TITLE: Is there a sequence with an uncountable number of accumulation points?
QUESTION [10 upvotes]: Let $(x_{n})_{n \geq 1}$ sequence in $\mathbb{R}$. Is there a sequence with an uncountable number of accumulation points?
Thank you!

REPLY [5 votes]: Terms of a sequence $$(\sin n)_{n\in\mathbb N}$$ are dense in $[-1,1]$ so each number in the interval is an accumulation point of the sequence.