# Rindler and Minkowski space future/past infinity

In my black holes course, we are looking at the Penrose diagram for 1+1 D Minkowski space. My notes don't specifically describe $i^{\pm}$ (future/past timelike infinity) but do say all timelike curves end there. However, when looking at 1+1 Rindler space, we have observers that approach the speed of light, but never reach it. In my notes, the Penrose diagram for Rindler space is a subdiagram of that for Minkowski space. However, I noticed that the worldlines of the Rindler observers do not end up at $i^{\pm}$, even though their worldlines are timelike.

Is there a description of what $i^{\pm}$ that explains this?