There's the Achilles and the tortoise paradox: In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

The Dichotomy paradox is in some sense a particular case of the above: Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

Paradoxes without self-reference?

  
  Leadership skills are also a valued facet in a friend. 
  


Can facet be used in this way?
