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

Since the rational numbers are countable, we know there is a bijection $f:\mathbb N\to\mathbb Q$. Let $x_n=f(n)$. Then this is a sequence which contains every rational number, and its set of accumulation points is $\mathbb R$.
