Question

what is the derived set of Q,the set of rationals?​

Answer 1

Answer:

Any real number is an accumulation point of the set of rationals. The set of accumulation points of a set A is called the derived set of A and denoted A'. Example

: If A = (3,5] then A' = [3,5]. If A = ℚ then A' = ℝ.

Answer 2

We know that a set of rational number Q is countable and it has no limit point but its derived set is a real number R!

By definition every point of real line is a limit point of set of rational number.

For every point in the real line you can always construct a sequence in rational number which will converge to that point. So derived set will be full of R.