This is the exercise given:
Find a sequence with two different adherent points, which has no boundaries. Write the subsequences of your sequence.
So the sequence I came up with was $(-1)^n$. This will result in the sequence: $-1, 1, -1, 1,...$ So the two adherent points are -1 and 1, because adherent points are points on which the sequence returns a lot?
The subsequences would be $x_{n} :=$ 1 if n even, and -1 if n odd. Is this correct? If not, what would be a better solution or example for this problem.
Could someone also explain a bit more about adherent points?
Definition adherent points from my cursus: $x_{n} \rightarrow a \Leftrightarrow \exists\epsilon > 0 \forall N \exists n \geq N : |x_{n} - a| \geq \epsilon$