Is Distance Between Positions in Infinite Space Always Finite?

[Number Nine]

step 1: at t = 0 I am shifting the line [0, 1] to position [-0.5, 0.5]
step 2: at t = 0.5 I am shifting the line at [-0.5, 0.5] to position [-0.75, 0.25]
step 3: at t = 0.75 I am shifting the line at [-0.75, 0.25] to position [-0.875, 0.125]
...

All shifting is done before t = 1. No action is done at t = 1. Countable infinity doesn't allow a last shift at t = 1, which clearly is needed for point -1 to be covered.

...what? Where does "countable infinity" enter into all of this? And what does it have to do with "moving at t=1"? You aren't even bothering to explain what it is that you're doing or asking, and it's making it very difficult to answer any of your questions. What does this have to do with "positions in infinite space"?