The discussion revolves around the question of whether the distance between any two positions in infinite space is always finite. Participants explore various interpretations of "infinite space," including mathematical and physical perspectives, and consider implications for travel between points in such spaces.
Participants do not reach a consensus on whether the existence of an infinite number of mathematicians traveling implies that some will never reach their destinations. There are competing views on the implications of infinite distances and the nature of travel in infinite space.
Participants highlight the distinction between finite distances and the concept of unbounded distances, noting that while individual travel times are finite, the distances involved can be arbitrarily large.
netzweltler said: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.