## 3.1. Sequences

### Examples 3.1.8(c):

Both statements are false. As a counter-example to the first statement, consider the sequenceEach term of this sequence is bounded by -1 or +1, so that the sequence is indeed bounded. But, as we have seen before, the sequence does not converge.{ (-1)^{j}}

As for the second statement, consider the simple sequence
*{n}*, i.e. the sequence consisting of the numbers
{1, 2, 3, 4, ...}. It is obviously increasing, but does
not converge to a finite number.

It does, however, get closer and closer to infinity, but we do not, at this time, consider this convergent.