Find all accumulation points of the following sequence:
an enumeration of all rational numbers in (0,1)
Every bounded sequence has a convergent sequence (hence, an accumulation point)
The Attempt at a Solution
Because the enumeration of all rational numbers in (0,1) is bounded, it must have at least one convergent sequence. But if there is an accumulation point for the rational numbers in (0,1) there must also be an accumulation point for the rational numbers in (0,0.5), and the logic continues so there must be infinitely many accumulation points in (0,1). So are the accumulation points every rational number in (0,1)?
This seems odd to me that any rational number can be an accumulation point