# If we should give an example of real sequences with partial limits set $\{0,1\}$ and $[0,1]$ what whould be the sequences?

If we should give an example of real sequences with partial limits set $\{0,1\}$ and $[0,1]$ what whould be the sequences ?
I am not sure if $0,1,0,1,\ldots$ sequence satisfies it? Because Inf of the sequence is $0$ for $\{1,0,1,0,1,\ldots\}$ and Sup is 1.
Sequence $0,\,1,\,2,\,0,\,1,\,2, \, \ldots$ has partial limits set $\{0,\,1,\,2 \}$ and its supremum is $2$ – M. Strochyk Oct 4 '12 at 18:57
When you say "satisfies it", do you mean "satisisfies the condition that its set of limit points is $\{0,1\}$", or "satisisfies the condition that its set of limit points is $[0,1]$"? – Trevor Wilson Oct 4 '12 at 20:45
Do you know that $\mathbb Q$ is countable? – Henning Makholm Oct 4 '12 at 21:08