1)In a middle of a battlefield there is an odd number of Soviet soldiers ( ). Each one is standing a different distance away from anyone else. Also each soldier has a Colt Python .357 Magnum Revolver.* The soldiers decide to play a game. Each one is going to shot his nearest oppenent. At a signal each Soviet shots instantenously at his target. Show that there will be one Soviet still standing alive.
(Assume that the Soviets had nothing to drink and hence they have perfect aim). What happens if there is an even number?
2)Let be a convergent sequence with . Show that the sequence is also convergent and furthermore, .
*)Look how beautiful that gun is!