Which of the following are subspaces of R[infinity]? If not, explain why. a) All sequences such that |xj+1| ≥ |xj | for each j. b) All convergent sequences: the xj has a limit as j → [infinity]. c) All arithmetic progressions: xj+1 − xj is the same for all j. d) All geometric progressions: (x1, k x1, k2 x1, . . .) allowing all k and x1
