# Math Help - monotone sequence

1. ## monotone sequence

Let {xn} be a sequence and {yn} = {xQ(n)} be a sequence. Prove the following:

a) If {xn} is a bounded sequence, the {yn} is also a bounded squence.

b) If {xn} is monotone, then {yn} is also monotone. (Consider two cases. 1. {xn} is monotone increasing. 2. {xn} is montone decreasing.)

2. Originally Posted by tigergirl
Let {xn} be a sequence and {yn} = {xQ(n)} be a sequence. Prove the following:

a) If {xn} is a bounded sequence, the {yn} is also a bounded squence.

b) If {xn} is monotone, then {yn} is also monotone. (Consider two cases. 1. {xn} is monotone increasing. 2. {xn} is montone decreasing.)
#1. Is it true that any subset of a bounded set must be bounded?

#2. What were you know about the sequence $Q_n$?