Can there be two sequences that are sub-sequences of each-other, but not identical.

Question

I have spent days thinking about it. I know that it is possible. I can let $x=\{1, 2, 3, 4, 5\}$ and $y=\{1, 2, 3, 4\}$.

Now the sequences are different, but I am not sure if $x$ is still the subsequence of $y$. I would accept any help towards this problem.

Thanks for the help in advance.

Answer 1

For example, consider $\{1,2,1,2,1,2,\ldots\}$ and $\{2,1,2,1,2,1,\ldots\}$.