Let (X,t) be a topological space. A subset A of X is dense if its closure cl(A)=X. Then .The set {1,2,3,., 100} is dense in usual topology of R The set of natural numbers is dense in usual .topology of R .The set of integers is dense in usual topology of R .The set of irrationals is dense in usual topology of R

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A number r ∈ R  is called algebraic provided for some n ∈ N there exists numbers  a0, a1, … , an ∈ Z such that r satisfies p( r ) = 0 where p ( x ) = a0 + a1x + a2x2 + ⋯ + anxn.   A number r ∈ R is called transcendental provided it is NOT algebraic prove the set of ALL algebraic numbers is countable and the set of ALL transcendental numbers is uncountable.