1. 1. Mark each statement True or False. Justify each answer. (a) If a monotone sequence is bounded, then it is convergent. (b) If a bounded sequence is monotone, then it is convergent. (c) If a...

1. 1. Mark each statement True or False. Justify each answer.

(a) If a monotone sequence is bounded, then it is convergent.

(b) If a bounded sequence is monotone, then it is convergent.

(c) If a convergent sequence is monotone, then it is bounded.

2. Mark each statement True or False. Justify each answer.

(a) If a convergent sequence is bounded, then it is monotone.

(b) If (s_n) is an unbounded increasing sequence, then lim s_n
= +
.

(c) The Cauchy convergence criterion holds in
, the ordered field of rational numbers.