Show uncountable set of real numbers has a point of accumulation [closed]
Show that every uncountable set of real numbers has a point of accumulation.
Solution 1:
Hint:
If $A$ is an uncountable set of real numbers then there exists $k\in\mathbb Z$ such that $A\cap[k,k+1]$ is infinite. Use the definition of compactness, and the fact $[k,k+1]$ is a closed and bounded interval.