Okay, so proving this in is pretty easy but carrying that over to is another thing altogether. I am tempted to just apply the infinite and bounded condition to every component of each term in a sequence in , but just because the set is infinite in doesn't mean that if we look at each component and the set of all possible elements for that component is infinite, for instance the set (x,y,z) where x = y = 1 and z in [-1,1] is bounded and infinite but there are not infinitely many choices for each component. How do I resolve this?