around!
If I remove n elements from R, the remainder has n+1 connected components.
The complement of Z in R has |Z| connected components.
The complement of Q in R has |R| connected components.
If I remove n elements from R, the remainder has n+1 connected components.
The complement of Z in R has |Z| connected components.
The complement of Q in R has |R| connected components.