Construct a sequence xn (from one to infinity) such that it contains one subsequence that converges to 1 and another subsequence which converges to 0.
Hi renolovexoxo,
The easiest way to construct such a sequence is to define all the even terms as one and odd terms as zero (or vice versa).
$\displaystyle x_n=\begin{cases}1&\mbox{ if }n=2k\mbox{ where }k\in\mathbb{Z}^{+}\\0&\mbox{ if }n=2k+1\mbox{ where }k\in\mathbb{Z}^{+}\cup\{0\}\end{cases}$