MHB Accumulation Points of Rationals: Explained

[Dustinsfl]

Accumulation points of rationals and open or closed.

I know the accumulation points are all real but I don't understand why.

The set is neither open nor closed to but I don't truly see it.

Can someone explain both?

 

[Amer]

Accumulation points of rationals and open or closed.

I know the accumulation points are all real but I don't understand why.

The set is neither open nor closed to but I don't truly see it.

Can someone explain both?

The definition of limit point or accumulate point, x is accumulate point of a set A if any open set U containing x, A\{x} intersect with U is not empty.

Let x in R any open set contains x will intersect with Q since the density property of Q which says between any two real numbers there exist a rational, that holds for any x real so the accumulate point of Q is R.

the set which contains all accumulate point of A called the derive set A'

what do you mean by "The set is neither open nor closed to but I don't truly see it." which set are you taking about ?