Denseness of sets

Let X be a metric space, E is a subspace in X, any given X belongs to X, any given a>0 (where A is small enough), and there is E belonging to E, so that X is included in the tee shot with E as the center and A as the radius (or the distance from X to E is less than A), then E is said to be dense in X.

For example, the set of rational numbers Q is dense in the set of real numbers R because Q is contained in R and any element in R can find a rational number to make their distance small enough (if the given element is rational, obviously if the given element is irrational, any irrational number can be approximated by rational number).

Please forgive my mistakes or carelessness in typing (I'm not good at math)