infinate set (countability of rational numbers)

quest1.java

abstract class ATree {
	Rational value;
	ATree(Rational value){
		this.value = value;
	}
	abstract Node expandOneLevel();
	
	// returns the integer value of the node/leaf
	public Double doubleValue(){
		return this.value.toDouble();
	}
	
	// makes n expansions of the tree from the given tree
	public ATree expandNLevels(int n){
		if(n <= 0) {
			return new Leaf(null);
		} else if (n == 1) {
			return this.expandOneLevel();
		} else {
			return this.expandOneLevel().expandNLevels(n-1);
		}
	}
	
	//Takes an ATree and prints the values of it's node
	// the order goes left to right on each level before moving to the next
	public abstract String toString();
}

class Node extends ATree{
	ATree left;
	ATree right;
	Node(Rational value, ATree left, ATree right){
		super(value);
		this.left = left;
		this.right = right;
	}
	public Node expandOneLevel(){
		return new Node(this.value, this.left.expandOneLevel(), this.right.expandOneLevel());
	}
	
	//Takes an ATree and prints the values of it's node
	// the order goes left to right on each level before moving to the next
	public String toString(){
		//return Double.toString(this.doubleValue()).concat(" ").concat(this.left.toString()).concat(this.right.toString());
		return Double.toString(this.doubleValue()).concat(" ").concat(Double.toString(this.left.doubleValue())).concat(" ").concat(Double.toString(this.doubleValue()))
				.concat(" ").concat(this.left.toString()).concat(this.right.toString());
	}
}

class Leaf extends ATree{
	Leaf(Rational value){
		super(value);
	}
	public Node expandOneLevel(){
		return new Node(this.value, new Leaf(new Rational(this.value.numerator,(this.value.numerator+this.value.denominator))), 
									new Leaf(new Rational((this.value.numerator+this.value.denominator),this.value.denominator)));
	}
	
	//Takes an ATree and prints the values of it's node
	// the order goes left to right on each level before moving to the next
	public String toString(){
		return Double.toString(this.doubleValue()).concat(" ");
	}
}

class Rational{
	int numerator;
	int denominator;
	Rational(int numerator, int denominator) {
		this.numerator = numerator;
		this.denominator = denominator;
	}
    
    //return the int value of this rational
    public Double toDouble() {
    	int n = this.numerator;
    	int d = this.denominator;
    	return ((double)n / (double)d);
    }
}

class ExamplesTrees{
	Rational oneHalf = new Rational(1,2);
	double pointfive = oneHalf.toDouble();
	
	ATree t_0 = new Leaf(new Rational(1,1));
	ATree t_n = t_0.expandNLevels(2);
	
	String ans = t_n.toString();
	//ATree t_4 = t_0.expandNLevels(4);
}